{
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"
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Homework 9\n",
    "## Problem 1\n",
    "![image.png](attachment:6ec80e01-e6f1-4709-9e7b-de5e0364f017.png)\n",
    "\n",
    "From Homework 1, we have the state space model.  \n",
    "\n",
    "![image.png](attachment:30649ed4-8307-4980-a923-f5e9e35f9ef9.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Breaking up the force of the propeller into its large and small signal parts, we have $f_P = F_P + f_p$.  The large signal parts give us $F_f = mg$.  The small signal state equation is $\\dot{x}$\n",
    "\n",
    "$$\\begin{equation*}\n",
    "\\mathbf{\\dot{x}} = \n",
    "\\begin{bmatrix}\n",
    "\\dot{v(t)} \\\\\n",
    "\\dot{h(t)}\n",
    "\\end{bmatrix}\n",
    "= \\begin{bmatrix}\n",
    "0 && 0 \\\\\n",
    "1 && 0\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "{v(t)} \\\\\n",
    "{h(t)}\n",
    "\\end{bmatrix} +\n",
    "\\begin{bmatrix}\n",
    "1/m \\\\\n",
    "0\n",
    "\\end{bmatrix} f_p(t)\n",
    "\\end{equation*}\n",
    "$$\n",
    "First we find the step response for the open loop system from $f_P(t)$ to $h(t)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "m =  1\n",
      "A =\n",
      "\n",
      "   0   0\n",
      "   1   0\n",
      "\n",
      "B =\n",
      "\n",
      "   1\n",
      "   0\n",
      "\n",
      "C =\n",
      "\n",
      "   0   1\n",
      "\n",
      "D = 0\n",
      "\n",
      "sys.a =\n",
      "       x1  x2\n",
      "   x1   0   0\n",
      "   x2   1   0\n",
      "\n",
      "sys.b =\n",
      "       u1\n",
      "   x1   1\n",
      "   x2   0\n",
      "\n",
      "sys.c =\n",
      "       x1  x2\n",
      "   y1   0   1\n",
      "\n",
      "sys.d =\n",
      "       u1\n",
      "   y1   0\n",
      "\n",
      "Continuous-time model.\n",
      "\n",
      "Transfer function 'P' from input 'u1' to output ...\n",
      "\n",
      "       1 \n",
      " y1:  ---\n",
      "      s^2\n",
      "\n",
      "Continuous-time model.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pkg load control\n",
    "pkg load signal\n",
    "clear all\n",
    "m = 1 % Assume the mass\n",
    "A = [[0, 0];[1, 0]]\n",
    "B = [[1/m; 0]]\n",
    "C = [0 1]\n",
    "D = 0\n",
    "\n",
    "\n",
    "sys = ss(A, B, C, D)\n",
    "step(sys)\n",
    "%g = place(sys, [-.1, -.2])\n",
    "P = tf(sys)\n",
    "%step(P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that it blows up (but not exponentially).  This is because with a constant force, we have a constant acceleration which means the height is going up as $t^2$.  So it isn't good without feedback!  This is what would happen if we had a unit step disturbance with no feedback."
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's look at putting a controller in the system. We use the small signal model, and we want the small signal output for $h(t)$ to approach zero quickly.  There can be a small signal disturbance and a small signal noise in our measurement of $h(t)$.  These are incorporated into the model in blue below.  (The black is the original system.)  ![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see the disturbance transfer function step response for some possible controllers, $K(s)$.  We want to make $K(s)$ large for low frequencies to make $G_d(s)$ small, but we want $K(s)$ small for large frequencies to make $G_n(s)$ small.  So maybe a solution might be $K(s) = K_{big}/(s/\\omega_0 + 1)$ or even  $K_{big}/(s^2 +as + b)$.  You need to be careful how many poles you put into $K(s)$ because each adds a phase delay, and too much delay is going to make the system unstable.  A solution I like is the PD controller, where $K(s) = k_p + k_ds$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Transfer function 'K' from input 'u1' to output ...\n",
      "\n",
      "      1e+04 s^2 + 1e+04 s + 1e+04\n",
      " y1:  ---------------------------\n",
      "                   s             \n",
      "\n",
      "Continuous-time model.\n",
      "\n",
      "Transfer function 'Gd' from input 'u1' to output ...\n",
      "\n",
      "                        s^3                  \n",
      " y1:  ---------------------------------------\n",
      "      s^5 + 1e+04 s^4 + 1e+04 s^3 + 1e+04 s^2\n",
      "\n",
      "Continuous-time model.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "K = tf([10000, 10000, 10000], [1, 0])  % For PD Controller (Looks like the D is really important for this system.)\n",
    "%K = tf([10, 10], [1])\n",
    "%K = tf(100, [1, 1])\n",
    "%Gd = feedback(P,K)\n",
    "%Gd = tf([1, 0],[1,0,10,0])  % Check the disturbance tronsfer function and make sure it isn't PK/(1+PK)\n",
    "Gd = P/(1+P*K)\n",
    "step(Gd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can play with $K(s)$ to see the effects.  First we look at the Nyquist plot to see how far from -1, the loop gain is."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Transfer function 'L' from input 'u1' to output ...\n",
      "\n",
      "      1e+04 s^2 + 1e+04 s + 1e+04\n",
      " y1:  ---------------------------\n",
      "                  s^3            \n",
      "\n",
      "Continuous-time model.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = P*K\n",
    "grid on\n",
    "nyquist(L)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Ni4cAgERTNJCEEIZhnJ2d9Xq9IHiCBQ5yhDR5OPUZMs0fhBDi/23JQz7NqU/9VUAIocsU9/bt2+C2+n8DFQ0k0zRlGgVnCoWC4zhCCLnMIXQ49UnOu38SQmTE9/LwTfdPt95u3EA+n2elfrLQZcmi/qcHRQNJLviu1Wry8PDwsFwu9/t9wzCGw+He3l7ocMZTnf+WQ78OmCbOAADUkbDvtdm2rWlaMIkXOpw047ObTCZiSTV83E4cuixZ1O8vRUdIlwkt777eau9fp/IYMAGAShIWSAsUmsojlgAgXssbSAEGTACgAgLpV6x9AIB4EUhhTOUBQCwIpEsxlQcAUSKQPoABEwBEg0CaFwMmALhVBNLVsPYBAG4JgXRNTOUBwGIpHUi+74/H48mdgRzH0TQtl8tNPYwFU3kAsBBKB9JgMHj//r2sGxsUNbdtu16vV6tVpUqYM5UHADekbiBVKhXXdR8+fCgPj4+PZVFz3/cbjUY2m1WzhDlTeQBwPeoG0tHRkWEYwaGu66Zp2rbtuq6u66GK5vE181JM5QHAlagbSCGapmWzWcuyXNetVquj0eiDJcwzmczkYSzVEoOXzIhvhBD3vvsi+jYkiPoFxBBClymOirG3Yn9/v1wuV6tVIcTW1lapVPpgCXMFSz3JWBIMmKZRv1gLQuiyZFH/00NiAilknhLmCmLtAwBcJjGB9ODBg1qtNhqNXNctlUrzlzBXE2sfACBkGUuYK4gBk0hal0HQZUmjfn8lZoQkLaSEuYKYygOAhAVS6jGVB2BpEUiK4mtMAJYNgaQ0BkwAlgeBlAwMmACkXnSBZNv2jJ/quh7vpt2JwNoHACkWXSC12+1SqTT1R67r1uv11CyZiwBTeQDSJ7pAKpVKspDERaZpZrPZyFqSJkzlAUiN6AKpXq/3+30hxM7OzvHxsWVZuVxub2+vUCjIHepwbQyYAKRAdIHUaDRyudzq6mqlUsnlcs1m03Xdx48fHx0dXfaQixVj5YaqwRkVKsYqhQETgOSKLpCGw6HctWI8Hhd/0+12ZzxksmKsEKLdbgshPM+T234rVTFWKax9AJBEMSz7zmaz84xpQhVj5SK9Tqfj+/7jx4+VrRirFKbyACSIut9DClWMPTk5WVtbM01TCNHr9QzDULxirFKYygOgvkgDKSgP9e23317j4c+fP6/X66PRqFar6bqeiIqxSlG/fK36BcQQQpcpjoqx09182/NSqSTX41UqFfHbAgeRqIqxSlGtfK36e+MjhC5LFvU/PUQXSJPzb5Mu+3JSyNra2mg0krd9309oxVilsPYBgFKivoZ0dnbmOI7cssF13am19aaqVquVSsUwDLmtQ9IrxiqFtQ8AVBB1xdhKpXJwcBCssqtUKr1eb/5YSmvFWKXENWCiyxKHLksW9fsr6hFScOFH0jTN87z5AymtFWOVwoAJQCyiDqSdnZ1Go1GtVnO53MnJied5hIqyWCwOIEpRB1Kr1TJN8/j42Pf9zc3Ng4ODiBuAq2LtA4BoRLrKTi6oq1arod1UTdPUdV1+0RXKYioPwK2KLpAGg4HrulN/5Hlep9OJrCW4IabyANyG6AKp1+vN+CnfJUocpvIALFZ0gcTihbRiKg/AQqi7uSoSh6k8ADdBIGHBGDABuJ4YAsk0zdFotLa2ls1mi8Ui9V7TigETgCuJOpDkZnS6ro9Go5WVld3d3SuVMBdCeJ4XlPijhLn6WPsAYE6/i/j1BoNBr9fb3NwUQuzt7em6LkvBXnbn58+fT57xfb9SqcgEqtVqpmnu7u7OeAao47z7J/lfpvlDEE4AEIh6hJTNZicP5XBn6j1DJcylbrebzWZ935fbqlLCPImYygMwVdSBVK/Xd3d3dV33PK/RaAghLtugIVTCXAjR7/fX1tY8z8vlco7jUMI80Vj7ACAk6kCqVqu6rluWpev62tpaaA+hGRzHcRyn1+udnJzIM5QwTwfZKxnxjfj0m0zzBwULq2MG9YuQLjlKmE93sWLsaDQKNrj7oH6/v7q6ahiGnKPLZDKUME8ZWaxFtcLqmEH9+jqYpP6nh8RUjN3b2xuPx0KI4XBYLpf//e9/n56eCkqYpw5TecDSii6Q5EioUqkcHR1NVoyds0BfcKlJfntJPpYS5inG2gdg2ShdMXbqbN7h4aG8cXR0ZNv2gwcP5h9mIXEYMAHLI9kVY1ntvTwYMAGpR8VYJAn7PgApFsNedhcrxgJXxVQekD5RB5LjOHKxXIBpN9wEU3lAakQdSK7rjkYjeXs4HAZL5oCbYMAEpEAMOzVMHjYaDd/32a4bi8KACUiumAv0ra6uuq7LIAmLxdoHIIniqYcUHLquW6/XI24DlgdTeUCCRB1I5XJZFkOSdF1nvg4RYCoPUF/UgWRZ1uT+C6Zp6rp+WQWKixVjHcfJ5XLBGSrG4koYMAEqiy6QHMfpdruu64am7GaUMB8MBu/fv5cB5vt+UEhJ1/VWq1Wr1TRNc1232WxyFQpXwoAJUFB0gVQoFA4PD+evNxGqGDsYDDY2NuRjt7a2CoUCFWNxQ6x9AJQSXSDVarVmsylvTJ4PNksNCVWMlRUrhBC+7wshqBiLBWIqD1BBdIFUr9c1TQstapifvG5k23a3263X66PRiIqx6RN7AbH/lK+Vh5Sv/ZDYuwyzUTF2umBWbfIa0pUYhnF2dtbr9TRNk6Vj5XkqxqaDguVHZTIxYLqMgl2GGdT/9BD1KrvHjx8LIVZXV4Mzc17+MU1TppE8LBQKjuMIKsbiNrH2AYhS1IF0fHx8vY9UjuN4nhdcfzo8POz3+1SMRQS4wgREIxPxvFa73a5Wq5d98eiqbNvWNG1qxVgmExInKV3GgCmQlC6DpH5/xbCXnfw6UXB42Sq7ebDaG9FjsThwS2LY7btcLkf8osBtYCoPWKyYd/sWE98oAhKKtQ/AQkQdSMPhcH9/X07ZyXXbmqaNx+MZGwgBicCACbihqAPp5OTk4OAgGBI1Go0nT57s7+9blsVUHtKBARNwPTGUMJ9cFJfNZl3XXVlZOTs7i7glwK1iwARcVdSBtLOz02g0yuVyNpu1bVsW6Ot2u8E3XoGUYcAEzCnq7yEJIWzbPjk5EUKsrKzs7OyMx2Px21Z1C6T+inuELEmXpWnAtCRdlhrq91cMq+yy2Wywv2q32y2Xy3ydCMuDARNwmagDSW724/t+UOZV1qQAlgpXmICLog6kwWDw448/mqYphKhWq6HaSCFTS5hP1iynhDmSjgETEPhdLK+qadpoNBJC6Lo+oxrFYDB4/vx5cFir1UzT3N3dtW374iGQXOfdP8n/Ms0fgnAClk0Mq+wqlcrBwUG73RZCDAaDBw8eTL1nqIS5ZVmTNct936eEOdKHAROWWdSB1Gq1bNvO5XK9Xs+yLFltb+o9QyXMQzXLdV2nhDnSiitMWE4xrLKTo5lCoXDVLexCNcspYZ4+6le0jJj6JdXpMsVRwny6yeHOpFarNeczTNYs13WdEuYpo/6XJGKnWkl1uixZ1P/0EF0gffvtt7quXzaa+aBQzXJKmGMJcYUJ6RZdIP3jH/+wLEsOborF4lW3Ui2Xy5M1y0OHt9RmQEFcYUJaxbB1kOM4106mUM1ySpinCV12PTEOmOiyZFG/v2IIJMnzvP39/cFgcEu/IPV/9Qihy24o+gETXZYs6vdX1KvsPM87Pj62LEsIUS6XX716FXEDgLTiChOSLrpA6vf7QQ7N+PoRgJvgChOSK7pA6na7q6urmqadnJzI8hPS4eFhZG0AlgcDJiROdIF0cHAQ2WsBkBgwIUGiCyS2mwNixIAJ6oth6yAAcWHABJURSMAyYsAEBRFIwPIKDZgEyYRYJSyQqBgL3AaSCSpITCD5vr+7u6vrum3b9Xpdlj/XNM113WazyYoJYCFIJsQoMYF0fHy8sbHRarV83280GtlsloqxwO0hmRC9xASSruumadq27bquruuhArJxtw5ILZIJkUlMIGmals1mLctyXbdarY5GIyrGpo/6BcSWWfD+CSrYik+/ocsUR8XYW7G/v18ul6vVqhBia2urVCpRMTZl1N+KGCH5fP7tp99MnmHwpDL1Pz0kJpBCqBgLqCCUQMG03tSfArMlJpAePHhQq9VGo5HruqVSiYqxgIJm59PFOwCTYivQdz1UjE0xuixxrtFlFyNKIqgioP5bLDEjJCm0vJvV3kCyXBY8BBVE4gIJQCpdNahmPwoJRSABUNfsyJkRV2RVEhFIAJJqRuqQVUlEIAFIIbIqiQgkAMvlGllFUEWDQAKAX11jbQVZtUAEEgB8AIOqaBBIAHB9fLNqgRIWSHJD1WBrBirGAlATQXUNSQqkdrsthPA8T277TcVYAInDZaoZEhNItm0LITqdju/7jx8/pmIsgDS56mWqVKZUYgLp5ORkbW3NNE0hRK/XMwyDirEAlsHU7Enl1F9iAkkI8fz583q9PhqNarWarusfrBgLAGmVymtUSQqkUqkkK8ZWKhXx2wIHcXnFWEqYJ476FS0RQpepJvRnLihhnhHfq/8XMDGBtLa2NhqN5G3f9+epGJusUk9Qv1gLQuiyZMl/F3cLPiRJBfoqlcrGxobrunKVnTyUFWPL5XLozrxVEieTSdL/jRB0WdKo/1cxYf8/UTE2xfjrljh0WbKo/1cxMVN2EhVjASCtfhd3AwAAECJxU3bzY/EPAIQoPmWX2kACACQLU3YAACUQSAAAJSxLIPm+32632+22ZVlxtwVX0O/3424C5mIYRrvdll9XR1Ko9v5alkAaDAbFYrHT6cjtWaE+z/MqlcrJyUncDcGHmaa5trbWbDa73W7cbcFc1Hx/LUsglUoluZvDeDyOuy2Yi6ZpR0dHcbcCc3Ecp1QqUSozQdR8f6UkkHzfD/ZaFUI4juP7vrxtmqZhGEII27ZrtdqTJ0/iaSImhPpLTHSZ7K/QT6GCGb3meR5ppKAZXaamhO3UcJnBYPD+/ftWqyWECFWSlRuEW5Zl2/bh4WHMDYUQ4r/7S/x3l8n+goJm9Jqu647jyBJlUMeMLlNzm5s0BFKlUnFd9+HDh0IIy7KmVpI9Pj72fb9WqwkhiKV4TfaXuLzLoJTZvdbpdLrd7urq6mVb7yN6SXyjpSGQjo6O5KScECL4mBaqJNvr9eJpHC6Y7C9xeZdJfHpQxOxe0zTtyZMnnucxSFLHPG801d5faQikECrJJg5dlkShXsvlclxGUpz6b7SULGqY9MFKslANXZZE9FriqN9laQukQqEgC8vOqCQLpdBlSUSvJU4iuixtU3blcrnf7xuGISvJxt0cfBhdlkT0WuIkosvSudv3jEqyUBNdlkT0WuIo3mXpDCQAQOKk7RoSACChCCQAgBIIJACAEggkAIASCCQAgBIIJACAEggkAIASCCQAgBIIJACAEggkAIASCCQAgBIIJACAEggkAIASCCQAgBIIJACAEggkAIASCCQAgBIIJACAEggkAIASCCQAgBIIJACAEggkAIASCCQAgBIIJACAEggkAIASCCQAgBIIJACAEggkAIASCCQAgBIIJACAEggkAIASCCQAgBIIJACAEggkAIASCCQAgBIIJACAEggkAIASCCQAgBIIJACAEggkAIASCCQAgBL+J+4G3JZ8Ph93EwBALW/evIm7CbOkNpCE8r96hGQymfPz87hbgSugy5JF/Y/pTNkBAJSQ5hESAMQrk8nE+OqJG78SSABwi+JKhXiz8HqYsgMAKIFAgiru3bsXdxNwNXQZFospOwBIiUzzh/8c/N/v/+tQCPU/PhBIAJAMoYC56Lz7p//c+cKi/Px3t9KqBSKQAEAVsyNnMm9SiUACgBhMzZ6bRM7p6enp6en29vYNGhUzAgkAbtfCs2eq09PTly9fEkgAgF9dXFmQ+qm2RVE6kBzHyeVymqbNuIOmablcLspWAUDg4uhn9soCzKBoIPm+v7u7q+u653m6rrdaLSHE/fv3dV0XQsgztVpN0zTXdZvNZrFYjLvJAJZCKIGuOvr54Eq5+aVv4KVoIA0Gg42NDZlDW1tbrVZLJtPh4aG8g2VZmqZ1Oh3P89rtNoEE4PZMpsgNYyB9KbJAigZSqVSSN3zflzc8z8vlcu12O5vN1ut1x3EKhYIQQtO04XAYW0MBpNENh0FxefHixevXr4UQ6+vrcbflOhQNJHndyLbtbrdbr9eFEL7vr66ubm5uuq7baDR0XQ+uLW1sbEx9ktDegmxzoj7167UgJGVd9vbTb+SNe999MXle/a+UCiG2t7dPT0+Dw7/97W/5fP7t27fBGfX/BioaSEIIwzDOzs56vZ4MnnK5XC6XhRDFYtGyLCGE53nynpeNkLiWmCz5fJ6aismSji6bPh3XXcy/K94tt0O9o/6nB0UDyTRNmUbBmX6/r+t6cK2oUCg4jiOEkNeW4mklgMQKcigp03HLQNFAchzH87xarSYPDw8PNzY2Go1GqVRyXbdarZbL5X6/bxjGcDjc29uLtbEAEoMcUlnC1sjbtq1pWnD1KHQ4KR2TCUuFLkucBHVZXDkU4/eQpmyuqnx/KTpCukxoeTervQHMJqOI8VAiJCyQAGAeTM0lEYEEIFVUGxLFu9AuWQgkACmhWhQJvnxyRQQSgMRTMIpwDQQSgKTiQlHKEEgAEok6Q+lDIAFIGCbo0opAApAYRFG6EUgAkoE5utQjkACojoHRkiCQACiNgdHyIJAAKIqB0bIhkACoiIHREiKQAKiFgdHSIpAAKISB0TL7XdwNAIBfkUZLjkACoATSCAQSgPiRRhAEEoDYkUaQolvUYNv2jJ/qup7L5SJrDABFkEYIRBdI7Xa7VCpN/ZHruvV6vVgsRtYYALFjeTdCogukUqnUarWm/sg0zWw2G1lLAMSOgREuii6QLksjIUS1Wo2sGQBiRxphqqi/GOs4zng8njyTzWYLhULEzQAQF9IIl4k6kIbD4f7+vq7rQgjP84QQmqaNx+Ojo6OIWwIgeqQRZog6kE5OTg4ODoIhUaPRePLkyf7+vmVZ5XI54sYAANQR9feQXNfVNC04zGazruuurKycnZ1F3BIAEWN4hNmiDqSdnZ1Go2GapmVZ7XZb5pNlWVNXhDuOI6f1Js/4vn/ZIQBlkUb4oKin7Fqtlm3bJycnQoi1tbVmszkej3u93uSwSQjh+/7u7q6u657n6bouV+jVajVN01zXbTabxWIxdBjxPwTA/EgjzCOG8hNy0LO2tia/exSKImkwGGxsbMgc2traarValmVpmtbpdDzPa7fbvu9PHhJIgLJII8wp6kAyDMN1XV3XR6PRysrK7u7u1PV1wQxeMCPnOI5cCqFp2nA41HV98jCq5gO4GtII84s6kAaDwatXr1zXPTk52dvbG41Gtm1fHN/IYZNt291ut16vT54UQmxsbFw8vCiTyUwe3rt3b3H/DtyKfD4fdxNwNbO77O2n39z77ov8d5E1B2Fv374Nbqv/NzDqQAptEeR53mWbBhmGcXZ2Nnl5KVjgIEdIk4dTn+H8/HwxjUYk8vn8mzdv4m4FruCDXZZp/kCfqkP9D3xRB1K9Xg9WKzQaDSHE1G0aTNOUaRScKRQKjuMIIeQyh9BhVM0HMC8m63BVUQdStVrVdd2yLF3X19bWLtvFTi74rtVq8vDw8LBcLvf7fcMwhsPh3t5e6DC6fwCAOZBGuIZMZPNahmFMPT9j09WLbNvWNC2YxAsdTmL+J3HossS5rMtIIzWp/xaL+ouxZ2dnx8fH8rbruqGNVj+oWCxOxk/oEEDsSCNcW9TlJyqVytHRUVActlKpeJ5HqAAAoh4hhbYC0jQtdAZAcjE8wk1EvahB7mVXrVZzudzJyYnneWyyAKQDaYQbimEvO9M0j4+Pfd/f3Nw8ODiIuAEAbgNphJuLLpAMw5CXkarVami1t2mawVZAAIDlFF0gDQYD13Wn/sjzvE6nE1lLACwWwyMsRHSBNLntwkXstgAkFGmERYkukFi8AKQPaYQFinrZNwAAUxFIAK7p7affMDzCAsVQMdY0zdFoJCvGFovFYNcGAAmSaf5w77svRFfpvdGQLFGPkAzDsCxLCDEajc7OznZ3dyNuAICb49IRbkPUgTQYDHq93ubmphBib29P13XbtiNuAwBAQVEH0vwVYwGoieERbomiFWMBqIk0wu1RtGIsAAWRRrhVMayyKxQKjIoAACFRX0NyHEfWMm80Gvl8vt1uR9wAANfD8Ai3LepAevz48ebmpuM4nue9efPGdV3HcSJuA4CrIo0QgagDyXXdYrHouu7GxoYQYmNjYzweR9wGAFdCGiEaUQfSzs6OYRimaZbLZcuyjo+P2ecbACCiD6Rms7mysrK3t1coFMbjcafTYesgQGUMjxCZqFfZ5XI5OU1n27amaXIbISpTAGoijRClqAPJMIzhcOj7fjAwajabEbcBwDxII0Qs6kAaDAY//vijaZpCiGq1WqvVIm4AgHmQRohePPWQNE0bjUZCCF3XXdeNpQ0AAKXEsMquUqnoun58fGwYxmAw0DQt4jYAmI3hEWIRdSC1Wq1ms5nL5Xq9nhCi1+vNCCTf9z3Pm/FsjuP4vr/4VgJLjDRCXKK+hiTzQ9ZAklWRZhgMBu/fv2+1WvLw/v378ktLuq63Wq1araZpmuu6zWaTdXrAQpBGiFHUgfT48WMhxOrqanDmsiypVCqu6z58+FAeep6n6/rh4aE8tCxL07ROp+N5XrvdJpCAmyONEK+oA+n4+PjNmzfz3PPo6Ehuwyp5npfL5drtdjabrdfrjuPILcM1TRsOh7fVXGBpkEaIXdTXkEql0vV2U/V9f3V1tVwur6ysyMp+wcUnuS0egGsjjaCC6EZI8itH4/FYVowNzgezcLOVy+VyuSyEKBaLcn+HYL3DZSOkTCYzeXjv3r1rNBtRyufzcTdhGb399Jt7332R/+46j6XLFPf27dvgtvp/A6MLpHq9fpOH9/t9XdeDa0WFQkGOtOS1pakPOT8/v8krImL5fH7O6Vws0K9jo+51fvN0WbKo/+khukDKZrP9ft/3fblG7qoP39jYaDQapVLJdd1qtVoul/v9vtyIaG9v7zYaDKQeM3VQSiayYUStVtN1vVAo9Pv9arVarVav8SRyS9bg6lHocBKf3RKHLovYzdOILksW9fsruhHScDgMLhddu0psaHk3q72B62FsBAXFsJcdBZCAeJFGUFM8m6sCiAtpBGVF+sXYyTUe3377rbyh+JwmkCbJYp+kAAAIpElEQVSkEVQWXSARPEC8SCMojik7YCmQRlBf1HvZAYhYpvmDEII0gvoIJCDNGBghQZiyA1KLNEKyMEICUohpOiQRgQSkDQMjJBSBBKQHAyMkGoEEpAFRhBQgkIDEY44O6UAgAQnGwAhpQiABiUQUIX0IJCBhiCKkFYEEJAZRhHQjkIAEIIqwDAgkQF0yhwRRhOVAIAEqYkiEJUQgAQphSIRlRiAB8SOHAEEgATEih4BJBBIQNXIImIpAAqIQhJAgh4BLEEjAbSGEgCshkIBFIoSAayOQgBuZTCBBCAE3oHQg+b4/Ho81TQvOOI6jaVoul5t6CESABAJuidKBNBgM3r9/32q15GGtVtM0zXXdZrNZLBZDh/E2FSlGAgHRUDeQKpWK67oPHz6Uh5ZlaZrW6XQ8z2u3277vTx4SSFiIUPZIJBAQDXUD6ejoyDCM4NBxnEKhIITQNG04HOq6PnkYWyuRWGQPoBp1A+mi4GLSxsbGxcOLMpnM5OG9e/dus3VYgHw+v9gnfPvpN5f96N53X0xpwHeLff30W3iXYbHevn0b3Fb/b2CSAsnzPHlDjpAmD6fe//z8PKKWYRHy+fybN2+u8cCpYx1p1oine53XwqRrdxliof6nh8QEUqFQcBxHCOF5npyvmzyMu3W4LTPCJsA8G5AOiQmkcrnc7/cNwxgOh3t7e6HDuFuHK7g0Yz795uKPCBtgeWSSNa9l27amacHVo9DhJCYTbts8Y5epLssYuixx6LJkUb+/EjNCkkLLu1ntPadrh8cMjF0ALFbCAklxt/F3f1HIDwCKS3MgxRIP/N0HgOtJcyCRDQCQIL+LuwHArya/wYdEoMuwWAQSAEAJBBIAQAkEEgBACQn7Yuz81N+1CQAipvgXY1MbSACAZGHKDgCgBAIJAKCEZQkk3/fb7Xa73bYsK+624Ar6/X7cTcBcDMNot9uyKAySQrX317IE0mAwKBaLnU7HNM2424K5eJ5XqVROTk7ibgg+zDTNtbW1ZrPZ7Xbjbgvmoub7a1kCqVQqlctlIcR4PI67LZiLpmlHR0dxtwJzcRynVCrlcrm4G4J5qfn+Skkg+b4fVDQXQjiO4/u+vG2apmEYQgjbtmu12pMnT+JpIiaE+ktMdJnsr9BPoYIZveZ5HmmkoBldpqaUbK46GAzev3/farWEELVaTdM013WbzWaxWKxWq0IIy7Js2z48PIy5oRBC/Hd/if/uMtlfUNCMXtN13XGcQqEQbwsRMqPL1Cwml4ZAqlQqrus+fPhQCGFZlqZpnU7H87x2ux380o+Pj33fr9VqQghiKV6T/SUu7zIoZXavdTqdbre7urqq63q87UQgiW+0NATS0dGRnJQTQgQf0zRNGw6HwX16vV48jcMFk/0lLu8yiU8Pipjda5qmPXnyxPM8BknqmOeNptr7Kw2BFKJpmryxsbERb0swJ7osiUK9lsvluIykOPXfaClZ1DApuIh38eM21ESXJRG9ljjqd1naAqlQKIxGIyGE53lMZycCXZZE9FriJKLL0jZlVy6X+/2+YRjD4XBvby/u5uDD6LIkotcSJxFdls7dvm3b1jQtmDCF+uiyJKLXEkfxLktnIAEAEidt15AAAAlFIAEAlEAgAQCUQCABAJRAIGEp5PP52gQF68jZtn3//v3JvV4+yDCM4P4XH2gYxtbWlm3bC2sicMvS9j0k4DKqbdt10c7OTrAx880t8KmAaDBCwpJyHMc0zVqtZhiGaZpbW1uTAxTDMO7fv1+pVEzTlFWGHccJfmqaphxjhR7oOE673W632/l8vtFoyMIz8qm2trZkqadgyNJut6dWpplsWPDwqW07OzuTZyzLKhQKvu/Ll65UKgoOAYEPYoSEZRH8QV9bW6tWq+PxuNvt9nq9bDb7+PFjWT2z0WjI+HFd99WrV0KISqVSKpWEEOPx2HVd+Qyj0UjTNJkckw/UNO34+Pjg4KDT6TQaDXn/4Km2t7f/+te/WpZVLBYdx3Fdd+pupEHDisWibdvD4fDHH3+ULZGPmmzb6uqqEMK27WazORgMstnsmzdvbNuWEXXbv1JgsQgkLIvNzU15I5vNyhu6rheLRcMwdF2X4aHr+mg0Ojs7q1arMi1kGk1lWVbogZqm6bouk0BGxcnJSblclk91cHCQy+X+/ve/dzody7LK5fJlzywbJoQoFosHBwe2bXue5/v+eDy2bXtq23K53OrqqmVZpmnqus58HZKIQMKymFGRzPO8k5MTeXttbe2yscsHH3jxDmdnZ0EQyqAqFouWZR0fH8uh1WyO4zQajVKptLa2Jpvk+36obUGdm3K5rGmazCRN06gBhsThGhKWnfxb32q1Wq3WyspKNpvVdT2ImWCabpLcvf/iAy/es1AoBE8l59yKxWK/3y8UCvNknmVZpVKp1WoFld03NzdDbZP3EUKYpul5XqvVOjo6Oj4+vurvAYgdIyQsu2q1allWrVbTNM113YODg2KxKJcMBPVjhBByds4wjLOzM5k9Fx94Mb12dnZ2d3fb7bbc879QKGia9vjx4yBgZtvc3Gw0GmIie5rN5u7ubqPRmCwiILNN07R2u+04znA43NnZWcTvBogUm6sCQgjhOM54PJ6c1pP7Ij9//lz8toTa933XdXVdnxzcXHzgRbZtZ7NZObHm+36lUvn+++8v3ufk5OTitR/P84LscV1XvtDkns2e5wWbN8sWBq9lGMbm5ubstgHqIJCAWeTavEWtEbBt2zTN1dXVi09o2/b+/n65XJ5z8PRBpmlallWv1wkkJMX/+d///d+42wCoK5PJrK2tLbZ+TL1ev3gym83KF/rDH/6wqBcqFAq6rv/+979f1BMCt4oREgBACayyAwAogUACACiBQAIAKIFAAgAogUACACiBQAIAKIFAAgAogUACACiBQAIAKIFAAgAogUACACiBQAIAKIFAAgAogUACACjh/wOoX+HpFetn3gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bode(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": []
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Transfer function 'Gn' from input 'u1' to output ...\n",
      "\n",
      "        -1e+04 s^5 - 1e+04 s^4 - 1e+04 s^3   \n",
      " y1:  ---------------------------------------\n",
      "      s^6 + 1e+04 s^5 + 1e+04 s^4 + 1e+04 s^3\n",
      "\n",
      "Continuous-time model.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Gn = -P*K/(1+P*K)\n",
    "bode(Gn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try to see what happens if we change the model a little by adding a viscous friction.  So the system looks like this now:\n",
    "$$\\begin{equation*}\n",
    "\\mathbf{\\dot{x}} = \n",
    "\\begin{bmatrix}\n",
    "\\dot{v(t)} \\\\\n",
    "\\dot{h(t)}\n",
    "\\end{bmatrix}\n",
    "= \\begin{bmatrix}\n",
    "-k/m && 0 \\\\\n",
    "1 && 0\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "{v(t)} \\\\\n",
    "{h(t)}\n",
    "\\end{bmatrix} +\n",
    "\\begin{bmatrix}\n",
    "1/m \\\\\n",
    "0\n",
    "\\end{bmatrix} f_p(t)\n",
    "\\end{equation*}\n",
    "$$\n",
    "\n",
    "Let's try with $ 0.001< k < 0.1 $ N/(m/s), because it is supposed to be small."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k =  0.10000\n",
      "A =\n",
      "\n",
      "  -0.10000   0.00000\n",
      "   1.00000   0.00000\n",
      "\n",
      "B =\n",
      "\n",
      "   1\n",
      "   0\n",
      "\n",
      "C =\n",
      "\n",
      "   0   1\n",
      "\n",
      "D = 0\n",
      "\n",
      "sys.a =\n",
      "         x1    x2\n",
      "   x1  -0.1     0\n",
      "   x2     1     0\n",
      "\n",
      "sys.b =\n",
      "       u1\n",
      "   x1   1\n",
      "   x2   0\n",
      "\n",
      "sys.c =\n",
      "       x1  x2\n",
      "   y1   0   1\n",
      "\n",
      "sys.d =\n",
      "       u1\n",
      "   y1   0\n",
      "\n",
      "Continuous-time model.\n",
      "\n",
      "Transfer function 'P' from input 'u1' to output ...\n",
      "\n",
      "           1     \n",
      " y1:  -----------\n",
      "      s^2 + 0.1 s\n",
      "\n",
      "Continuous-time model.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = 0.1\n",
    "A = [[-k/m, 0];[1, 0]]\n",
    "B = [[1/m; 0]]\n",
    "C = [0 1]\n",
    "D = 0\n",
    "\n",
    "\n",
    "sys = ss(A, B, C, D)\n",
    "%step(sys)\n",
    "%g = place(sys, [-.1, -.2])\n",
    "P = tf(sys)\n",
    "step(P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note how the viscous friction makes a terminal velocity.  Now the step response after the controller is installed shows a limited velocity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": []
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Transfer function 'Gd' from input 'u1' to output ...\n",
      "\n",
      "                         s^3 + 0.1 s^2                    \n",
      " y1:  ----------------------------------------------------\n",
      "      s^5 + 1e+04 s^4 + 1.1e+04 s^3 + 1.1e+04 s^2 + 1000 s\n",
      "\n",
      "Continuous-time model.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Gd = P/(1+P*K)\n",
    "step(Gd, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Octave",
   "language": "octave",
   "name": "octave"
  },
  "language_info": {
   "file_extension": ".m",
   "help_links": [
    {
     "text": "GNU Octave",
     "url": "https://www.gnu.org/software/octave/support.html"
    },
    {
     "text": "Octave Kernel",
     "url": "https://github.com/Calysto/octave_kernel"
    },
    {
     "text": "MetaKernel Magics",
     "url": "https://metakernel.readthedocs.io/en/latest/source/README.html"
    }
   ],
   "mimetype": "text/x-octave",
   "name": "octave",
   "version": "5.2.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
