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    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Phase-lead-and-Phase-lag-compensator-with-pre-filters\" data-toc-modified-id=\"Phase-lead-and-Phase-lag-compensator-with-pre-filters-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Phase-lead and Phase-lag compensator with pre-filters</a></span></li><li><span><a href=\"#Pre-requisites\" data-toc-modified-id=\"Pre-requisites-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Pre-requisites</a></span></li><li><span><a href=\"#Source-code\" data-toc-modified-id=\"Source-code-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Source code</a></span></li><li><span><a href=\"#Design-requirements:-phase-lead-compensator\" data-toc-modified-id=\"Design-requirements:-phase-lead-compensator-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>Design requirements: phase-lead compensator</a></span></li><li><span><a href=\"#Phase-lead-compensator\" data-toc-modified-id=\"Phase-lead-compensator-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>Phase-lead compensator</a></span><ul class=\"toc-item\"><li><span><a href=\"#Determine-the-gain-$K$-for-a-step-response-overshoot-no-more-than-10%\" data-toc-modified-id=\"Determine-the-gain-$K$-for-a-step-response-overshoot-no-more-than-10%-5.1\"><span class=\"toc-item-num\">5.1&nbsp;&nbsp;</span>Determine the gain $K$ for a step response overshoot no more than 10%</a></span></li><li><span><a href=\"#Matlab-script\" data-toc-modified-id=\"Matlab-script-5.2\"><span class=\"toc-item-num\">5.2&nbsp;&nbsp;</span>Matlab script</a></span></li><li><span><a href=\"#Design-of-the-Phase-lead-compensator\" data-toc-modified-id=\"Design-of-the-Phase-lead-compensator-5.3\"><span class=\"toc-item-num\">5.3&nbsp;&nbsp;</span>Design of the Phase-lead compensator</a></span></li><li><span><a href=\"#Phase-Lead-compensator-Matlab-script\" data-toc-modified-id=\"Phase-Lead-compensator-Matlab-script-5.4\"><span class=\"toc-item-num\">5.4&nbsp;&nbsp;</span>Phase-Lead compensator Matlab script</a></span></li><li><span><a href=\"#Evaluation-of-the-compensated-system-to-a-unit-ramp-input\" data-toc-modified-id=\"Evaluation-of-the-compensated-system-to-a-unit-ramp-input-5.5\"><span class=\"toc-item-num\">5.5&nbsp;&nbsp;</span>Evaluation of the compensated system to a unit ramp input</a></span></li><li><span><a href=\"#Evaluation-the-performance-of-the-compensated-system\" data-toc-modified-id=\"Evaluation-the-performance-of-the-compensated-system-5.6\"><span class=\"toc-item-num\">5.6&nbsp;&nbsp;</span>Evaluation the performance of the compensated system</a></span></li><li><span><a href=\"#Matlab-script\" data-toc-modified-id=\"Matlab-script-5.7\"><span class=\"toc-item-num\">5.7&nbsp;&nbsp;</span>Matlab script</a></span></li><li><span><a href=\"#Conclusion\" data-toc-modified-id=\"Conclusion-5.8\"><span class=\"toc-item-num\">5.8&nbsp;&nbsp;</span>Conclusion</a></span></li></ul></li><li><span><a href=\"#Design-requirements:-phase-lead-and-phase-lag-compensator\" data-toc-modified-id=\"Design-requirements:-phase-lead-and-phase-lag-compensator-6\"><span class=\"toc-item-num\">6&nbsp;&nbsp;</span>Design requirements: phase-lead and phase-lag compensator</a></span></li><li><span><a href=\"#Phase-lead-and-phase-lag-compensator\" data-toc-modified-id=\"Phase-lead-and-phase-lag-compensator-7\"><span class=\"toc-item-num\">7&nbsp;&nbsp;</span>Phase-lead and phase-lag compensator</a></span><ul class=\"toc-item\"><li><span><a href=\"#Determine-the-location-of-closed-loop-dominant-poles\" data-toc-modified-id=\"Determine-the-location-of-closed-loop-dominant-poles-7.1\"><span class=\"toc-item-num\">7.1&nbsp;&nbsp;</span>Determine the location of closed-loop dominant poles</a></span></li><li><span><a href=\"#Matlab-script\" data-toc-modified-id=\"Matlab-script-7.2\"><span class=\"toc-item-num\">7.2&nbsp;&nbsp;</span>Matlab script</a></span></li><li><span><a href=\"#Demonstrate-the-desired-poles-do-not-belong-to-the-root-locus\" data-toc-modified-id=\"Demonstrate-the-desired-poles-do-not-belong-to-the-root-locus-7.3\"><span class=\"toc-item-num\">7.3&nbsp;&nbsp;</span>Demonstrate the desired poles do not belong to the root-locus</a></span></li><li><span><a href=\"#Design-of-the-Phase-Lead-compensator\" data-toc-modified-id=\"Design-of-the-Phase-Lead-compensator-7.4\"><span class=\"toc-item-num\">7.4&nbsp;&nbsp;</span>Design of the Phase-Lead compensator</a></span></li><li><span><a href=\"#Matlab-script\" data-toc-modified-id=\"Matlab-script-7.5\"><span class=\"toc-item-num\">7.5&nbsp;&nbsp;</span>Matlab script</a></span></li></ul></li><li><span><a href=\"#Adding-a-Pre-filter\" data-toc-modified-id=\"Adding-a-Pre-filter-8\"><span class=\"toc-item-num\">8&nbsp;&nbsp;</span>Adding a Pre-filter</a></span><ul class=\"toc-item\"><li><span><a href=\"#Matlab-script\" data-toc-modified-id=\"Matlab-script-8.1\"><span class=\"toc-item-num\">8.1&nbsp;&nbsp;</span>Matlab script</a></span></li><li><span><a href=\"#Design-of-the-Phase-Lag-compensator\" data-toc-modified-id=\"Design-of-the-Phase-Lag-compensator-8.2\"><span class=\"toc-item-num\">8.2&nbsp;&nbsp;</span>Design of the Phase-Lag compensator</a></span></li><li><span><a href=\"#Matlab-script\" data-toc-modified-id=\"Matlab-script-8.3\"><span class=\"toc-item-num\">8.3&nbsp;&nbsp;</span>Matlab script</a></span></li><li><span><a href=\"#Evaluation-of-the-performance\" data-toc-modified-id=\"Evaluation-of-the-performance-8.4\"><span class=\"toc-item-num\">8.4&nbsp;&nbsp;</span>Evaluation of the performance</a></span></li><li><span><a href=\"#Matlab-script\" data-toc-modified-id=\"Matlab-script-8.5\"><span class=\"toc-item-num\">8.5&nbsp;&nbsp;</span>Matlab script</a></span></li><li><span><a href=\"#Performance-results\" data-toc-modified-id=\"Performance-results-8.6\"><span class=\"toc-item-num\">8.6&nbsp;&nbsp;</span>Performance results</a></span></li><li><span><a href=\"#New-Phase-Lead-compensator\" data-toc-modified-id=\"New-Phase-Lead-compensator-8.7\"><span class=\"toc-item-num\">8.7&nbsp;&nbsp;</span>New Phase-Lead compensator</a></span></li><li><span><a href=\"#Evaluation-of-the-performance-with-the-second-Phase-Lead-compensator\" data-toc-modified-id=\"Evaluation-of-the-performance-with-the-second-Phase-Lead-compensator-8.8\"><span class=\"toc-item-num\">8.8&nbsp;&nbsp;</span>Evaluation of the performance with the second Phase-Lead compensator</a></span></li><li><span><a href=\"#Matlab-script\" data-toc-modified-id=\"Matlab-script-8.9\"><span class=\"toc-item-num\">8.9&nbsp;&nbsp;</span>Matlab script</a></span></li><li><span><a href=\"#Performance-results\" data-toc-modified-id=\"Performance-results-8.10\"><span class=\"toc-item-num\">8.10&nbsp;&nbsp;</span>Performance results</a></span></li><li><span><a href=\"#Conclusion\" data-toc-modified-id=\"Conclusion-8.11\"><span class=\"toc-item-num\">8.11&nbsp;&nbsp;</span>Conclusion</a></span></li></ul></li></ul></div>"
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    "# Phase-lead and Phase-lag compensator with pre-filters\n",
    "\n",
    "The first part is the design of a phase-lead compensator using the Bode analysis in the frequency domain. The second part is the design of a phase-lead compensator, and a phase-lag compensator in series with the first phase-lead compensator using root-locus approach.\n",
    "\n",
    "\n",
    "# Pre-requisites\n",
    "\n",
    "- Control Systems theory.\n",
    "- Bode and root-locus analysis theory\n",
    "- Jupyter Notebook with Matlab-kernel.\n",
    "- Matlab.\n",
    "\n",
    "# Source code\n",
    "\n",
    "Version [PDF](https://raw.githubusercontent.com/paulomarconi/Phase-lead_phase-lag/master/week4/week4.pdf)/[HTML](../../files/Phase-lead_phase-lag/Phase-lead_phase-lag.html). Matlab and LaTex source code on [GitHub](https://github.com/paulomarconi/Phase-lead_phase-lag). \n",
    "\n"
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    "# Design requirements: phase-lead compensator\n",
    "For the plant,\n",
    "\\begin{align*}\n",
    "G(s) &= \\dfrac{K}{s(s+2.5)(s+27)}\n",
    "\\end{align*} \n",
    "\n",
    "- Using the frequency domain approach, determine the gain K required to give an overshoot, in response to a step input, of no more than 10%.\n",
    "- Using frequency domain approach, design a phase-lead compensator to achieve a velocity error constant no less than 25 and a step response overshoot of no greater than 10%.\n",
    "- Plot the response of the control system, to a unit ramp, showing both system output and ramp input, and evaluate the percentage steady state error to the ramp input signal.\n",
    "- Evaluate the performance in the time and frequency domain."
   ]
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   "source": [
    "# Phase-lead compensator\n",
    "\n",
    "The aim of this task is to design a Phase-lead compensator using the Bode analysisin the frequency domain, and evaluate it on Matlab. Although the plant $G(s)$ is a third-order system (1), the design requirements can be approximated in terms of the natural frequency ($\\omega_n$) and damping ratio ($\\zeta$) of a second-order system.\n",
    "\n",
    "\\begin{align}\n",
    "G(s) & =\\dfrac{K}{s(s+a)(s+b)} \\tag{1}\\\\\n",
    "G(s) &= \\dfrac{K}{s(s+2.5)(s+27)} \\nonumber\n",
    "\\end{align} "
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    "## Determine the gain $K$ for a step response overshoot no more than 10%\n",
    "\n",
    "There are two steps to follow in order to obtain the required gain $K$, the first one uses the second-order performance approximation in the frequency domain, and the second step uses the gain and angle condition.\n",
    "\n",
    "The relation between the Percentage Overshoot ($PO$) in response to a unity step input of a second-order system in the $\\textbf{time domain}$, and the Phase Margin ($PM$) of the Bode analysis in the $\\textbf{frequency domain}$, can be written as follows,\n",
    "\\begin{align}\n",
    "PO &= 100~e^{-\\zeta\\pi/\\sqrt{1-\\zeta^2}} \\tag{2} \\\\\n",
    "PM &\\approx 100 ~\\zeta \\tag{3}\n",
    "\\end{align}\n",
    "applying the requirement of $PO\\leq10\\%$,\n",
    "\\begin{align}\n",
    "\\zeta &= \\dfrac{ \\ln\\left(\\frac{100}{P.O.}\\right) }{\\sqrt{\\pi^2+\\left[ \\ln \\left(  \\frac{100}{P.O.}\\right)\\right]}}\t\\tag{4} \\\\\n",
    "\\zeta &= 0.59 \\approx 0.60 \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "Using (3), the desired Phase Margin ($PM_d$) the system should have in order to satisfy the $PO$ is defined as,\n",
    "\\begin{align*}\n",
    "PM_d = 100\\times 0.6 = 60°\n",
    "\\end{align*}\n",
    "\n",
    "Now, it is necessary to obtain the new crossover frequency ($\\omega_c^\\prime$) where the $PM_d$ is satisfied. Using the $PM_d$ equation and the phase angle condition ($\\phi(\\omega_c^\\prime)$)  as follows,\n",
    "\n",
    "\\begin{align}\n",
    "&\\phi(\\omega_c^\\prime) = -180° + PM_d \\tag{5}\n",
    "\\end{align}\n",
    "applying the rule of angles into the (1),\n",
    "\\begin{align}\n",
    "&\\phi(\\omega_c^\\prime) = -90° - \\arctan \\frac{\\omega_c^\\prime}{a} - \\arctan \\frac{\\omega_c^\\prime}{b} \\tag{6}\\\\\n",
    "\\end{align}\n",
    "and after some algebraic operations $\\omega_c^\\prime$,\n",
    "\\begin{align*}\n",
    "& PM_d - 180°  = -90° - \\arctan \\frac{\\omega_c^\\prime}{a} - \\arctan \\frac{\\omega_c^\\prime}{b}   \\\\\n",
    "& \\frac{\\omega_c^\\prime(a+b)}{a~b} = \\left(1-\\frac{\\omega_c^{\\prime 2}}{a~b}\\right) \\tan(180° - 90° -PM_d) \\\\\n",
    "\\end{align*}\n",
    "solving the quadratic equation with the corresponding values $a$, $b$, and $PM_d$, and using the high value of the solution,\n",
    "\\begin{align}\n",
    "& \\omega_c^{\\prime 2}  + \\frac{a+b}{\\tan(180° - 90° -PM_d)} \\omega_c^\\prime - a~b = 0 \\tag{7}\\\\\n",
    "& \\omega_c^\\prime  = 1.29 ~rad/sec \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "Finally, the gain $K$ can be obtained from the $\\textbf{gain condition}$, where it is established that the new crossover frequency $\\omega_c^\\prime$ should be at $0~dB$ of magnitude, in other words,\n",
    "\\begin{align}\n",
    "& \\arrowvert G(j\\omega_c^\\prime) \\arrowvert = 1 \\tag{8}\\\\\n",
    "\\end{align}\n",
    "applying into the plant $G$ (1), and replacing the values,\n",
    "\\begin{align*}\n",
    "&\\dfrac{K}{\\omega_c^\\prime \\sqrt{\\omega_c^{\\prime 2}+a^2} \\sqrt{\\omega_c^{\\prime 2}+b^2 }} = 1 \\\\\n",
    "& K\t= \\omega_c^\\prime \\sqrt{\\omega_c^{\\prime 2}+a^2} \\sqrt{\\omega_c^{\\prime 2}+b^2 } \\\\\n",
    "& K = 97.96 \\nonumber\n",
    "\\end{align*}\n",
    "therefore, the plant becomes,\n",
    "\\begin{align*}\n",
    "& G(s)=\\dfrac{97.96}{s(s+2.5)(s+27)}\n",
    "\\end{align*}\n",
    "\n"
   ]
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   "source": [
    "## Matlab script\n"
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      "\n"
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% Paulo Loma Marconi\n",
    "clear variables;\n",
    "\n",
    "% plant G parameters\n",
    "s = tf('s');\n",
    "a = 2.5; b = 27;\n",
    "\n",
    "%% a) Gain K for PO=10\n",
    "PO = 10; % percentage overshoot\n",
    "zeta = log(100/PO)/sqrt(pi^2+ (log(100/PO))^2 ); % damping ratio\n",
    "PM_d = round(100*zeta)+1; % PM desired at the nearest round value\n",
    "h = tand(180-90-PM_d); \n",
    "omega_c = roots([1 (a+b)/h -a*b]); % new omega_c\n",
    "K = omega_c(2)*sqrt(omega_c(2)^2+a^2)*sqrt(omega_c(2)^2+b^2); % new gain K\n",
    "G = K/( s*(s+a)*(s+b) ); % Plant G\n",
    "\n",
    "figure;\n",
    "margin(G);\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "ans = \n",
      "\n",
      "  struct with fields:\n",
      "\n",
      "        RiseTime: 1.0050\n",
      "    SettlingTime: 3.1834\n",
      "     SettlingMin: 0.9147\n",
      "     SettlingMax: 1.0836\n",
      "       Overshoot: 8.3592\n",
      "      Undershoot: 0\n",
      "            Peak: 1.0836\n",
      "        PeakTime: 2.1523\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure;\n",
    "step(feedback(G,1));\n",
    "stepinfo(feedback(G,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results show the desired $PM_d = 60°$ is satisfied with the new gain, and step response has an $PO = 8.36$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Design of the Phase-lead compensator\n",
    "\n",
    "The Phase-Lead compensator has the following transfer function,\n",
    "\\begin{align}\n",
    "Gc = \\dfrac{s+z}{s+p} \\tag{9}\n",
    "\\end{align}\n",
    "where the location of the zero is to the left of the pole, $|z|<|p|$.\n",
    "\n",
    "The design requirements are the velocity error constant $K_v\\leq 25$, and the step response $PO\\leq 10\\%$\n",
    "\n",
    "The first step is to calculate the loop gain that satisfies the $K_v$ is calculated as follows,\n",
    "\\begin{align*}\n",
    "K_v &= \\lim\\limits_{s \\rightarrow 0} s \\dfrac{K}{s(s+2.5) (s+27)} \\tag{10}\\\\\n",
    "K_g &= 1687 \n",
    "\\end{align*}\n",
    "therefore, the new plant is,}\n",
    "\\begin{align*}\n",
    "G(s) &= \\dfrac{K_g}{s(s+a)(s+b)} \\tag{11}\\\\\n",
    "G(s) &= \\dfrac{1687}{s(s+2.5)(s+27)} \n",
    "\\end{align*}\n",
    "\n",
    "Using (2), (3), and (4), for an overshoot of $PO=10 \\%$, the damping ratio is $\\zeta = 0.6$, and the desired phase margin is $PM_d=60°$.\n",
    "\n",
    "In order to obtain the  $\\omega_c$ that satisfies the gain condition with the new gain $K$, (8) is applied as follows,\n",
    "\\begin{align*}\n",
    "&\\arrowvert G(j\\omega_c) \\arrowvert = 1 \\nonumber\\\\\n",
    "&\\left| \\dfrac{K_g}{j\\omega_c(j\\omega_c+a)(j\\omega_c+b)} \\right| = 1 \\nonumber\\\\\n",
    "\\end{align*}\n",
    "after some algebraic operation, \n",
    "\\begin{align*}\n",
    "&\\omega_c^2(\\omega_c^2+a^2)(\\omega_c^2+b^2)-K_g^2 = 0 \\nonumber \\\\\n",
    "&\\omega_c = 7.55 ~rad/sec \\nonumber\n",
    "\\end{align*}\n",
    "\n",
    "Now, the actual phase margin $PM_{act}$ is needed to calculate the additional phase ($\\phi_m$) required from the compensator,\n",
    "\\begin{align*}\n",
    "PM_act &= 180° + \\phi(\\omega_c) \\tag{12}\\\\\n",
    "PM_act &= 180° - 90° -\\arctan \\frac{\\omega_c}{a} - \\arctan \\frac{\\omega_c}{b} \\nonumber \\\\\n",
    "PM_act &= 2.65 \\nonumber\n",
    "\\end{align*}\n",
    "so, the additional phase angle is,\n",
    "\\begin{align}\n",
    "\\phi_m &= PM_d+\\theta-PM_act \\tag{13}\n",
    "\\end{align}\n",
    "where $\\theta$ is a factor of correction. \n",
    "\n",
    "If $\\theta=0$,\n",
    "\\begin{align*}\n",
    "\\phi_m &= 60° + 0° - 2.65 \\nonumber\\\\\n",
    "\\phi_m &= 57° \\nonumber\n",
    "\\end{align*}\n",
    "\n",
    "The additional phase margin is related with the zero and the pole of the Phase-Lead compensator,\n",
    "\\begin{align*}\n",
    "\\alpha &= \\dfrac{\\sin \\phi_m+1}{1-\\sin \\phi_m} \\tag{14}\\\\\n",
    "\\alpha &= 11 \\nonumber \n",
    "\\end{align*}\n",
    "where $\\alpha$ is,\n",
    "\\begin{align}\n",
    "\\alpha &= \\dfrac{p}{z}  \\tag{15}\n",
    "\\end{align}\n",
    "\n",
    "The next step is to determine the new $\\omega_c^\\prime$ using the following logarithm gain condition,\n",
    "\\begin{align}\n",
    "&20\\log|G(j\\omega_c^\\prime)| = -10 \\log \\alpha \\tag{16}\\\\\n",
    "&\\dfrac{K_g}{\\omega_c^\\prime \\sqrt{\\omega_c^{\\prime 2}+a^2} \\sqrt{\\omega_c^{\\prime 2}+b^2 }} = \\dfrac{1}{\\sqrt{\\alpha}} \\tag{17}\\\\\n",
    "\\end{align}\n",
    "after some operations,\n",
    "\\begin{align*}\n",
    "&\\omega_c^{\\prime 2}(\\omega_c^{\\prime 2}+a^2)(\\omega_c^{\\prime 2}+b^2)-K_g^2~\\alpha = 0 \\nonumber \\\\\n",
    "&\\omega_c^\\prime = 13.50 ~rad/sec \\nonumber\n",
    "\\end{align*}\n",
    "now, calculating the zero of the compensator,\n",
    "\\begin{align}\n",
    "\\omega_c^\\prime &= \\sqrt{p~z} \\tag{18}\\\\\n",
    "z &= \\dfrac{\\omega_c^\\prime}{\\alpha} \\nonumber\\\\\n",
    "z &= 4.07 \\nonumber\\\\\n",
    "\\end{align}\n",
    "and the pole of the compensator using (15) is,\n",
    "\\begin{align}\n",
    "p &= \\alpha ~z \\nonumber\\\\\n",
    "p &= 44.78 \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "The last step is to obtain the new gain of the $\\textbf{compensated system}$,\n",
    "\\begin{align}\n",
    "K_{new} &= \\sqrt{\\alpha} K_g \\tag{19} \\\\\n",
    "K_{new} &= 5596.80 \\nonumber\\\\\n",
    "\\end{align}\n",
    "therefore, the compensated open-loop transfer function is as follows,\n",
    "\\begin{align}\n",
    "G_{ol} &= \\dfrac{s+z}{s+p} \\quad \\dfrac{K_{new}}{s(s+a)(s+b)} \\tag{20} \\\\\n",
    "G_{ol} &= \\dfrac{s+4.07}{s+44.78} \\quad \\dfrac{5596.80}{s(s+2.5)(s+27)} \\nonumber\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Phase-Lead compensator Matlab script"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "K_new =\n",
      "\n",
      "   5.5968e+03\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%% b) Phase-lead compensator\n",
    "Kv = 25; % velocity error\n",
    "Kg = Kv*a*b; % loop gain to satisfy Kv\n",
    "G = Kg/( s*(s+a)*(s+b) ); % Plant G\n",
    "\n",
    "% omega_c for the uncompensated system\n",
    "omega_c = real( sqrt( roots([1 a^2+b^2 a^2*b^2 -Kg^2]) ) );\n",
    "\n",
    "% obtaining actual PM\n",
    "PM_act = 180-90-atand(omega_c(3)/a)-atand(omega_c(3)/b);\n",
    "\n",
    "% additional phase angle from the compensator PM\n",
    "theta = 0; % factor of correction\n",
    "PM_c = round(PM_d+theta-PM_act);\n",
    "\n",
    "% calculating alpha\n",
    "alpha = round( (sind(PM_c)+1)/(1-sind(PM_c)) );\n",
    "\n",
    "% Determine the new cross over frequency\n",
    "omega_c_new = real( sqrt( roots([1 a^2+b^2 a^2*b^2 -Kg^2*alpha]) ) );\n",
    "\n",
    "% Calculating the zero of the compensator\n",
    "z = omega_c_new(3)/sqrt(alpha);\n",
    "\n",
    "% Calculating the pole of the compensator\n",
    "p = alpha*z;\n",
    "\n",
    "% lead compensator\n",
    "Gc = (s+z)/(s+p);\n",
    "\n",
    "% new gain of the compensated system\n",
    "K_new = sqrt(alpha)*Kg\n",
    "\n",
    "% compensated open-loop \n",
    "Gol = K_new*Gc*G/Kg;\n",
    "\n",
    "% closed-loop \n",
    "Gcl = feedback(Gol,1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation of the compensated system to a unit ramp input\n",
    "\n",
    "The unit ramp in the LaPlace domain has the following equation,\n",
    "\\begin{align}\n",
    "R(s) &= \\frac{1}{s^2} \\tag{21}\n",
    "\\end{align}\n",
    "and the steady-state error to that unit ramp is,\n",
    "\\begin{align}\n",
    "ess_v &= \\frac{1}{K_v} \\tag{22}\n",
    "\\end{align}\n",
    "where,\n",
    "\\begin{align}\n",
    "K_v &= \\lim\\limits_{s\\rightarrow 0} s~G(s) \\tag{23}\n",
    "\\end{align}\n",
    "evaluating $K_v$ for the compensated system $G_{ol}$,\n",
    "\\begin{align*}\n",
    "K_v &= \\lim\\limits_{s\\rightarrow 0} s~ \\left[\\dfrac{s+z}{s+p} \\quad \\dfrac{K_{new}}{s(s+a)(s+b)} \\right] \\nonumber\\\\\n",
    "K_v &= 7.53 \\nonumber\n",
    "\\end{align*}\n",
    "\n",
    "Therefore,\n",
    "\\begin{align*}\n",
    "ess_v &= 0.13 \\\\\n",
    "\\end{align*}\n",
    "which is a relatively small steady-state error. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation the performance of the compensated system\n",
    "\n",
    "Using the Matlab script below, we obtaint the Bode plot, the unit step response, and the unit ramp response, where you can see the desired $PM_d=60°$ and the $PO=10\\%$ are satisfied, and the system has an improved the settling time to $t_s=1.04$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matlab script"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% c) evaluating the system to unit step and unit ramp\n",
    "figure(2);\n",
    "margin(Gol);\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "ans = \n",
      "\n",
      "  struct with fields:\n",
      "\n",
      "        RiseTime: 0.2395\n",
      "    SettlingTime: 1.0357\n",
      "     SettlingMin: 0.9079\n",
      "     SettlingMax: 1.1038\n",
      "       Overshoot: 10.3821\n",
      "      Undershoot: 0\n",
      "            Peak: 1.1038\n",
      "        PeakTime: 0.5700\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(3);\n",
    "subplot(2,1,1);\n",
    "step = 1/s; % step input\n",
    "impulse(step,Gcl*step); \n",
    "title('Step response');\n",
    "subplot(2,1,2);\n",
    "ramp = 1/s^2; % ramp input\n",
    "impulse(ramp,Gcl*ramp);\n",
    "title('Ramp response');\n",
    "\n",
    "% evaluating Kv for the new compensated system\n",
    "Kv_new = (z/p)*K_new/(a*b);\n",
    "\n",
    "% steady-state error to a unity ramp\n",
    "ess_ramp = 1/Kv_new;\n",
    "stepinfo(Gcl)\n",
    "\n",
    "% bandwidth of Gcl\n",
    "BW = bandwidth(Gcl);\n",
    "\n",
    "% resonant frequency\n",
    "omega_r = 4/(0.6*1.03) *sqrt(1-2*0.6^2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>Table 1: Performance evaluation </center>\n",
    "\n",
    "| Quantity                          | Value   | \n",
    "|:----------------------------------|:-------:|\n",
    "| Steady state error to a unit ramp |    0.13 |\n",
    "| Rise Time                         |    0.24 |\n",
    "| Settling Time                     |    1.04 |\n",
    "| Percentage Overshoot              |   10.38 |\n",
    "| Phase Margin                      |   60.20 |\n",
    "| Gain Margin                       |   22.90 |\n",
    "| Bandwidth                         |    8.19 |\n",
    "| Peak Magnitude                    |    0.57 |\n",
    "| Resonant frequency                |    3.42 |\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "Comparing the uncompensated system, and the Phase-Lead compensated system, the desired phase margin $PM_d=60°$ and the overshoot $PO\\leq10 \\%$ were satisfied. Moreover, the settling time $t_s$ was improved three times in the Phase-lead compensated, which demonstrates this compensator improves the transient response without altering the desired phase margin."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Design requirements: phase-lead and phase-lag compensator\n",
    "\n",
    "For the plant,\n",
    "\\begin{align*}\n",
    "& G(s)=\\dfrac{K}{s^2(s+9)(s+50)}\n",
    "\\end{align*} \n",
    "\n",
    "- Determine the location of the dominant poles of the closed-loop transfer function in order to achieve the following performance specification for a unit step input:\n",
    "    - The settling time for a step input should be less than $2.9~[s]$.\n",
    "    - The overshoot should be no more than 20%.\n",
    "- Demonstrate analytically that the desired poles do not belong to the uncompensated root-locus.\n",
    "- Use the root-locus approach to design a cascaded phase-lead compensator with the zero placed in $-1$, to yield the desired specifications. If specifications are not met, perform additional design iterations.\n",
    "- Design a phase-lag compensator in series with the previous phase-lead compensator such that the steady-state error for a parabolic input $0.5~At^2$ is less than $2.5%$ of $A$. \n",
    "- Evaluate the performance of your final design in the time and frequency domain.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Phase-lead and phase-lag compensator\n",
    "The objective of this task is to design a Phase-Lead compensator, and a Phase-Lag compensator in series with the first Phase-Lead compensator using two different approaches. \n",
    "\n",
    "The plant to be studied is,\n",
    "\\begin{align}\n",
    "& G(s)=\\dfrac{K}{s^2(s+a)(s+b)} \\tag{24}\\\\\n",
    "& G(s)=\\dfrac{K}{s^2(s+9)(s+50)} \\nonumber\n",
    "\\end{align} \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Determine the location of closed-loop dominant poles\n",
    "\n",
    "The design requirements are the settling time $t_s\\leq 2.9~ sec$, and the overshoot $PO\\leq 20\\%$. Although the plant is a fourth-order system, the compensator can be designed using the properties of a second-order system. \n",
    "\n",
    "The settling time is,\n",
    "\\begin{align}\n",
    "t_s &= \\frac{4}{\\zeta\\omega_n} \\tag{25}\n",
    "\\end{align}\n",
    "where $\\zeta$ is the damping ration and $\\omega_n$ is the natural frequency. \n",
    "\n",
    "Using (4), and (25),\n",
    "\\begin{align*}\n",
    "\\zeta &= 0.45, \\quad \\omega_n = 3.06 ~rad/sec \n",
    "\\end{align*}\n",
    "\n",
    "Therefore, the desired closed-loop dominant poles are,\n",
    "\\begin{align*}\n",
    "r_{1,2} &= -\\omega_n\\zeta\\pm j~\\omega_n\\sqrt{1-\\zeta^2} \\tag{26}\\\\\n",
    "r_{1,2} &= -1.38\\pm j~2.73\n",
    "\\end{align*}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matlab script"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "clear variables;\n",
    "%% plant G parameters\n",
    "s = tf('s');\n",
    "a = 9; b = 50;\n",
    "\n",
    "%% a) Location of the dominant poles for PO=20 and ts=2.9\n",
    "PO = 20; % percentage overshoot\n",
    "ts = 2.9; % settling time\n",
    "zeta = log(100/PO)/sqrt(pi^2+ (log(100/PO))^2 ); % damping ratio\n",
    "zeta = round(zeta,2)-0.01;\n",
    "omega_n = 4/(zeta*ts);\n",
    "\n",
    "% desired location of dominant poles\n",
    "s1 = -omega_n*zeta+omega_n*sqrt(1-zeta^2)*1i;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Demonstrate the desired poles do not belong to the root-locus\n",
    "\n",
    "In order to demonstrate that the desired dominant poles $r_{1,2}$ do not belong to the root locus of the plant $G(s)$, the angle condition must not be satisfied.\n",
    "\n",
    "Choosing the pole, $r_1=-1.38\\pm j~2.73$, \n",
    "\\begin{align}\n",
    "&\\measuredangle(G(r_1)) = -180°  \\tag{27}\\\\\n",
    "&\\measuredangle \\left( \\dfrac{K}{r_1^2(r_1+9)(r_1+50)} \\right) = 180° \\nonumber\\\\\n",
    "&-\\measuredangle r_1 -\\measuredangle r_1 - \\measuredangle(r_1+9) - \\measuredangle (r_1+50) = -80° \\nonumber\\\\\n",
    "&- 2~ \\arctan \\frac{2.73}{-1.38} - \\arctan \\frac{2.73}{9-1.38} - \\arctan \\frac{2.73}{50-1.38} = -180° \\nonumber\\\\\n",
    "&103.44 \\neq -180° \\nonumber\n",
    "\\end{align}\n",
    "if the second pole $r_2$ is evaluated,\n",
    "\\begin{align}\n",
    "&-103.44 \\neq -180° \\nonumber\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Design of the Phase-Lead compensator\n",
    "\n",
    "The Phase-Lead compensator has the following transfer function,\n",
    "\\begin{align}\n",
    "G_{lead} = \\dfrac{s+z_{lead}}{s+p_{lead}}, \\quad |z_{lead}| < |p_{lead}| \\tag{28}\n",
    "\\end{align}\n",
    "\n",
    "The design requirement is that the location of the compensator's zero is 1. Once again, the angle criteria is applied with the desired pole $r_1$ as follows,\n",
    "\\begin{align}\n",
    "&\\measuredangle \\left( \\dfrac{s+z_{lead}}{s+p_{lead}} \\quad \\dfrac{K}{s^2(s+a)(s+b)}  \\right) = -180° \\tag{29} \\\\\n",
    "&\\measuredangle \\left( \\dfrac{r_1+z_{lead}}{r_1+p_{lead}} \\quad \\dfrac{K}{r_1^2(r_1+a)(r_1+b)}  \\right) = -180° \\nonumber \\\\\n",
    "&\\measuredangle z_{lead} -\\measuredangle p_{lead}- 2~\\measuredangle s -\\measuredangle a - \\measuredangle b = -180° \\nonumber\\\\\n",
    "\\end{align}\n",
    "if $r_1 = -x+j~y$ \n",
    "\\begin{align}\n",
    "&\\left( 180°-\\arctan\\dfrac{y}{x-z_{lead}} \\right) - \\arctan\\dfrac{y}{p_{lead}-x} - 2\\left( 180° -\\arctan\\dfrac{y}{x} \\right) ... \\nonumber\\\\\n",
    "&\\quad -\\arctan\\dfrac{y}{a-x}-\\arctan\\dfrac{y}{b-x} = 180° \\nonumber\n",
    "\\end{align}\n",
    "after some operations,\n",
    "\\begin{align}\n",
    "p_{lead} &= 8.36 \\nonumber\\\\\n",
    "\\end{align}\n",
    "so, the Phase-Lead compensator is,\n",
    "\\begin{align}\n",
    "G_{lead} &= \\dfrac{s+1}{s+8.36} \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "Now, the gain $K$ of the compensated system can be found using the gain condition,\n",
    "\\begin{align}\n",
    "&\\left|  \\dfrac{s+z_{lead}}{s+p_{lead}} \\quad \\dfrac{K}{s^2(s+9)(s+50)} \\right| = 1 \\nonumber\\\\\n",
    "&\\left|  \\dfrac{r_1+1}{r_1+8.38} \\quad \\dfrac{K}{r_1^2(r_1+9)(r_1+50)} \\right| = 1 \\nonumber\\\\\n",
    "&K = 10047 \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "Therefore, evaluating the following open-loop compensated system,\n",
    "\\begin{align}\n",
    "G_{ol} &= G_{lead} ~G(s) \\tag{30}\\\\ \n",
    "G_{ol} &= \\dfrac{s+1}{s+8.36}~ \\dfrac{10047}{s^2(s+9)(s+50)}  \\nonumber\n",
    "\\end{align}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matlab script"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "%% c) Phase lead compensator\n",
    "z_lead = 1; % location of the desired zero\n",
    "% using the angle condition to determine the location of the pole\n",
    "x = -real(s1); y = imag(s1);\n",
    "h = 180 + 180 - atand(y/(x-z_lead))-2*( 180-atand(y/x) )-atand(y/(a-x))...\n",
    "-atand(y/(b-x));\n",
    "p_lead = y/tand(h)+x;\n",
    "\n",
    "% Gc compensator TF\n",
    "Gc_lead = (s+z_lead)/(s+p_lead);\n",
    "\n",
    "% obtaining the gain K with the gain condition equation\n",
    "K = ((-x)^2+y^2)*sqrt((-x+a)^2+y^2)*sqrt((-x+b)^2+y^2)*...\n",
    "sqrt((-x+p_lead)^2+y^2)/sqrt((-x+z_lead)^2+y^2);\n",
    "\n",
    "% the open-loop system\n",
    "G = K/(s^2*(s+a)*(s+b));% plant G\n",
    "Gol_lead = Gc_lead*G; % open-loop with the Lead compensator\n",
    "Gcl_lead = feedback(Gol_lead,1); % closed-loop with the Lead compensator\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current plot held\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = figure(1);\n",
    "rlocus(Gcl_lead);\n",
    "hold;\n",
    "% ploting the s1 and zeta in the rlocus\n",
    "n = 0:1:160; m = n*sqrt(zeta^2/(1-zeta^2));\n",
    "axis ([ -4 1 -4 4]);\n",
    "plot (-m,n,'--'); % zeta\n",
    "plot (-x,y,'rd');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "ans = \n",
      "\n",
      "  struct with fields:\n",
      "\n",
      "        RiseTime: 0.3741\n",
      "    SettlingTime: 2.7890\n",
      "     SettlingMin: 0.9447\n",
      "     SettlingMax: 1.5146\n",
      "       Overshoot: 51.4599\n",
      "      Undershoot: 0\n",
      "            Peak: 1.5146\n",
      "        PeakTime: 1.1018\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = figure(2);\n",
    "step(Gcl_lead);\n",
    "stepinfo(Gcl_lead)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "BW_lead =\n",
      "\n",
      "    4.8699\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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rDx06tG/fPq7RxtYu4p62FjvzXl5e3bp14/4VJkyY0KlXGgskx44dY0GIfSOzYDZlyhS2DUufNPvr28ILtdkTyyKu6UrwZlZtNzxy+y+/lj5+s1oKSAsWLDBz/m3o8hMIjLJrHvty1Gq1Op2ODXPKyMhg/wcMtWpl6BMnTmzYsMH0vTZt2iQWi7mn9+/ff/LJJxsaGo4fPx4YGPjMM8+8+uqrAQEBU6dO5bYZOHDg+vXrFy9ezDru+/Xrl5+f7+zszDUjMjMzu3fvPmbMmMTExE8//fSxxx7j9mWrYpuuzG1YpZYW/Dbchi3azbLBZHYd7pZYUltnZ+eqqqqSkhI2zC8oKCg+Pn7r1q2su6ahoeF//ud/9u3b16tXL9beatZD1/k2f06OHDnCvtTYlNtHjhxRKBTdunV74okn5s+fz83lEx4efuXKlaysrPHjxz/0s7ekrq6uoaFBJBL17t07NjaWfU1T69cgt+Ri+/bbb9PS0pYtWzZ69Ojdu3dz2xiN62t2+SWy7EI1c2JZL5PpSvAhISFkdtV2pv2XX0sf33INDQ2pqamBgYFPP/20mc1s6PKzOgSk5kVGRrKV0A4ePMiuhvv37xPRl19+OWvWLG6zVq0MrVKptm3bZlrOfvNyfvzxR7VaHRcXFxUVRUR//OMfZ82a9e233xr+PyeiN998c+rUqefOnVMoFOvWrcvPz+/duzeLo2KxmF3ZbJzrvXv3zH9YFhgMtbTgt+HnNVpL+6HrcJuysLZubm7coHO2JZvrWqvVPv300z/88INCofjpp59kMllLb2ThOt+GuHNy7dq1srKySZMmEVFAQMCvv/768ccfp6enl5SUfPXVV1999dW+ffu4c2V6Wlpr9+7dhkejB4vstXYNcksutq+//pqI1q1bt379elbtb7/9dteuXWwlXG5pWlYB03H/Fl6oRrgTy/6hW1oJ3syq7c0WtuHya+nj19XVmd+Rs2vXrurqahZvzLChy8/qEJCaJxKJ5s6d+8knnyxatIj7squrq+N69ttg3LhxrCfQiGHziB78Pi0tLWVP2QP2fcS+Gtzc3AoKCtauXdu7d++lS5fSg1+LY8aMGTt2rKura3V1dUFBQZ8+fdh/9S5duhgev6WVuVtiuOC3YTlrQt24cYM9fegS2qb/VczUlvukZ8+ejYuL69KlS3Z2NhGVlJQQ0ejRo4lowYIFP/zwQ9++fQ8fPmz+9peHrvNt5pwcO3aMe0e2gvgLL7zw6aefXrt2bcmSJdu3b//uu+/YNwL7lzJs3jHcZzFTww5nycUmkUhYSoOIamtr1Wq1m5ubRCIZN26ci4vLtWvX7t+/7+3tfenSJSJi4yENP4uZC5Vj5sSy68d0JXh2GZhZtd1w9/Zcfi19fLL4nywjI4OIzN8CRda+/GyMtfsMhauysrJfv35E5O7u/swzzzzzzDNcz/68efM6byFOjUbD+mGmT5++YsUK9qYss8KtMVpdXc0ex8fHswYcl0Fhw4F69eo1Z84cdpw9e/YYvQUbAjBq1KiPPvooIiKCfSjDHNLQoUMnTpw4ceJEdgaohZy2j4+P0RkIDg7etWvXmjVr2F5sPPeTTz5JRJMnT/7kk0+MjtBSbQ1XU5XL5UTEUnfs++LAgQPcf2ZXV1evBxYuXGh0fKOL3EwlWzon8fHxXK6Y9Qr6+/t/8cUXO3bsGDlyJBFxA6Xc3d39/f1NzxJrzTy0c990lB3Dz5KvRkkUlpYbM2YMu9NILpezsQPcv4ve7IVqqKUTW1tby+LB66+/npqayh6zUS0sMRYUFDR9+nQfHx+WRDRNArX/8mvp4xt+TKbZHBKr54ULF1o6rBAuP9uCgGQOG1zLRt8SkYuLy5gxY9j4y079mjh16hR3UXp5eXG5YsP/J+np6Wz0ERE9+eSTLB2q1+sbGxsTExNZk9/d3b3Zoa4trcytt2DBb0PsY7IhXmbW4d60aROrD5cn57RUW8NPevHiRfbznJ0NNv642TvqTRPvRt8IZirZ0jlRKBSGue5PPvmEO+2urq7ckD+WBmg2K26LAenWrVvshw4R9e7d+9y5c4aV5L6pW7pQDZm52FpaCb6lVduNjtz+y6+lj29hQGJXgpl/WSFcfrYFAckipaWl+fn5D70LvWPdunXr4sWLZt60qanp4sWLzYaK+vr6M2fOmK9wRUVFO8fk7N+/n35/B0ZtbS0bHGVan9LSUjNj6C2pbUf9E7RUSX1z5+TIkSOFhYVGm1VWVhp9HDa1QbO3hWo0GldX13bX2goqKytNB5SbeuiFqjd7sdXW1t64cYPbvbGxcdu2benp6ex+W/2D733Tf7KOuvx4xvPlZ1uwHhK0S//+/bt37/7zzz9buyJWNnbs2Nu3b7N0i5HRo0dPmjRp1apV/NfKFrVq1XZcfoyZy8/GWDsigm1jmXMeprcRMpbQMs3VMWZyDNCs/fv3s7tqmKFDh3J9hkZw+ekfdvnZFrSQoL2qqqrEYnGzs0E7CK1WW1dX1+xMzNBmFq7ajsvPni4/BCQAABAELNAHAACCgIAEAACCgIAEAACCgIAEAACCgIAEAACC4LhjJUHIVJV1RKRS1/7uaWUz0zDLpWLugVziwT0FAJtj5wGpoqKitLS0W7du3DJiRtavX9/sHeDQ4TROnkSkcfYkoionT41zF66cK+Q28NJVE1FXfTXbhj31evDU9LBsxyonT42zp5euuqu+2ktXHdR0u6u+OqjpVid/MgDbEB4evnjxYmvXwixr35nbiY4fP/7WW2/985//XLp06e7du5vdptlJrDtKmw9u4Y7mNzPzarMvmRYalRg+LbpTOyPpj0V3ajMLKjMLKlN+LUv5tSz5P1eT/3M1/uvc+K9zlZ+dVn52Wv7BUfkHR+nNn+jNn9hjVh7/dS7bOPk/V1N+LWMHKbpTW3SntqV3t9CcOXNYrVJ+LWPVYO8b/3VuZkHlQ0/CQ19t26kzLcGFZ6bQ/Lnq1FPX5uNbvpcVL7zOPnXtZ7ctJJ1Ot3379iVLlshkMo1Gs3z58lGjRgUEBPBZB/MrlbV/R/ObGb5q1NnlpRhzqFBt9NJpt4iV+4vY42J1HREdcx8ZvSH7t83UdXe6TN28+LfloORS8R2P6KyN2XKJmIjkUg8iCpGI2d9yqXh2ZCARySUeZNCr1iptO3tTp06VS8VyqZjCKD5Sxj6gSl17qODuqv1FCeo8Ipo9Qqbs42v52XtouWmhJSWdRzgXniUvPfRc8Xnq2vx2lu9lxxdeB7B2ROws586dW7p0Kff0888/N52+Xq/XD3/tb9xPdZ7/sJaEJX9Yq6LZP+znv9Ef1iIx/PPfl179F9dMoekfssZK/Ne5NPkdrmLyGX9iLZ6UX8viV3zENV+SP/zvtMopKSncr62UlBTDciE/Zo2n+K9z2XlgzSar1GfOnDkCOSc291ipVFq9Djb6WPgtJLsdZVddXW2YN/Lw8Lh+/brpZhpN1d696ewPW/+RKS5Wdfbj8WG+7A9dO2v+cfLkUHn5keTJoeyP4WPlrX9nzhvG/nCP9esnxFd+qV8/gf2Jr/yyaPmj7E+89kDR8kcz5w/LnD8s3vN85vxhKXGKlDhFvOzWysmh7I/SvSQ+Usb+UOk5ZZhEGSaRS8XF509w9T98+DD3y+vw4cOG5UJ+LJeKlWGSlDhFvPZA5rxhqvPHEzYdSjjqlpCWx5qMrTpmaGhom+szdepUgZwTm3vMFmwUTn0E/jg9PT0pKSkpKemvf/0rCZ7dzmV39OjRCxcuzJ07lz398ssviejll1822iwpKWnTpk18Vw6ERFVZl3qy/HChWqWuU4ZJZkcGKsMkD99LpYqOji4qKuKhhgAdQvhfd3abQxKJRE1NTdxTvV7vyPMBgxlyqXjl5FCiUBaZWKqJ5ZksiUwA0FHs9jva19e3pKSEe6rRaEaMGGHF+oDwGUWmhLTfRkDER8pwexMAD+w2hxQeHk5EOTk5RFRWVpaXl6dQKKxdKRCWhISE1NRU03IWmYqWP5oSpyhW10VvzI7ekJ16spz3CgI4FrttITk5OSUmJm7ZsiUoKKi4uDghIcHb29valQJhSUlJMb8BG9Chqqw7VKg+XHh3VUaR5UkmAGgtuw1IRNSvX79169ZZuxZg8+RScbxUFh8pY5GJJZnkLvcoeLC1qwZgV+w5IAF0LMPIlHqyXNX0TujqY0gyAXQUu80hATxUSzmkh5JLxfH9nGjLi5nzhiHJBNBR0EICx/XQHJIZcrmc3YSUEqdAkgmgQyAgAbRXs0km3MkE0FoISAAdxijJxO5kSp4UyqZ5BQDzkEMCx9XmHBIRqVSq0NDQll5ldzJlzhuWPCn0cOHd0NXHuOnyAKAlaCGB4+qQHJK5bdCVB9AaaCEBdDq5VBwfKcucPyxz3jAiit5wJnT1MYzKAzCCFhIAf1hXXnykDKPyAEyhhQSOq/NySOaxBlNKnCJz3rAQiXjV/qLQ1ce45XoBHBZaSOC4OjuH9PCDGMwvviqjKHT1MTSYwJEhIAFYn1wq5m6w5cY+YEYicDQISABCYXQbU/TGbDSYwKEghwSOy1o5pIfibmMaH+aLDBM4DrSQwHFZPYf0kLcwaDAhwwSOAAEJQOiazTCtnNxZ7TMAa0FAArANaDCB3UMOCRyXYHNI5rEGE7uHKSEtD0sxgd1ACwkcl8BzSA+pgMGkD1tPlq/KKEI/Htg6BCQAG4Z+PLAn6LIDsAem/XhY7QJsjhUCUlVV1aVLl06ePHnixInc3Nw7d+7wXwcAstkckhncDUyzI2W4gQlsDq9ddj/++OMrr7xSUlJCRB4eHiKRSKPREJG/v/9777332muv8VkZAJvOIZlh2o+HiYjAJvDUQrp9+3aPHj1mz569dOnSGzduNDU11dTU3L9/X6/X37p16x//+MdHH33UpUuXjIwMfuoD4Ai4fjwiit6YjVVrQeB4aiGNHDly//79AwcONH2pe/fu06ZNmzZtWnl5eUxMTGRkpESCfCxAh+HG46WeLE9Iy8OoBxAsnlpIRUVFzUYjQzKZ7NSpU4hGwBv7yyGZYTg/XkJaHpasBQGy5rDv27dvi0QiRCCwFnvNIZnB0kvKMAnuXgIB4m+U3c2bN6Ojo8eOHatWq4koLCzM399fKpU+8sgjvNUBAOjBkrWZ84dlzhtWrK7DYDwQCP4GNQQGBubm5paWlkql0hkzZtTV1eXn5//yyy8XLlx48cUX+akGABjiRj0gLIEQ8BSQnn/+eblcfvPmzaKiovfffz8tLS07Ozs8PPyxxx5LS0vbt29few6u0WiuGKipqeFeqqioOHv2bGlpabs/Adghh8ohmWE4GI+FJVVlnbUrBY6IpxxSSUlJcHAwezxr1qw//elPXOooMjKyqqqqPQfPysravXu3q6sre5qUlDRgwAAiOnHixM6dOxUKRUFBQVRUVGxsbHveBeyPA+aQzDAcjBe9MRu3LgH/+BvUIBL99l7Ozs7c30Tk4uLSziOXlJQ8//zzSqXSsFCn023fvn3JkiUymUyj0SxfvnzUqFEBAQHtfC8A+2YUlpRhkuRJoQhLwA97mMuupKSERR2tVssV5uTkeHp6ymQyIvLy8oqIiMjNzbVeHQFsCTdGPEQiZnfUohMPeMBfC+nQoUPR0dHc08cff7xDDqvT6W7fvp2WlqbRaKqrqx999NGXX36ZiKqrq7lOQiLy8PC4fv16s0dISkpiD6ZOnRoTE9MhtQKbkJCQMH78+Pj4+Dbsq1KpoqOj7azXzghaS3YgPT1979691q6FpXgKSD4+Pj4+PmfOnOGeco+JyNvbu81HVqvVQ4YMee655/z8/O7evbtmzZojR46MGzdOp9NxvYJE5OTkpNfrmz3Cpk2b2vzuYNOQQ7LE7yd6yJVLPRCWbEhMTAz3O5v78S1YPAWk7OzsDjxaWlpaVlYWEYnF4rVr13Jn2dfXd8iQIVeuXBk3bpxIJGpqauJ20ev1XBILAFqLhSVVJVpL0Il4+o4uLi42v0FISIjlR1MqlYMHDyYiFxeXW7duXbly5bHHHmMvabVa1jDy9fVl04ozGo1mxIgRra43ABhAJx50Kp4GNUyYMEH+e/369VMoFOyxQqFo1dECAwMVCoVCoQgPD29oaPjXv/5VXl5ORHfv3j137lxUVBQRhYeHE1FO/DWCdQAAIABJREFUTg4RlZWV5eXltfZdwO7hPqS2wZAH6CQ8tZDy8/PZg2+++WbBggV5eXls/FtNTc3MmTPbM51dcHDw888/v2bNGrlcrlKpYmJi2E1ITk5OiYmJW7ZsCQoKKi4uTkhIaE+mCuwSckjtgfuWoMO1mOrvJFKp9Ny5cz179jQsFIlEVVVVYrEVLuWkpCQMagBoJ1VlXerJ8q2nyjFVq5AJ/+uO7/uQGhoa3NzcTMtra2t5rgkAdBSuE48eTD5k7RqBTeI7IEVGRkZHR7MJv4mooaHhueee6969OxahAP4hh9SxEJagnfgeCZ2ZmRkeHi6VSr28vIhIo9FIJJIbN27wXA0AQg6pc3C5pVUZRaGrj6ETDyxnhVtzLl++XFxcfOPGDZ1OFxAQ0Lt3b/7rAACdis0grqqsS0jLDV1dnjwpND5SZu1KgdDxFJDKy8vZsDomJCSk2RuP6urqrDK0AQA6g1wqzpw/LPVk+aqMolUZRSlxCmUYOuehRTzlkCZPnhwdHX3z5s2WNrh//35SUpJUKm3nUhQAlkMOiR/xkbLMecOSJ4UmpOXhpiUwg6eAdP78+VmzZvXo0aNHjx5PP/302bNnCwoKiouLc3Jy/vCHP4SEhPj4+Li7u9fU1HTt2pWfKgGkpKS0bWZVQg6plX5bNP3BvbRYAxCaxd8ou4SEBK1W+/HHH587d27kyJF9+/aVy+VDhgzJyMhYvHhxbW3t3//+d94qAwD8MxyGx8KStWsEwsL3oIbp06dPnz6diBoaGnQ6HTJGAI7GcIoHDMMDQ1ZboM/NzQ3RCKwLOSQr4lpLhwvVoauPHSpUW7tGYH1YkQEcF+5DsjpuGF5CWh7mDgd7WMIcAGwaxjsAg4AEANaH8Q5AVglIOp0uOTl5wIABWVlZ58+fP3r0KP91ACDkkISHC0vF6jrMhueA+A5IVVVVLi4umzdvzsvLIyKVSjVmzJhVq1bxXA0Awn1IQsWmHcJ4BwfEd0AaMWLE22+/XV5eztYgnzZt2v79+//85z/zXA0AEDi5VJwSN2D2CNmq/UVILDkIvgNSaWnpu+++a1gyadIkkUjELUgBAMCwHryUuAGExJJj4DsgiUSimpoawxKdTldfX+/q6spzTQCQQ7IJWGbJcfB9H9LMmTMHDRp05coV9rSqqurJJ5+Uy+WYwg74h/uQbAg3v0P0xuytp8oz5w3DHUv2h++AtGHDhvz8fH9/fyJ6/PHHq6urPT09Kysrea4GANgiuVScOY/dSJs7PkyCOYfsjBVmavjpp5+uXbvGFujz8/Pr06cP/3UAABvFmkqqSkyFZ4d4yiEV/55Op/P39w8MDHR1dWUl/FQDwBBySLYLU+HZJZ5aSBMmTLh69aphibu7u7Ozc21tLRF5eHgYjXQA4AFySLYOU+HZGZ5aSPn5+Y2NjY2NjV999ZWPj09ZWVldXV1NTU11dXVsbOwLL7zATzUAwP4YTYVn7epA2/EUkEQPLFy48MKFCzKZjJV36dJl9+7dX375ZV0d7noDgDbC0HD7wPd9SA0NDW5ubqblrO8OgE/IIdkZLixtPVUeuvoYJnewOXwHpMjIyOjoaG5ehoaGhueee6579+4SiYTnmgBgLju7xIaGzx4hQw+ezeE7IGVmZmq1WqlU6u3t7e3t7e7ufvDgQYyyA4AOhB48G2WF+5AuX75cXFzM7kMKCAjo3bs3/3UAALvHTe6QkJYburo8JU6hDENPjKBZZ4G+kJCQqKio0aNHIxqBFSGH5AjY0HBu1nBrVwfM4buF1FLvXEhISKuOc/HixYiICMOSioqK0tLSbt26BQcHmy8EYHAfkuPA5A42ge+ANGbMmNLSUqNCiUTSquns9u3bd+TIkbVr13IlJ06c2Llzp0KhKCgoiIqKio2NbakQABwTevCEj++AZPSj8t69ey+//PLo0aMt3L26unrnzp3Z2dli8X/vx9bpdNu3b1+yZIlMJtNoNMuXLx81alT37t1NCwMCAjrywwCArTGc3GH2CFl8pAyTOwgH3wFJJPrdO/r5+e3evdvd3f29996zZPc9e/Z07dp11qxZO3bs4ApzcnI8PT3ZzbZeXl4RERG5ubl+fn6mhc0GpKSkJPZg6tSpMTExbf5oYHMSEhLGjx/ftpHfKpUqOjoavXY2Kj5SpgyTpJ4sj96Ybd89eOnp6Xv37rV2LSxlhVF2Rth9snfu3PHz83voxjNmzHBycsrJyTEsrK6uNkwReXh4XL9+XSwWmxY2e8xNmza1sepg45BDcmQO0oMXExPD/c7mfnwLFt8BqaCgwKjkjTfecHd3tyQaEZGTk5NpoU6nc3Z2NtxGr9c3W9imKgOA3UIPnqDwHZCio6ONBjX4+PiYaVGmpaVlZWURkVgsNhzFYEgkEjU1NXFP9Xo9mzfPtLC9tQcAe+Q4PXgCZ+VBDQ8NEkqlcvDgwUTk4uLS0ja+vr4lJSXcU41GM2LEiGYL21hpsFPIIQHHQXrwBI7vG2OHDBlSXl7OTf5NRGq1WiQStTTbd2BgoEKhUCgU4eHhLR2TvcQSS2VlZXl5edz2RoWd8YnAdmEuOzDCevCSJ4UmpOWt3F+E6Vl5xlML6fDhwytWrCCiixcvzpw50/Cl6urqpqam9vSnOTk5JSYmbtmyJSgoqLi4OCEhwdvbm4iaLQQAMA89eNbCX6p/xIgRd+7cUalUcrncsNzV1XXu3LlvvvkmP9UwkpSUhFF2ANAsVWVdQlquSl1nHz14wv+64y+HdOrUKSIaP378V1991bNnT97eF6AlyCGBeUZj8NBU6mw8BaRLly4RUf/+/Tdt2lRdXc2eGurfvz8/NQHg4D4ksATXg4d58DobTwFp2rRpTU1NhYWFkydPNr1B1dnZuaGhgZ+aAAC0Fsbg8YOngHT58mX2AGvxAYCNYj14K/cXrdpfdCjsLppKHc4K6yFVVVUVFBRc+j3+qwGA9ZCgDVZODk2JG0BYi7YT8H1j7Ndff2007JuIXFxctFotzzUBQA4J2saoBy9z3jBMONQh+G4hvfnmm/Pmzauvr9cbQDQCAJvDrUUbvTEbTaUOwXdAunfvXnJyMpvhGwDA1q2cHJo5bxihB68j8B2QevXqdfr0aZ7fFKBZyCFBh2A9eJnzhm09VR66+hgmHGozvnNIhw8fDgwMXLdu3dSpUw3LcR8S8A85JOhAcqk4c94wTDjUHny3kNiU22+//bbCwMCBA3muBgBAh+OaSoQevDbhOyBdu3ZNbwKDGgDAbhj24EVvyEYPnuX47rIzWn38t0qIRB4eHiEhITxXBhwc5rKDzoMevDbgOyC99NJL586dIyJPT08iqq6uJiIXF5empiYXF5fi4uIePXrwXCVwWMghQafibldi8+AlTwqNj5RZu1KCxneX3fz584ODgysqKqqqqqqqqu7duzd06NAPP/ywvr5+7ty5I0eO5Lk+AACdioWllDjFqoyihLQ89OCZwXdAeuedd44fP+7n58eeent7HzhwYNmyZW5ubn//+9/LyspaWjoWAMB2KcMkmfOGhUjEuIvWDL4DklarNVoclpvq29nZmYgw7TfwBvchAZ+4wQ7F6rrQ1ccOFaqtXSPB4TuHNHz48GnTpmVmZnbp0oWI6urqnn76aTbse+/eve7u7lhoHHiDHBLwTy4Vp8Qp2KJ/yjBJ8qRQzIPH4buFdPjwYbVa7enpKZVKpVKph4fH5cuXs7Ozi4uLY2Ji1qxZw3N9AAD4Fx8pQw+eKb5bSER0+fLl4uLiq1evlpaWRkVFhYeHE1FISMi9e/fQPAIAB4FF/0xZYT0ktVrd1NTUs2fP0aNHOzs75+bmrlq1iogQjYBnyCGB1bEpw5Mnha7aX4SmEt8tpK1bt5rehxgYGJicnMxzTQCQQwKBiI+UKcMk7HYlR76Llu8W0rJly5YtW9bY2BgUFHTlypXKykqlUrl06VKeqwEAICjcGLzDhWqHnTKc74CkVqsXLVokEomCg4MzMjIkEsmBAwfeeecdnqsBACBAcqk4JW6Awy76x3dAcnNzY/cbLVq0aPPmzUQkEom8vLzUagzJB74hhwQC5MhThvMdkCIiIhYsWFBVVRUVFXXp0iWtVltQUFBRUeHh4cFzTQBSUlLaNrMqIYcEncwxpwznOyD9/PPPGRkZixcv7tOnj0wmc3V17du377hx48Ri3BoGAPA7bMrw8WESB+nB43uUnbOz8927d9njoqKi06dPu7u7Y4E+AIBmOdSU4Va4D8nQ8OHDEY3AWpBDAlvhIFOG89RCanZdPkOtDUsXL16MiIjgnmo0mhs3bnBPe/TowebKq6ioKC0t7datW3BwcKuOD44A9yGBbWFThtvxon88BaTY2NirV6+29KqLi0urVjHft2/fkSNH1q5dy5VkZWXt3r3b1dWVPU1KShowYMCJEyd27typUCgKCgqioqJiY2PbXH8AACHgevBWZRSFrj5mZxMO8RSQBg8eXFxcHBAQ8PbbbycmJrZ5lqDq6uqdO3dmZ2cbDYIoKSl5/vnnlUolV6LT6bZv375kyRKZTKbRaJYvXz5q1KiAgID2fAoAACGw1ynDecohff/991qt9qefftq2bZuPj09ISMjWrVvbsBbfnj17unbtOmvWLKPykpISFni4llZOTo6np6dMJiMiLy+viIiI3NzcZo+Z9EB6enpr6wM2DTkksGmWTBmenp7OfcXxXL024HWUXf/+/bOzs4koJyfn+eefj4+P792799/+9rcnnnjCaNW+lsyYMcPJyckoI6XT6W7fvp2WlqbRaKqrqx999NGXX365urraMG/k4eFx/fr1Zo+5adOmdnwmsGHIIYGte+iU4TExMTExMeyx8GOSFZafIKKBAwfm5ubqdLqjR4+OGzfO8hySk5OTaaFarR4yZMhzzz3n5+d39+7dNWvWHDlyxMXFhU0Jwe2o1+s77AMAAAgGmzI89WT5qv1Fh8Lu2u5gB+sEJCLKycmJi4u7ePGil5fXCy+80NJmaWlpWVlZRCQWiw1HMRjy8/PjIr+vr++QIUOuXLkycODApqYmbhu9Xm9hIwwAwBbZwZThfN+HlJOTM3DgQCcnp5EjRw4YMEClUt2/f/8f//hHS9srlcq5c+fOnTv3lVdeaWmbW7duHT16lHuq1WqdnZ19fX1LSkq4Qo1GExYW1lGfAuwDckhgZ2x9ynCeAhIXh4YNG9arV6/CwsKampodO3aEhISY3zEwMFChUCgUCrawbLMaGhr+9a9/lZeXE9Hdu3fPnTvHLUTLsk1lZWV5eXkKhaJDPxPYPMxlB3bJdqcM5+8+pNu3b3/xxRd9+vQhouvXrxsNMRg7dmybDx4cHPz888+vWbNGLperVKqYmJgBAwYQUWJi4pYtW4KCgoqLixMSErAiLQA4CKMJh2ylB4+nVP+wYcPM3Bjr7OxcWVnJQzVMJSUlYZQdANgxVWVd9MZsuUQsO//V9s8/tHZ1zOGpyy47O/tuy6wVjcDBIYcEjoCbMnyvR7TAs0oYeAaOC/chgYNgPXjl36+RS2OsXRdzrDzbNwAAAIOABAAAgoCABI4LOSQAQUEOCRwXckgAgoIWEgAACAICEgAACAICEjgu5JAABAU5JHBcyCEBCApaSAAAIAgISAAAIAgISOC4kEMCEBTkkMBxIYcEIChoIQEAgCAgIAEAgCAgIIHjQg4JQFCQQwLHhRwSgKCghQQAAIKAgAQAAIKAgASOCzkkAEFBDgkcF3JIAIKCFhIAAAgCAhIAAAgCAhI4LuSQAAQFOSRwXMghAQgKWkgAACAICEgAACAICEjQRunp6dauQntZMYdkB2fPWnDq7JjtBaTy8vKzZ88WFhYalVdUVJw9e7a0tPShhdAh9u7da+0qtFdKSkp8fHzb9m1nDskOzp614NTZMRsLSGlpaZ988kl2dvb27dvXrVvX2NjIyk+cOLF27drs7OwNGzbs2bPHTCGf2vxTzsIdzW9m5tVmXzItNCrh+Zdp297O8r3advbadupaVbH2w4XXHrjwrMiWAtK1a9d+/vnn5cuXJyYmvvfee7W1tb/++isR6XS67du3v/nmm4mJiUuXLv3pp59u3rzZbCHPFW7zTzkLdzS/mZlXm33JtNCohOdfpm17O8v3atvZa9upa1XF2g8XXnvgwrMiJ71eb+06WEqtVt+4cUOhULCnmzZtCgoKiomJOX/+fFpa2l/+8heuPDw83M/Pz7QwOjra6Jjr16+/fPkybx8BBOXQoUNBQUHh4eFt2Fej0ezdu3fGjBkdXiuAThIeHr548WJr18IcW7oPSSKRSCQS9vjWrVvnz59/6qmniKi6ujo4OJjbzMPD4/r162Kx2LTQ9JgC/+cBAHActtRlx7l79+5HH300ZcqUnj17EpFOp3N2/u8HcXJy0uv1zRZaoa4AAGAZobeQ0tLSsrKyiEgsFq9du5aIVCrVp59++sQTT0ycOJFtIxKJmpqauF30er1IJGq2kN+6AwBAKwj9O1qpVA4ePJiIXFxciCgvL2/z5s2zZs0aOnQot42vr29JSQn3VKPRjBgxotlCHisOAACtI/Quu8DAQIVCoVAowsPDKyoqPv/884SEhEGDBmm1Wq1Wq9PpiIglpXNycoiorKwsLy+PbW9aaNWPAgAA5thSZmXnzp0HDhwwLFEqlWyYU35+/pYtW4KCgoqLi19++eXhw4e3VAgAAMJkSwEJAADsmNC77AAAwEEgIAEAgCDYeUDC5KoAALZC6MO+2+PEiRM7d+5UKBQFBQVRUVGxsbHWrhEAALTIbgMSm1x1yZIlMplMo9EsX7581KhRAQEB1q4XAAA0z24DUk5Ojqenp0wmIyIvL6+IiIjc3FzTgITJVR0ZJlcFh4LJVa2m2RlXTTd7q2wodR1qWs4/uVTMPb5Tccevm5/xBhKxUUn+5cuTRw02LAl5sI1cKt6aunV2/GzusHKJB/cuSUlJmzZtMjqaaaFRifmnHa5tx7d8r6SkpPz8/NYep22nzrSkU89emw9u4Y7mNzPzKi68h27ZGRce91j4P77tNiBZOLnqnKpvOu/iTk9Pj4mJsXBjVWUd9zgr69jo0cOMN1DXGpVclje6dfdt9iCHC+/Kx8YeLry79WTtg93ruA28ukzNWH1MLhHLpR5EFCIRy6XiO4EjDhWq5RIPLoZNnTrV8OBGTztb297O8r3Mb9nSq82WmxZaUtJ52vxeFu7YtlPX0ksPPVe48Foqt/DC476FDIOTMNntjbEnTpw4derUggUL2NNt27aJRKKZM2cabdbZv7aEiYUllbr2tweVdcW/hatalbpOVVnHYpIyTEJE48N85VIxe2zIMU9dR8HZazOcujYT/qmz2xYSJlc1g8UbuVRMYc1voKqs48IVa2ZFF56RS8WsUcVCFM+/WztDQkLC+PHj4+Pj27CvSqWKjo4uKipq21vbwdmzFpw6O2a3AYmbXHXgwIFsctWXX37Z2pWyGXKpmAtX8ZEyVshFKRaiVGq/ReePKcMkLTWhhC8lJaXN+8rl8jZHIyKyvC8XjODU2TG7DUhOTk6JiYnc5KoJCQne3t7WrpRt46IUC1Gs/XSoUM3iU4I6jwUnZZjEcIAGAICF7DYgEVG/fv3WrVtn7VrYLRZ14qUyLj6x4JSQlieXimePkCn7+NpiswkArMXOpw4C3sil4vhIWUqcomj5oylxCiJatb8odPWxhLS8Q4Vqa9eueQkJCampqW3bV6VShYaGdmh1ABydPbeQwCpYz54yTEIUqqqsSz1ZnpCWR0TJk0K5dJRAWDGHBACmEJCgE8ml4pWTQ+MjZaw3b1VGkTJMkjwpFEkmADCFgASdTi4Vs1QTazBFb8xWhklmRwYiwwQAhpBDAv6wBlPmvGEhEnFCWp7V00vIIQEIClpIwDfDfryEtDy5RJwSN8AqnXjIIQEIClpIYB1sVF7mvGHjwyTRG7NX7seXO4CjQ0ACa+I68YgodPUxhCUAR4aABNbHhaWtp8qjN2QbTnzeqZBDAhAUBCQQCrlUzPXgpZ4s5+EdU1JS2jazKiGHBNAJEJBAQLim0qqMInTfATgaBCQQHNZUIqLQ1cd4674DAKtDQAIhYk2l2SNk0Rs7MaWEHBKAoOA+JBCulZNDiSh6Y/bsETL2uGPhPiQAQUELCQSNpZQOF6qRUgKwewhIIHRyqTglbsDWU+WISQD2DQEJbAAb5tDhMQk5JABBQQ4JbAOLSdEbs+lBbqn9kEMCEBS0kMBmdFI7CQAEAgEJbAmLSRjjAGCXEJDAxrAxDocL1e2fXgg5JABBQQ4JbA+LSdEbs+VScXuWnUUOCUBQ0EICmySXipMnhSak5WFuIQC7gYAEtio+UsbmFrJ2RQCgYyAggQ1j890lpOW1bXfkkAAExQo5pKqqqtLSUo1Go9PpvLy8AgIC/Pz82nnM8vLymzdvBgUF+fv7G5ZXVFSUlpZ269YtODi4nW8BwhQfKUtIy125v6gNNychhwQgKLwGpB9//PGVV14pKSkhIg8PD5FIpNFoiMjf3/+999577bXX2nbY7777Lisra8CAAd9///3IkSOnTp3Kyk+cOLFz506FQlFQUBAVFRUbG9tRHwSEgw1wSEjLPVTo254BDgBgdTx12d2+fbtHjx6zZ89eunTpjRs3mpqaampq7t+/r9frb9269Y9//OOjjz7q0qVLRkZGa4+sUqkOHjy4fPnyxMTE995779ixYyqVioh0Ot327dvffPPNxMTEpUuX/vTTTzdv3uz4DwYC8CAmYYADgG3jKSCNHDly//79169fnzt3bkBAgLPzf9+3e/fu06ZNKywsLCwsXLZsmVqtbtWRy8vLIyIiJBIJEbm6uvbp0yc7O5uIcnJyPD09ZTIZEXl5eUVEROTm5nboZwIBYYPuWjvAATkkAEHhqcvOkt52mUx26tSp1h7Z1dX1zp073NOamhonJyciqq6uNswbeXh4XL9+vdkjJCUlsQdTp06NiYlpbQVAIOIjZarKuoS0vJQ4hYW7IIcEdi89PX3v3r3WroWl+B7UkJOT00wlRCIPD4+QkJA2HFChUHz99dfffffdoEGDrl27VlxcrFAoiEin0xm2w5ycnPR6fbNH2LRpUxveFwSoPQMcAOxSTEwM9zub+/EtWHwHpJdeeuncuXNE5OnpSUTV1dVE5OLi0tTU5OLiUlxc3KNHj4ceJC0tLSsri4jEYvHatWvfeuutPXv2/Pvf/+7fv39UVFRtbS0RiUSipqYmbhe9Xi8SYVoKO8fN4KDsgwEOALaH7/uQ5s+fHxwcXFFRUVVVVVVVde/evaFDh3744Yf19fVz584dOXKkJQdRKpVz586dO3fuK6+8UldXV1dXN3fu3Lfeemvq1Kk3b94MCwsjIl9fXzacj9FoNKwc7FurZnBADglAWPT88vHxKS0tNSypqKjw9PTU6/WsQVNbW9uqA1ZWVs6bN0+tVuv1+sLCwjfeeKO6ulqv1+t0unfeeefChQt6vf769esLFiy4d++e6e5z5sxp82cBwUr+z1XlZ6etXQsAYRH+1x3fvVhardao68zZ2bmhoYE9IKKGhgaxWGz5ASUSyXPPPZecnNyrV6+Kioq5c+d26dKFiJycnBITE7ds2RIUFFRcXJyQkODt7d2hHwWEKz5SxpaoQDIJwIbwHZCGDx8+bdq0zMxMFjbq6uqefvrpgQMHEtHevXvd3d3bEDYmTJgwYcIE0/J+/fqtW7eu/XUGm4O7ZQFsEd85pMOHD6vVak9PT6lUKpVKPTw8Ll++nJ2dXVxcHBMTs2bNGp7rA/ZKLhUnT35IMgk5JABBscLAs8uXLxcXF1+9erW0tDQqKio8PJyIQkJC7t27h1416EDKMAmbDrxo+aPNboD7kAAExQqzfet0ui+++GLBggV9+vSpq6s7evQoK0c0gg7XzunAAYBPfAekqqoqFxeXzZs35+XlEZFKpRozZsyqVat4rgY4jvhImaqyduV+tGYAhI7vgDRixIi33367vLx88ODBRDRt2rT9+/f/+c9/5rka4DjYAIfDhepDhcbTJCKHBCAofOeQSktL3333XcOSSZMmiUQitVrNJkgF6HDcDA6Z84bJpf+9qQA5JABB4buFJBKJampqDEt0Ol19fb2rqyvPNQGH0rbpwAGAT3wHpJkzZw4aNOj27dvsaVVV1fjx4+VyedeuXXmuCTia+EjZ7BGy0NXHrF0RAGge3wFpw4YNw4cP9/f3P3fu3OOPP+7l5XXmzJn8/HyeqwGOicUkbtAdckgAgmKF+5B++umna9eu3bhxQ6fT+fn59enTh/86gGOSS8VsiQq2bBJySACCwlNAKi4uNirx9/c3fKltiyEBtBY3qxBmugMQGp4C0oQJE65evWpY4u7u7uzszNYu8vDwMBrpANB5uEF3RISYBCAcPOWQ8vPzGxsbGxsbv/rqKx8fn7Kysrq6upqamurq6tjY2BdeeIGfagAwcqk4c96wrafKEzZntu0IyCEBdDieApLogYULF164cEEmk7HyLl267N69+8svv6yre/hyagAdSC4VK2/9+1DB3bZN4oAcEkCH43uUXUNDg5ubm2k567sD4NX9m7NlN7eeKsfEQgBCwHdAioyMjI6OVqt/m8SloaHhueee6969O6ZpAKuQS37ru0NMArA6vgNSZmamVquVSqXe3t7e3t7u7u4HDx40HYMHwBuWT2IrzFq+F3JIAB3OCstPXL58WaVSHThwYP/+/YWFhZWVlc124gHwho27K1bXWb5QBXJIAB2Op4BUXl5u+DQkJCQqKmr06NG9e/c2LMfQBrAWNtldiESMuYUArIWngDR58uTo6OibN2+2tMH9+/eTkpKkUmlVVRU/VQIwwuZxSJ4UGrr6mJmFzwGgk/AUkM6fPz9r1qwePXr06NHj6aefPnv2bEFBQXFxcU5Ozh/+8IeQkBAfHx93d/eamhrMsgpWxGKX9NHJAAAd3UlEQVQSW/jcfEoJOSSADsdfDikhIUGr1X788cfnzp0bOXJk37595XL5kCFDMjIyFi9eXFtb+/e//523ygCYsXJy6EOHOSCHBNDh+B7UMH369KKiooaGhvr6+traWq1WW1xcvGjRIrFY/PCdAfjCDXNA9x0Ab6wwyo5xc3NDEAIhY8McLOm+A4AOYbWABCB8cqmYdd+Z3jmLHBJAh7PVgHTx4kWjkps3b549e/batWuGhRUVFWfPni0tLeWxamBv2J2zRGTYfYccEkCHs8ICfe23b9++I0eOrF27liv58ccf9+/fr1AoVCpV3759X375ZSI6ceLEzp07FQpFQUFBVFRUbGys9aoMto01lYgoemP27BEyLFoB0BlsLCBVV1fv3LkzOzvbMP+k1+u///77FStWBAUF1dTUvPXWW0qlskePHtu3b1+yZIlMJtNoNMuXLx81alRAQIAVKw+2buXk0PhIWerJ8tDVx1LiFMowTMAI0JGs0GWn0+mSk5MHDBiQlZV1/vz5o0ePWr7vnj17unbtOmvWLKNyvV7P5h9yc3NzcnLSarU5OTmenp5snQsvL6+IiIjc3FzTA54+fZp7vHLlSjzGY/OP5VIxZW1NnhSasOlQ6Mxkq9cHj/G4DY8Fi+8WUlVVlZeXV2Bg4I0bN4hIpVLFxsauXLkyOTnZkt1nzJjh5OSUk5NjWOjk5DRz5swNGzYMHjz40qVLY8eODQ0NzcrKCg4O5rbx8PC4fv16s8dMSkpiDzQaTRs/FdimlJQUatN/1PhImTLsydSTQ1btzCIshQ4Clp6evnfvXiI6ffr08OHDrV2dh3DS6/V8vl///v2nTZv2v//7v0OGDNm4cePo0aMzMjKeeuoprVZr+UFycnK+/PJLwxzSF198cfv27aioqJycHK1WO2/evFOnTl24cGHu3Llsgy+//JKIWG7JUFJS0qZNm9r9scBBqSrrojdmK8MkyZNC5VLcxgCCJvyvO75bSKWlpe+++65hyaRJk0QikVqtbnZJpLS0tKysLCISi8WGEcjQuXPnCgsL//znPzs7OyuVyo8//vjAgQPdu3dvamrittHr9SKRjSXMQPjYALzUk+UY7ADQfnx/R4tEopqaGj8/P65Ep9PV19e7uro2u71SqRw8eDARubi4tHTM6urqHj16ODv/lg/z9/e/fft23759S0pKuG00Gs2IESM65jMAGGAD8LjBDghLAG3G96CGmTNnDho06Pbt2+xpVVXV+PHj5XJ5S3OqBgYGKhQKhUIRHh7e0jF79uyZm5vLklI1NTVXrlzp168f255lm8rKyvLy8hQKRcd/HgAi+v0ttJhtCKBt+G4hbdiwIT8/39/fn4gef/zx6upqT0/PysrK9hyzZ8+eL7zwwpo1a0JCQoqLix977LFHH32UiBITE7ds2RIUFFRcXJyQkODt7d0xnwGgBejBA2gPvgc1MNeuXbtx44ZOp/Pz8+vTpw//FeAIP8sHtkhVWZd6snzrqXKEJRAO4X/dWeE+pG+++Uan00VGRu7du3fEiBGYEAzsD9eDx+YLx9ysAJbgOyC99957cXFx9+7dKy8v/+CDD15//fXg4OAePXrwXA0AHsil4pQ4BVtaKXT1sUOFamvXCEDQ+A5In3/++a+//vrII4+sW7fOx8dn1apVP//8c1lZWU1NDc81AeCHXCrOnD8seVJoQlpeQloexjsAtITvgFRdXd2vXz8i+uabb7jbht3d3evr63muCQCf4iNlmfOGhUjE0RuzEZYAmsV3QJJIJL/88sudO3fKyso+++wzIjp8+HB9fX2zd8UC2BMuscTC0sr9RQhLAIb4DkgbN26cMmVKt27dIiIi+vfvn5KSolQqFy9ezHM1AKyFC0tEhLVoAQzxHZCmTZtWUVFRWFjIblmdMWNGYWHh//3f//FcDQDrMgxLGIYHwFhh2Deb46egoKCgoKC0tLSurm7VqlX8VwPA6hCWAAzxHZC2bt0qlUrDwsL6PhAREfH555/zXA0A4cBNSwAM3wFp2bJly5Yta2xsDAoKunLlSmVlpVKpXLp0Kc/VABAao5uWEJbAAfEdkNRq9aJFi0QiUXBwcEZGhkQiOXDgwDvvvMNzNQCEid20xIWl1JPl1q4RAH/4Dkhubm4sh7Ro0aLNmzcTkUgk8vLyUqtxEzvAb7h7abeeLEdYAsfBd0CKiIhYsGBBVVVVVFTUpUuXtFptQUFBRUWFh4cHzzUBELj4SBnCEjgUvgPSzz//nJGRsXjx4j59+shkMldX1759+44bN04sxvLPAM0wCkuYEA/sGN/rITk7O9+9e5c9LioqOn36tLu7+8CBA3muBoBtiY+UsUVpE9LyiCglTqEMw+QmYG/4DkhEpFarb9++rdPpiMjT05OILl261L9/f/5rAmBb4iNlyjDJoUI1whLYJb4D0t69e2NiYojIxcWFK3R2dm5oaOC5JgC2SC4Vx0t/C0ur9hclqPMQlsBu8J1DSkhIWLhwYWNjo9YAohFAq8ilYi63tGp/EYY8gH2wwvITS5cuFYms0FUIYH9YWEqJU2AkHtgBvgNSr169Tp48yfObAtg3ZZgEA8TBDvDUUrl06RJ7sHPnzkGDBn3wwQfPPPMMu0OWwaAGgHbiRuJtPVm+KqNo9gjZysmh1q4UQCs46fV6Ht4mLCzs6tWrLb3q4uKi1Wp5qIappKSkTZs2WeWtATqPqrIuIS1Xpa5DWAKO8L/ueOqyKyws1LfMWtEIwF4ZzYmHqVrBJvCaQyouLs7Nzb19+zafbwrgsLiwhIUtwCbwF5CGDRsml8sjIiL8/f0TEhJ4e18AB8ctbEEPlgFUVdZZu1IAzeApIH366adnzpw5cuTIvXv3tm3blpqaWlBQ0LZDlZeXnz17trCwkCvRaDRXfu/mzZvspYqKirNnz5aWlnbAZwCwZYar00ZvzEZYAgHiaVBD//79fXx8Tpw4wZ6GhoY++uij//rXv1p7nLS0tPPnz/fp0+f69etisfiNN95wdXU9c+ZMamoqt01DQ8PYsWNnzpx54sSJnTt3KhSKgoKCqKio2NhY0wMKP8sH0OFUlXWpJ8u3nipXhklmRwZiogcHIfyvO56GfTc2Nnbp0oV76uPjc/HixdYe5Nq1az///PP//u//shnw3n///V9//fWxxx4bOnTo0KFD2Ta5ubnbtm2LjY3V6XTbt29fsmSJTCbTaDTLly8fNWpUQEBAR30iANvFWkvcbK0ISyAQtjRjQteuXV977TUWjYgoICCgsrLScIP6+vqtW7fOmjXL09Pz/Pnznp6eMpmMiLy8vCIiInJzc5sNSElJSezB1KlT2Tx7AI6AC0vcbK3Jk0LjI2XWrhd0pPT09L1791q7FpaypYAkkUgkkt9+xN26dev8+fNPPfWU4Qb/+c9/goODIyIiiKi6ujo4OJh7ycPD4/r1680eVuBtWIBOxWZrxR219iomJob7nc39+BYs/gLSoUOHRo8ezR6fO3eOiLinzs7OR48etfxQd+/e/eijj6ZMmdKzZ0+usLGx8aeffnrzzTfZU51OZzgThJMTT9kyABvFJnpQVdatyigKXX0MYQn4x1NACgwMrKmpUalU3FMi4p4aRg4jaWlpWVlZRCQWi9euXcv2+vTTT5944omJEycabnn69Olu3brJ5XL2VCQSNTU1ca/q9XrM6ArwUGyMOBv1ELr6GNJLwCeevqNb1QAypFQqBw8eTA/WT8rLy9u8efOsWbO4UQycnJwcw0JfX9+SkhLuqUajGTFiRNvqAOBoMOoBrILv2b5bKzAwUKFQKBSK8PDwioqKzz//PCEhYdCgQWwhJbbsLHPp0qXQ0P/2MISHhxNRTk4OEZWVleXl5SkUCv7rD2C7uFuXxof5slWXMNcDdCpb6sU6dOhQXV3dZ599xpUolcoZM2YQkV6v12g0hiklJyenxMTELVu2BAUFFRcXJyQkeHt7W6HSADaOG/VgmF6Kj5TJpWJrVw3sjaOn+oV/pxiAoOCmWtsl/K87oXfZAYCgoB8POo8tddkBgEBw/XiHCtVbT95g/XjKPr5oMEF7ICABQNspwyTKMAnrx8N0D9BOCEgA0F6GsxBx0z1g4AO0FgISAHQMw/F4D+6r9Z0dKUODCSyEgAQAHcy0wYQheWAJBCQA6BRGDSaWYcIUeWAGhn0DQOdiDaai5Y+mxCmK1XWhq48lpOWlniy3dr1AcNBCAgCecEPy0JUHzUJAAgBeGXblHSpUr9pflKDG/K1AhIAEANZilGRCZAIEJACwMpZkIgo1ajOND/PFkHGHgoAEAEJh1JvH8kxyiXh2pEwZJsFttnYPAQkABMcoMh0uvJuQlieXijFjnn1DQAIA4eIiU/KkUCIyTDWND/OVS8UITvYEAQkAbADrrzNMNR0uvLv1ZC2Ckz1BQAIAG8M1m4hIVVmnUtduPXkDwckOICABgA2TS8Vc+DFqOcklYrnUY3yYLwZE2AoEJACwE6Ytp0MFd7eeLGcDItB4Ej4EJACwQwYtp1D6feMpuvCMXCrm2k8IUcKBgAQA9s+w8UQP2k+qyjquf4+IWFhCiLIiBCQAcDis/URhxPXvEdGhQjURNduKYrsgSnU2BCQAcHRsyEO8VEZEzbaiiIiLUmTQlmL7yiUeGDTRIRCQAACaYdSKYozaUkS09WStSl2nqqzjWlRkEKuICOHKcghIAACWarYtRQ8CFWtRkUGsIiIuXBERF7FCJOLfShC0DNheQCotLa2oqJDJZAEBAYblGo3m6tWrYrG4X79+XGFFRUVpaWm3bt2Cg4N5r6mdS09Pj4mJsXYtbBXOXpsJ89T9N7qEEf0+VjFGEcuwJ5AeBC3uOGQQuogoRCL+3Vv8toGH4VP7YGMBaffu3adPn+7Tp8+33347ZsyYJ598kpXn5OSkpqYqFIpbt265urouXrzYycnpxIkTO3fuVCgUBQUFUVFRsbGx1q28ndm7d68AvxdsBc5em9noqTOKWC1hYYkMQhdXaBjAiEilrjPc3jCSPSjx4A7LQtppt4iO+CidSW87rl+/Pn/+/KqqKr1ef/fu3blz596/f1+v1zc1NS1evDg/P59ttnLlylOnTjU1NS1atKisrEyv19+/f3/hwoU3btwwPeacOXM6r8L//ve/O3VH85uZebXZl0wLjUqMnnbqqWu2Ph27V9vOXttOnWkJLjwzhbjwLCw3LCy6U1t0p/aTrTsyCyrZn5Rfy1J+LXv2T5tTfi1L/s/V5P9cHf7a3yyspLU4WzsgtoJMJluxYoWnpycRiUQinU7X1NRERBcuXPDz8wsPD2ebJScnDx8+PCcnx9PTUyaTEZGXl1dERERubm6zh016ID09vWMrvHfv3k7d0fxmZl5t9iXTQqOSNn+ctmnb21m+V9vOXttOXasq1n648NrDRi88NgTjwtEflWES9ic+UhYfKfO7cSpry8ry79eUf79meMNFCytpLU56vd7adWgdnU539OjRQ4cODRkyhLXcjx07lpubKxaLjx8/7uLiMmXKlEmTJmVlZZ05c2b+/Plsr23btjk7O7/00ktGR1u/fv3ly5f5/gwAALwLDw9fvHixtWthjo3lkIhIo9E0Njb6+vrm5uZOmDDB09OzrKwsOzt7xowZL730Umlp6fr164ODg3U6nbPzf9t/Tk7Nh16B//MAADgOoXfZpaWlvf7666+//vq7777LSnx8fCZMmLBw4UI3N7cff/yRiPz9/f39/ceOHUtEwcHBQ4cOPXXqlEgkYh16jF6vd3FxscpHAAAASwi9haRUKv9/e/cf1GT9BwD8s40xpG23iWMOGSB6wzVBCEEvC8ggZEwL0QQx/HH9OMpLDzqls7pKsRA9zOvyvOOsqCwPisBmQTvNSXjW4Qby08E5UCa4DNhgwBzj+8fn+32+S2CNIT4bvF9/PT8/z/vzvgfePD94PitWrEAI0Wi07u7u5ubmZ555Bq/icDh9fX0IIRaLZbsLhULBazs7O4mFRqNx5cqVjy5uAAAAU+TqV0gLFy4Ui8VisVgkElmt1pKSku7uboSQwWBoamoKDw9HCIWGhhqNxvr6eoSQ0WhsbGyMjo7G7zg0NDQghHQ6XXNzs1gsJrUrAAAA7HGzlxqUSmVpaenSpUvb2tqSkpKI/0PSaDSnT5/mcrk6nS4hISE5ORkh1NraWlRU5Ofn19HR8dJLL0VGRpIaOwAAAHvcrCABAACYrVz9lh0AAIA5AgoSAAAAl+Dqb9mRxWq1FhYW7tmzx8MDUuSo+vr68vLy0dHR9evXwxO7qYJTzmkXL16srq6+f/9+VFSUO37mjkS//fbbpUuXqFSqTCaLiIggOxwoSBPp6+v7/PPP4QsOU9LX11dSUvL2228jhI4cORIYGLhgwQKyg3IbcMo5rb29/cqVK7m5uR4eHsePH6+trYU/hhx08+bN6urqAwcOmM3mgwcPLl68mMPhkBsS3LKbQFVVVUJCApPJJDsQd9La2ioSiby9vb29vSMiIvBb+MBBcMo5jcVipaWl0el0CoUSEhJy+/ZtsiNyG3w+f8eOHR4eHvjH1mQykR0RXCFN5MUXXyQ7BPdz69atoKAgPM3n8zUaDanhuBk45ZyGP9SCEDIajUqlcu/evWRH5DZwHbp69apSqQwKCvLz8yM7orlxhdTY+I9v3P71119qtdr2LymtVqtWq9VqdX9//yOPzj38aw7v379v+/FAQPjX1AE7HMxeX1/fsWPHUlNTFy5c+Aijc2kOpi4gIEAqld64caO9vf0RRjex2f8bRC6XFxcXE7NXr17Nz8+/du3aZ599Vl5ejhdqtVqVSqVSqfC3iMADHMlhQEBAV1cXnjYYDD4+PiQE6nocSR2YjIPZ6+joKCgo2LRpU1RUFBlhuiJHUmexWEwmk0AgkEgkCQkJ1dXVJAX7f7P5lt3g4GBpaem1a9e8vP47hKLVaj1z5kxubq5AIDAajQcOHFi9ejWfz4+Li4uLiyM1WBfleA4DAwMvXbqEt6mrq9u8eTN5UbsEx1NHbpyuyfHs9fb2njp1KisrSygUkhuzi3A8dbW1tWq1+rXXXkMI3bx5E48eR67ZfIVUXl7OZDIzMzOJJY6P2gcwx3Po7+8vkUg++uijI0eOBAUFEc+T5iw4/abD8exVVlb29fUdPXoUDwtQWlpKWtCuwfHURUdHUyiUwsLCwsLC4eHh+Ph40oL+n9l8hZSenk6hUPD3VbHBwUF/f39idt68ecRdpvGOHTs2s/G5gynl8Pnnn8dfEYT/pEFOnX5wyhEcz15aWlpaWhoJIboqx1NHoVBeffVVi8WCXOZn1iWCmCF4HApbDo7aBwhTzaGLnNauAE6/6YDsOc2tf2Zn8y278WDUvumDHDoNUjcdkD2nuVHq5lZBGj9q35IlS0iMxx1BDp0GqZsOyJ7T3Ch1c6sgwah90wc5dBqkbjoge05zo9S50N3DR4BCoezatYsYtW/nzp1sNpvsoNwM5NBpkLrpgOw5zY1SN0cfDI6MjHh6eo5/+gccBzl0GqRuOiB7TnP91M3RggQAAMDVzK1nSAAAAFwWFCQAAAAuAQoSAAAAlwAFCQAAgEuAggQAAMAlQEECAADgEqAgAbeXl5e3cRyFQkF2XDPi2Weftf2Q81Rt3LixtrYWT1ssFh6Phz/2PKE1a9a0tLQ4fSwApgoKEnB7V65caWho8PunefPmkR3Xw3f8+PGAgIDly5c73UJZWVlPTw+eVigUy5cvt/Ox5w8++GDr1q1OHwuAqZpbnw4Cs1VkZOSnn35KdhQzy2Qy5eXlXb58+WE1WFVVtW7dOjsb4BHbzp49u2XLlod1UADsgCskMJvJZDKFQrF48eKwsLCBgYHh4eF9+/YJhUIOh/PCCy+0tbXhzfR6/fbt2zkczrJly0pKSjZt2vTnn3/i3fEE0RqenawdmUxWUVGRkJDAZrPDwsJ+/PFHYt+BgYHs7OxFixZxOJz09PSurq4TJ05kZ2cTGxgMBplMduPGjcn68vXXXwuFwmXLlk3YtY6Oju3bt/N4PDab/cQTT3z11VdE13bu3Im7ZhsPQuiXX34hBgmtqKhYtWoVm80WiUQHDx4kttm2bduJEyemmnYAnDQGgJtLTk5OTU012hgaGsKrEEISieSTTz75+OOPx8bGUlJSJBKJUqnUarVZWVm+vr53794dGxuLjIyMj4/v7OxsbGwMDQ2l0+lyuRzvjieI1vDsZO0ghPz8/E6fPl1ZWbljxw4ajabT6fC+iYmJK1asqKmpaW1tXb9+vVgsvnDhAkLo9u3beIOTJ08GBQXZ6WZSUlJOTo5tMETXRkdHg4ODU1NTVSpVa2vrnj17EELt7e1jY2PR0dExMTEqlUqpVOJvPOMu6HS6BQsW4KY0Gg1CqKioqL+//9y5cywWq6ioCK9SqVQIIdw7AGYaFCTg9vC46bbS0tLwKoTQ4cOH8TT+3drY2EjsKJFIDh06pFQqbQsD3sxOQZqsHbxBQUEBXjg0NETsfv36ddtduru7MzMz7969GxAQgCvl2NjYk08++f7779vpJoPB+O6772yDIbr2999/5+TkEGUDj8Yml8tx1zo7O8d3raioaNu2bXi5XC6n0WharRbP1tTU1NXVEU3RaLSysjI7gQHwsMAzJDAbpKamfvHFF8Ss7YN6iUSCJ3BVyM/PJ1YZjca6ujo/Pz8ul7to0SK8MDw8nMFg2DnWZO3g6aVLl+IJLy8vhJDZbEYINTc3MxiMxx9/HK/i8/lffvklQigzM/Obb77Zv39/W1tbTU0NcZ9tPLPZPDIywmKxbBcSXeNyuUePHq2qqmppaVGpVMSrcW1tbVwuVygUEl2j0+l4WqFQbNiwAU8/99xz4eHhS5YsWbVqVXx8fEpKSlhYGF5FpVK9vLyMRqOdhADwsEBBArMBnU5nMpkTriKKk8ViYTAYMTExxKqYmJjAwMBbt25Ntost4vXoydqxE57ZbKZSJ3he+/LLLx86dEitVpeXl8fFxQUHB9tpZDwiTpPJ9NRTT+n1+ri4uIiIiF27dtmGN34Xq9V67tw54jUQDw+PP/744/z582VlZcXFxR9++GFBQcFbb72F104YOQAzAQoSmCt4PN7IyIhUKhUIBHjJ+fPnH3vsMaFQaDAYent7uVwuQujevXuDg4PEXkQd6urqst+OnUP7+/sPDQ319PTw+XzcZlJS0uHDh6OiouLi4r7//vuSkpL9+/fbacHT05NGo9kGZqusrKy+vr6np8fHx8c2VD6fbzAYDAYDHpBNr9fjG4m///67SCTCGyOEWlpa6urqtmzZIpPJEELZ2dn5+flEQTKZTA9cmQEwQ+BvHzBXSKXS4ODgV155ZWBgACFUUVGRnJys1+vXrl0rEolef/11s9lssVh2795N7BIcHPztt99arVaDwZCTk2O/HTuHjo2NFYvFe/fuxXfw3nnnnYaGhtDQUIRQZmbmmTNntFptenq6/fijoqLq6+snXIWve/A/GBkMhjfeeAMhZLFY1q1bFxgYmJWVZbFYzGbzm2++ibdXKBS2D956enoyMjIuXryIELJarW1tbcS/OrW0tIyOjhI3GwGYUVCQwFxBpVJ//fVXvV4/f/58JpO5devWgoKCDRs2UKnUyspKjUbDZrOZTCZx3YAQOnny5IULF7y8vHx9fVevXo0vFCZrx/7Rf/rpJ3wIb2/vs2fP/vDDD/ghU0ZGxp07dzIyMvCsHVKpFL+kMF5KSopUKg0LC+PxeCEhIWvXrpVIJM3NzVQq9eeff75+/TqTyWSz2QKBAD8es33hGyEUGxv77rvvJiYmMplMb29vnU5XXFyMVymVypCQEJFI9O/5BWDaYMRYMOeYzWa9Xi8QCB54OnLv3j0Wi4XHeJbL5VKpFCFktVr1er2Pj8/4B0uTtWPH8PBwf38/vnGHWSyW+fPny+Xyp59+2v6+er1eKBRqNBriJYXx8fT39/N4vPGriK7h2cuXL69Zs+aBsK1W6507d3x8fGxLY2xs7ObNm22vGgGYOVCQAHiQbUGaOb29vRaLJS8vr6qqqqmpyZFd9u3bR6fT8/LyZjQwQlNTU2JiYnt7O1HJAJhR8FIDAA9iMBiP5tUyX19fFosll8sd3P69995buXLl7t27ifcpZlRubu6pU6egGoFHBq6QACCNyWTy9PS083nT8YaHhz08PKa0i9MGBgYme5kegJkABQkAAIBL+A9UWIGlDSQP0AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = figure(3);\n",
    "margin(Gcl_lead);\n",
    "BW_lead = bandwidth(Gcl_lead) % bandwidth"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can be seen that the close-loop desired poles belong to the root locus of the compensated system, but the overshoot is too high, so, it is recommended to use a Pre-filter to reduce the overshoot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adding a Pre-filter\n",
    "The use of a Pre-filter in series with the closed-loop systems can reduce the overshoot canceling the effect of the Phase-Lead's zero.\n",
    "\n",
    "The Pre-filter is written as follows,\n",
    "\\begin{align}\n",
    "G_{pf} &= \\dfrac{p}{s+p} \\tag{31}\n",
    "\\end{align}\n",
    "where $p$ can be at the exact point of the $z_{lead}=1$,\n",
    "\\begin{align}\n",
    "G_{pf} &= \\dfrac{1}{s+1} \\nonumber\n",
    "\\end{align} \n",
    "applying to the closed-loop Phase-Lead compensated system and evaluating it,\n",
    "\\begin{align}\n",
    "G_{lead+prefilter} &= G_{pf}~ \\dfrac{G_{ol}}{1+G_{ol}} \\nonumber\\\\\n",
    "G_{lead+prefilter} &=  \\dfrac{1}{s+1} ~\\dfrac{10047~(s+1)}{(s+50)(s+13.07)(s+1.64)(s^2+2.76~s+9.40)}\\nonumber\n",
    "\\end{align}  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matlab script\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "ans = \n",
      "\n",
      "  struct with fields:\n",
      "\n",
      "        RiseTime: 1.0081\n",
      "    SettlingTime: 3.0813\n",
      "     SettlingMin: 0.9039\n",
      "     SettlingMax: 1.0007\n",
      "       Overshoot: 0.0749\n",
      "      Undershoot: 0\n",
      "            Peak: 1.0007\n",
      "        PeakTime: 4.2068\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% Using prefilter to reduce the overshoot\n",
    "pf = z_lead; % selecting the zero of the lead compensator (z_lead)\n",
    "Gpf = pf/(s+pf);\n",
    "\n",
    "fig = figure(3);\n",
    "step(Gpf*Gcl_lead);\n",
    "stepinfo(Gpf*Gcl_lead)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "BW_lead_prefilter =\n",
      "\n",
      "    2.3106\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = figure(4);\n",
    "margin(Gpf*Gcl_lead);\n",
    "BW_lead_prefilter = bandwidth(Gpf*Gcl_lead) % bandwidth"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result on implementing a Pre-filter decreases the overshoot dramatically with a small change in the settling time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Design of the Phase-Lag compensator\n",
    "\n",
    "The Phase-Lag compensator has the following transfer function,\n",
    "\\begin{align}\n",
    "G_{lag} = \\dfrac{s+z_{lag}}{s+p_{lag}}, \\quad |p_{lag}|< |z_{lag}| \\tag{32}\n",
    "\\end{align}\n",
    "\n",
    "This compensator will be used in series with the Phase-Lead compensator designed in the previous task. And now, the design requirement is the steady-state error ($ess_a$) for a parabolic input $0.5At^2\\leq2.5\\%$.\n",
    "\n",
    "First, obtaining the LaPlace transform of the parabolic input,\n",
    "\\begin{align}\n",
    "r(t) &= 0.5 A t^2, \\quad R(s) = \\frac{A}{s^3} \\nonumber\n",
    "\\end{align}\n",
    "according to the final value theorem,\n",
    "\\begin{align}\n",
    "ess &= \\lim\\limits_{s\\rightarrow 0}~ s~\\dfrac{A}{s^3} \\dfrac{1}{1+G}  \\tag{33} \n",
    "\\end{align}\n",
    "if $K_a = \\lim\\limits_{s\\rightarrow 0} s^2~G$, the steady-state error is, \n",
    "\\begin{align}\n",
    "ess_a &= \\dfrac{A}{K_a} \\tag{34}\n",
    "\\end{align}\n",
    "where $K_a$ is the acceleration error constant.\n",
    "\n",
    "If $ess_a=0.025$ and $A=1$, the $\\textbf{desired}$ acceleration error constant ($K_{a_d}$) is obtained using (34),\n",
    "\\begin{align}\n",
    "K_{a_d} &= \\frac{1}{ess_a} \\nonumber\\\\\n",
    "K_{a_d} &= 40 \\nonumber\n",
    "\\end{align}\n",
    "and again, with $A=1$ and $G=G_{ol}$ from (30), the $\\textbf{actual}$ acceleration error constant $K_{a_{act}}$ is,\n",
    "\\begin{align}\n",
    "K_{a_{act}} &= \\lim\\limits_{s\\rightarrow 0} s^2~ G_{ol} \\\\\n",
    "K_{a_{act}} &= 2.67 \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "The relation between the zero $z_{lag}$ and the pole $p_{lag}$ of the Phase-Lag compensator can be written as follows,\n",
    "\\begin{align}\n",
    "\\alpha &= \\dfrac{K_{a_d}}{K_{a_{act}}} = \\dfrac{z_{lag}}{p_{lag}} \\tag{35} \\\\\n",
    "\\alpha &= 14.97 \\nonumber\n",
    "\\end{align}\n",
    "choosing a $z_{lag}$ ten times smaller than the real part of the desired dominant pole $r_1$,\n",
    "\\begin{align}\n",
    "z_{lag} &= \\left| \\dfrac{-1.38}{10} \\right| \\nonumber\\\\\n",
    "z_{lag} &= 0.14 \\nonumber\n",
    "\\end{align}\n",
    "and the pole should be,\n",
    "\\begin{align}\n",
    "p_{lag} &= \\dfrac{z_{lag}}{\\alpha} \\nonumber\\\\\n",
    "p_{lag} &= 0.0092 \\nonumber\n",
    "\\end{align}\n",
    "therefore, the Phase-Lag compensator becomes,\n",
    "\\begin{align}\n",
    "G_{lag} &= \\dfrac{s+0.14}{s+0.0092} \\nonumber\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matlab script"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "%% d) Phase-lag compensator\n",
    "ess_a = 0.025; % steady-state error for a parabolic input 0.5At^2\n",
    "Ka_d = 1/ess_a; % Ka desired\n",
    "Ka_act = (z_lead/p_lead)*(K/(a*b));\n",
    "\n",
    "% calculating the zero and pole of the compensator\n",
    "alpha = Ka_d/Ka_act;\n",
    "z_lag = abs(x)/10;\n",
    "p_lag = z_lag/alpha;\n",
    "\n",
    "% Gc phase-lag compensator\n",
    "Gc_lag = (s+z_lag)/(s+p_lag);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation of the performance\n",
    "\n",
    "Finally, the open-loop of the Phase-Lead compensator in series with the Phase-Lag compensator is written as follows,\n",
    "\\begin{align}\n",
    "G_{ol1} &= G_{lag}~G_{lead} ~G(s) \\tag{36} \\\\ \n",
    "G_{ol1} &= \\dfrac{s+0.14}{s+0.0092}~ \\dfrac{s+1}{s+8.36}~ \\dfrac{10047}{s^2(s+9)(s+50)}  \\nonumber\n",
    "\\end{align}\n",
    "and the Pre-filter with the closed-loop systems is,\n",
    "\\begin{align}\n",
    "G_{lag+lead+prefilter} &= G_{pf}~ \\dfrac{G_{ol1}}{1+G_{ol1}} \\tag{37} \\\\\n",
    "G_{lag+lead+prefilter} &= G_{pf}~ \\dfrac{10047(s+1)(s+0.14)}{(s+50)(s+13.05)(s+1.78)(s+0.14)(s^2+2.51~s+8.75)} \\nonumber\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matlab script"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current plot held\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% Evaluating the performance with the phase-lead, phase-lag and prefilter\n",
    "Gol_lead_lag = Gc_lead*Gc_lag*G;\n",
    "Gcl_lead_lag = feedback(Gol_lead_lag,1);\n",
    "\n",
    "fig = figure(5); \n",
    "rlocus(Gcl_lead_lag);\n",
    "hold;\n",
    "% ploting the s1 and zeta in the rlocus\n",
    "n = 0:1:160; m = n*sqrt(zeta^2/(1-zeta^2));\n",
    "axis ([ -4 1 -4 4]);\n",
    "plot (-m,n,'--'); % zeta\n",
    "plot (-x,y,'rd');\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "ans = \n",
      "\n",
      "  struct with fields:\n",
      "\n",
      "        RiseTime: 0.9398\n",
      "    SettlingTime: 3.3125\n",
      "     SettlingMin: 0.9033\n",
      "     SettlingMax: 1.0179\n",
      "       Overshoot: 1.7873\n",
      "      Undershoot: 0\n",
      "            Peak: 1.0179\n",
      "        PeakTime: 1.9419\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = figure(6);\n",
    "step(Gcl_lead,Gpf*Gcl_lead,Gcl_lead_lag,Gpf*Gcl_lead_lag)\n",
    "legend('Lead','Pre-filter + Lead','Lead + Lag','Pre-filter + Lead + Lag'...\n",
    ",'Location','southeast');\n",
    "stepinfo(Gpf*Gcl_lead_lag)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = figure(7);\n",
    "margin(Gcl_lead_lag);\n",
    "BW_lead_lag = bandwidth(Gcl_lead_lag); % bandwidth\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = figure(8);\n",
    "margin(Gcl_lead_lag);\n",
    "BW_lead_lag_prefilter = bandwidth(Gpf*Gcl_lead_lag); % bandwidth\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Ka =\n",
      "\n",
      "    40\n",
      "\n",
      "\n",
      "ess_parabolic =\n",
      "\n",
      "    0.2250\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%% Verifing Ka = 40\n",
    "Ka = (z_lag/p_lag) * (z_lead/p_lead) * ( K/(a*b) )\n",
    "ess_parabolic = a/Ka "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performance results\n",
    "\n",
    "The step response plot of the system with and without the Pre-filter shows that the Pre-filter reduces the overshoot in both cases with good settling time. On the other hand, the root-locus plot shows that the desired dominant poles are slightly out of the target , it is recommended to add a second Phase-lead compensator in series in order correct that gap.\n",
    "\n",
    "<center>Table 2: Performance results </center>\n",
    "\n",
    "| Quantity             | Lead      | Prefilter+Lead      | Lead+Lag      | Prefilter+Lead+Lag |\n",
    "|:---------------------|:---------:|:-------------------:|:-------------:|:------------------:|\n",
    "| Rise Time            | 0.37      | 1.00                | 0.36          | 0.94               |\n",
    "| Settling Time        | 2.79      | 3.08                | 3.59          | 3.31               |\n",
    "| Percentage Overshoot | 51.46     | 0.07                | 57.96         | 1.79               |\n",
    "| Phase Margin         | 40.80     | -180                | 36.60         | 36.60              |\n",
    "| Gain Margin          | 8.96      | 7.07                | 8.51          | 8.51               |\n",
    "| Bandwidth            | 4.87      | 2.31                | 4.89          | 2.58               |\n",
    "| Peak Magnitude       | 1.51      | 1.00                | 1.58          | 1.02               |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## New Phase-Lead compensator\n",
    "\n",
    "The previous root-locus plot demonstrates that the desired dominant closed-loop poles have moved slightly from the root-locus, therefore, a new Phase-Lead compensator is calculated to correct that shift.\n",
    "\n",
    "This time, the location of the zero is exactly below the real part of the desired pole, $z_{lead~2}=1.38$. Applying the angle condition with the desired pole $r_1$ as follows,\n",
    "\\begin{align}\n",
    "&\\measuredangle \\left( \\dfrac{s+z_{lead~2}}{s+p_{lead~2}} \\quad \\dfrac{s+z_{lag}}{s+p_{lag}} \\quad \\dfrac{s+z_{lead}}{s+p_{lead}} \\quad \\dfrac{K}{s^2(s+a)(s+b)}  \\right) = -180° \\tag{38} \\\\\n",
    "&\\measuredangle \\left( \\dfrac{r_1+z_{lead~2}}{r_1+p_{lead~2}} \\quad \\dfrac{r_1+z_{lag}}{r_1+p_{lag}} \\quad \\dfrac{r_1+z_{lead}}{r_1+p_{lead}} \\quad \\dfrac{K}{r_1^2(r_1+a)(r_1+b)}  \\right) = -180° \\nonumber \\\\\n",
    "&\\measuredangle z_{lead~2} +\\measuredangle z_{lag} +\\measuredangle z_{lead}   -  \\measuredangle p_{lead~2} -\\measuredangle p_{lag} - \\measuredangle p_{lead} - 2~\\measuredangle s -\\measuredangle a - \\measuredangle b = -180° \\nonumber\n",
    "\\end{align}\n",
    "if $r_1 = -x+j~y$,\n",
    "\\begin{align}\n",
    "& \\arctan\\dfrac{y}{x-z_{lead~2}} + \\left( 180° - \\arctan\\dfrac{y}{x-z_{lag}} \\right) + \\left( 180°-\\arctan\\dfrac{y}{x-z_{lead}} \\right) ... \\nonumber\\\\\n",
    "& \\quad - \\arctan\\dfrac{y}{p_{lead~2}} - \\left( 180°-\\arctan\\dfrac{y}{x-p_{lag}}  \\right)  -\\arctan\\dfrac{y}{p_{lead}-x} - 2\\left( 180° -\\arctan\\dfrac{y}{x} \\right) ... \\nonumber\\\\\n",
    "&\\qquad -\\arctan\\dfrac{y}{a-x}-\\arctan\\dfrac{y}{b-x} = 180° \\nonumber\n",
    "\\end{align}\n",
    "after some operations,\n",
    "\\begin{align}\n",
    "p_{lead~2} &= 1.48 \\nonumber\n",
    "\\end{align}\n",
    "so, the second Phase-Lead compensator is,\n",
    "\\begin{align}\n",
    "G_{lead~2} &= \\dfrac{s+1.38}{s+1.48} \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "Now, the new gain $K_{new}$ of the compensated system can be found using the gain condition,\n",
    "\\begin{align}\n",
    "%&\\left|  \\dfrac{r_1+1}{r_1+8.38} \\quad \\dfrac{K}{r_1^2(r_1+9)(r_1+50)} \\right| = 1 \\nonumber\\\\\n",
    "&\\left| K_{new} \\quad \\dfrac{s+z_{lead~2}}{s+p_{lead~2}} \\quad \\dfrac{s+z_{lag}}{s+p_{lag}} \\quad \\dfrac{s+z_{lead}}{s+p_{lead}} \\quad \\dfrac{K}{s^2(s+a)(s+b)}  \\right| = 1 \\tag{39} \\\\\n",
    "&\\left| K_{new} \\quad \\dfrac{r_1+z_{lead~2}}{r_1+p_{lead~2}} \\quad \\dfrac{r_1+z_{lag}}{r_1+p_{lag}} \\quad \\dfrac{r_1+z_{lead}}{r_1+p_{lead}} \\quad \\dfrac{K}{r_1^2(r_1+a)(r_1+b)}  \\right| = 1 \\nonumber\\\\\n",
    "&K_{new} = 1 \\nonumber\n",
    "\\end{align}\n",
    "which means that the gain has not changed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "K_new =\n",
      "\n",
      "    1.0095\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%% New phase-lead compensator\n",
    "z_lead2 = x; % given zero lead right below the desired pole\n",
    "f = 180 + atand(y/(x-z_lead2))+(180-atand(y/(x-z_lag)))...\n",
    "+(180-atand(y/(x-z_lead))) - (180-atand(y/(x-p_lag)))-atand(y/(p_lead-x))...\n",
    "-2*(180-atand(y/x))-atand(y/(a-x))-atand(y/(b-x));\n",
    "\n",
    "% p_lead2 = y/tand(180+f) - x;\n",
    "p_lead2 = y/tand(f) + x;\n",
    "Gc_lead2 = (s+z_lead2)/(s+p_lead2);\n",
    "\n",
    "% Calculating the new gain K with the lead 2 compensator\n",
    "K_new = sqrt((-x+p_lead2)^2+y^2)*sqrt((-x+p_lag)^2+y^2)*...\n",
    "sqrt((-x+p_lead)^2+y^2)*((-x)^2+y^2)*sqrt((-x+a)^2+y^2)*sqrt((-x+b)^2+y^2)/...\n",
    "( sqrt((-x+z_lead)^2+y^2)*sqrt((-x+z_lag)^2+y^2)*sqrt((-x+z_lead)^2+y^2)*K )\n",
    "Gol_lead2_lead_lag = K_new*Gc_lead2*Gol_lead_lag;\n",
    "Gcl_lead2_lead_lag = feedback(Gol_lead2_lead_lag,1);\n",
    "\n",
    "%% Verifing Ka = 40 \n",
    "Ka_new = K_new*(z_lead2/p_lead2)*(z_lag/p_lag)*(z_lead/p_lead)*(K/(a*b));\n",
    "ess_parabolic_new = a/Ka_new; "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation of the performance with the second Phase-Lead compensator\n",
    "\n",
    "The open-loop of the new Phase-Lead compensator in series with the previous compensators is written as follows,\n",
    "\\begin{align}\n",
    "G_{ol2} &= G_{lead~2}~G_{lag}~G_{lead} ~G(s) \\tag{40}\\\\ \n",
    "G_{ol2} &= \\dfrac{s+1.38}{s+1.48}\\quad \\dfrac{s+0.14}{s+0.0092} \\quad \\dfrac{s+1}{s+8.36} \\quad \\dfrac{10047}{s^2(s+9)(s+50)}  \\nonumber\\\\\n",
    "\\end{align}\n",
    "and the Pre-filter with the closed-loop systems is,\n",
    "\\begin{align}\n",
    "G_{lag+lead+prefilter} &= G_{pf}~ \\dfrac{G_{ol2}}{1+G_{ol2}} \\tag{41} \\\\\n",
    "G_{lag+lead+prefilter} &= G_{pf}~ \\dfrac{10047(s+1.38)(s+1)(s+0.14)}{(s+8.36)(s+1.48)(s+0.009)s^2(s+9)(s+50)} \\nonumber\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matlab script "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% Comparing the new compensator of the previous designs.\n",
    "fig = figure(9);\n",
    "rlocus(Gcl_lead2_lead_lag)\n",
    "hold on;\n",
    "% ploting the s1 and zeta in the rlocus\n",
    "n = 0:1:160; m = n*sqrt(zeta^2/(1-zeta^2));\n",
    "axis ([ -4 1 -4 4]);\n",
    "plot (-m,n,'--'); % zeta\n",
    "plot (-x,y,'rd');\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "ans = \n",
      "\n",
      "  struct with fields:\n",
      "\n",
      "        RiseTime: 0.9670\n",
      "    SettlingTime: 1.6766\n",
      "     SettlingMin: 0.9081\n",
      "     SettlingMax: 1.0125\n",
      "       Overshoot: 1.2543\n",
      "      Undershoot: 0\n",
      "            Peak: 1.0125\n",
      "        PeakTime: 2.0002\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = figure(10);\n",
    "% step(Gcl_lead2_lead_lag,Gpf*Gcl_lead2_lead_lag)\n",
    "step(Gcl_lead,Gpf*Gcl_lead,Gcl_lead_lag,Gpf*Gcl_lead_lag,...\n",
    "Gcl_lead2_lead_lag,Gpf*Gcl_lead2_lead_lag)\n",
    "legend('Lead','Pre-filter+Lead','Lead+Lag','Pre-filter+Lead+Lag'...\n",
    ",'Lead 2+Lead+Lag','Pre-filter+Lead2+Lead+Lag','Location','southeast');\n",
    "stepinfo(Gpf*Gcl_lead2_lead_lag)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "fig = figure(11);\n",
    "margin(Gcl_lead2_lead_lag);\n",
    "BW_lead2_lead_lag = bandwidth(Gcl_lead2_lead_lag); % bandwidth\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
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   "source": [
    "fig = figure(12);\n",
    "margin(Gpf*Gcl_lead2_lead_lag);\n",
    "BW_lead2_lead_lag_prefilter = bandwidth(Gpf*Gcl_lead2_lead_lag); % bandwidth"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performance results \n",
    "\n",
    "From the root-locus plot, it can be seen that the desired closed-loop poles are exactly in the root locus. Also, the Bode plot shows that the $PM$ has changed a little with respect of the previous compensated system, from $36.60°$ to $39.50°$. On the other hand, the step response has been improved with the Pre-filter and the new Phase-Lead compensator, see Table 3.\n",
    "\n",
    "<center>Table 3: Performance results </center>\n",
    "\n",
    "| Quantity             | Lead   | Prefilter+Lead  | Lead+Lag   | Prefilter+Lead+Lag    | Lead_2+Lead+Lag     | Prefilter+Lead_2+Lead+Lag       |\n",
    "|:---------------------|:------:|:---------------:|:----------:|:---------------------:|:-------------------:|:-------------------------------:|\n",
    "| Rise Time            | 0.37   | 1.00            | 0.36       | 0.94                  | 0.37                | 0.97                            |   \n",
    "| Settling Time        | 2.79   | 3.08            | 3.59       | 3.31                  | 2.87                | 1.68                            |\n",
    "| Percentage Overshoot | 51.46  | 0.07            | 57.96      | 1.79                  | 55.00               | 1.25                            |\n",
    "| Phase Margin         | 40.80  | -180            | 36.60      | 36.60                 | 39.50               | -180                            |\n",
    "| Gain Margin          | 8.96   | 7.07            | 8.51       | 8.51                  | 8.79                | 6.79                            |\n",
    "| Bandwidth            | 4.87   | 2.31            | 4.89       | 2.58                  | 4.88                | 2.42                            |\n",
    "| Peak Magnitude       | 1.51   | 1.00            | 1.58       | 1.02                  | 1.55                | 1.01                            |\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "The settling time requirement $t_s\\leq2.9$ was satisfied by three of the six compensators, and only the last one with the Pre-filter achieved the desired overshoot $PO\\leq 20 \\%$. It is clear that the use of the Pre-filter reduces the overshoot drastically.  \n"
   ]
  }
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  "nikola": {
   "category": "",
   "date": "2020-09-10 17:49:42 UTC-04:00",
   "description": "",
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   "slug": "Phase-lead_phase-lag",
   "tags": "control systems, phase-lead, phase-lag, compensator, Bode, root-locus, pre-filter",
   "title": "Phase-lead and phase-lag compensators with pre-fiter usign Bode and root-locus approaches",
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