EE 222 HW 10.ipynb

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   "source": [
    "# Alex Walczak | EE 222 | HW 10 | Spring 2017\n",
    "#### https://inst.eecs.berkeley.edu/~ee222/sp17/homework_sp17/problem10.pdf"
   ]
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   "source": [
    "# Import libraries\n",
    "# Created with Python 2.7\n",
    "%matplotlib inline\n",
    "from __future__ import division\n",
    "import numpy as np\n",
    "import sympy\n",
    "from sympy import *\n",
    "init_printing(use_latex='mathjax') # initialize pretty printing\n",
    "from IPython.display import display # use instead of 'print' for pretty printing"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 1: Magnetic Levitation System\n",
    "### Setup"
   ]
  },
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     "text": [
      "Examine system dynamics in symbolic form\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}x_{2}\\\\G - \\frac{L_{0} a x_{3}^{2}}{2 m \\left(a + x_{1}\\right)^{2}} - \\frac{k x_{2}}{m}\\\\\\frac{u}{L_{0} + \\frac{L_{1}}{1 + \\frac{x_{1}}{a}}} + \\frac{\\frac{L_{0} a x_{2} x_{3}}{\\left(a + x_{1}\\right)^{2}} - R x_{3}}{L_{0} + \\frac{L_{1}}{1 + \\frac{x_{1}}{a}}}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡              x₂               ⎤\n",
       "⎢                               ⎥\n",
       "⎢                 2             ⎥\n",
       "⎢          L₀⋅a⋅x₃      k⋅x₂    ⎥\n",
       "⎢   G - ───────────── - ────    ⎥\n",
       "⎢                   2    m      ⎥\n",
       "⎢       2⋅m⋅(a + x₁)            ⎥\n",
       "⎢                               ⎥\n",
       "⎢              L₀⋅a⋅x₂⋅x₃       ⎥\n",
       "⎢              ────────── - R⋅x₃⎥\n",
       "⎢                      2        ⎥\n",
       "⎢     u        (a + x₁)         ⎥\n",
       "⎢─────────── + ─────────────────⎥\n",
       "⎢       L₁               L₁     ⎥\n",
       "⎢L₀ + ──────      L₀ + ──────   ⎥\n",
       "⎢         x₁               x₁   ⎥\n",
       "⎢     1 + ──           1 + ──   ⎥\n",
       "⎣         a                a    ⎦"
      ]
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     "output_type": "stream",
     "text": [
      "Examine equilibria in symbolic form\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left [ \\left ( - a - \\frac{\\sqrt{2} u \\sqrt{G L_{0} a m}}{2 G R m}, \\quad 0, \\quad \\frac{u}{R}\\right ), \\quad \\left ( - a + \\frac{\\sqrt{2} u \\sqrt{G L_{0} a m}}{2 G R m}, \\quad 0, \\quad \\frac{u}{R}\\right )\\right ]$$"
      ],
      "text/plain": [
       "⎡⎛            __________      ⎞  ⎛            __________      ⎞⎤\n",
       "⎢⎜     √2⋅u⋅╲╱ G⋅L₀⋅a⋅m      u⎟  ⎜     √2⋅u⋅╲╱ G⋅L₀⋅a⋅m      u⎟⎥\n",
       "⎢⎜-a - ─────────────────, 0, ─⎟, ⎜-a + ─────────────────, 0, ─⎟⎥\n",
       "⎣⎝          2⋅G⋅R⋅m          R⎠  ⎝          2⋅G⋅R⋅m          R⎠⎦"
      ]
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     "output_type": "stream",
     "text": [
      "Examine Jacobian in symbolic form\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}0 & 1 & 0\\\\\\frac{L_{0} a x_{3}^{2}}{m \\left(a + x_{1}\\right)^{3}} & - \\frac{k}{m} & - \\frac{L_{0} a x_{3}}{m \\left(a + x_{1}\\right)^{2}}\\\\- \\frac{2 L_{0} a x_{2} x_{3}}{\\left(L_{0} + \\frac{L_{1}}{1 + \\frac{x_{1}}{a}}\\right) \\left(a + x_{1}\\right)^{3}} + \\frac{L_{1} u}{a \\left(1 + \\frac{x_{1}}{a}\\right)^{2} \\left(L_{0} + \\frac{L_{1}}{1 + \\frac{x_{1}}{a}}\\right)^{2}} + \\frac{L_{1} \\left(\\frac{L_{0} a x_{2} x_{3}}{\\left(a + x_{1}\\right)^{2}} - R x_{3}\\right)}{a \\left(1 + \\frac{x_{1}}{a}\\right)^{2} \\left(L_{0} + \\frac{L_{1}}{1 + \\frac{x_{1}}{a}}\\right)^{2}} & \\frac{L_{0} a x_{3}}{\\left(L_{0} + \\frac{L_{1}}{1 + \\frac{x_{1}}{a}}\\right) \\left(a + x_{1}\\right)^{2}} & \\frac{\\frac{L_{0} a x_{2}}{\\left(a + x_{1}\\right)^{2}} - R}{L_{0} + \\frac{L_{1}}{1 + \\frac{x_{1}}{a}}}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡                                         0                                   \n",
       "⎢                                                                             \n",
       "⎢                                             2                               \n",
       "⎢                                      L₀⋅a⋅x₃                                \n",
       "⎢                                    ───────────                              \n",
       "⎢                                              3                              \n",
       "⎢                                    m⋅(a + x₁)                               \n",
       "⎢                                                                             \n",
       "⎢                                                              ⎛L₀⋅a⋅x₂⋅x₃    \n",
       "⎢                                                           L₁⋅⎜────────── - R\n",
       "⎢                                                              ⎜        2     \n",
       "⎢        2⋅L₀⋅a⋅x₂⋅x₃                   L₁⋅u                   ⎝(a + x₁)      \n",
       "⎢- ─────────────────────── + ────────────────────────── + ────────────────────\n",
       "⎢  ⎛       L₁  ⎞         3             2              2             2         \n",
       "⎢  ⎜L₀ + ──────⎟⋅(a + x₁)      ⎛    x₁⎞  ⎛       L₁  ⎞      ⎛    x₁⎞  ⎛       \n",
       "⎢  ⎜         x₁⎟             a⋅⎜1 + ──⎟ ⋅⎜L₀ + ──────⎟    a⋅⎜1 + ──⎟ ⋅⎜L₀ + ──\n",
       "⎢  ⎜     1 + ──⎟               ⎝    a ⎠  ⎜         x₁⎟      ⎝    a ⎠  ⎜       \n",
       "⎢  ⎝         a ⎠                         ⎜     1 + ──⎟                ⎜     1 \n",
       "⎣                                        ⎝         a ⎠                ⎝       \n",
       "\n",
       "                   1                   0      ⎤\n",
       "                                              ⎥\n",
       "                                              ⎥\n",
       "                  -k               -L₀⋅a⋅x₃   ⎥\n",
       "                  ───             ─────────── ⎥\n",
       "                   m                        2 ⎥\n",
       "                                  m⋅(a + x₁)  ⎥\n",
       "                                              ⎥\n",
       "   ⎞                              L₀⋅a⋅x₂     ⎥\n",
       "⋅x₃⎟                             ───────── - R⎥\n",
       "   ⎟                                     2    ⎥\n",
       "   ⎠            L₀⋅a⋅x₃          (a + x₁)     ⎥\n",
       "──────  ───────────────────────  ─────────────⎥\n",
       "     2  ⎛       L₁  ⎞         2          L₁   ⎥\n",
       "L₁  ⎞   ⎜L₀ + ──────⎟⋅(a + x₁)    L₀ + ────── ⎥\n",
       "────⎟   ⎜         x₁⎟                      x₁ ⎥\n",
       "  x₁⎟   ⎜     1 + ──⎟                  1 + ── ⎥\n",
       "+ ──⎟   ⎝         a ⎠                      a  ⎥\n",
       "  a ⎠                                         ⎦"
      ]
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   "source": [
    "# Add symbols to namespace\n",
    "var('x1 x2 x3 G k m L0 L1 a R u')\n",
    "\n",
    "# Helper function L(x1)\n",
    "def L(x1_val):\n",
    "    x1 = Symbol('x1')\n",
    "    expr = L0 + L1 / (1 + x1 / a)\n",
    "    return expr.subs(x1, x1_val)\n",
    "\n",
    "# System dynamics (xi' = fi(x))\n",
    "f1 = x2\n",
    "f2 = G - (k / m) * x2 - L0 * a * x3 ** 2 / (2 * m * (a + x1) ** 2)\n",
    "f3 = (1 / L(x1)) * (-R * x3 + L0 * a * x2 * x3 / (a + x1) ** 2)\n",
    "f = Matrix([f1, f2, f3])\n",
    "g = Matrix([0, 0, 1 / L(x1)])\n",
    "x_prime = f + g * u\n",
    "x = Matrix([x1, x2, x3])\n",
    "print('Examine system dynamics in symbolic form')\n",
    "display(x_prime)\n",
    "\n",
    "# Examine equilibria in symbolic form\n",
    "print('Examine equilibria in symbolic form')\n",
    "display(solve(x_prime, x))\n",
    "\n",
    "# Examine Jacobian in symbolic form\n",
    "print('Examine Jacobian in symbolic form')\n",
    "J = x_prime.jacobian(x)\n",
    "display(J)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1(a): Find $i_{ss}$, $v_{ss}$ when $y$ is identically $0.05$ m."
   ]
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Set state to desired and solve for i_ss, v_ss, checking if solution makes sense:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left ( 1.9809088823063, \\quad 19.809088823063\\right )$$"
      ],
      "text/plain": [
       "(1.9809088823063, 19.809088823063)"
      ]
     },
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   ],
   "source": [
    "# If yD = x1D = 0.05 and yD' = x2D = 0.00 occurs at an equilibrium point,\n",
    "# then we must be able to find some x3D and u\n",
    "# such that x' = f(x, u) = 0.\n",
    "\n",
    "# Set parameters\n",
    "G = 9.81\n",
    "k = 0.001\n",
    "R = 10.\n",
    "m = 0.01\n",
    "a = 0.05\n",
    "L0 = 0.01\n",
    "L1 = 0.02\n",
    "\n",
    "# Reset dynamic equations with parameters set to above values.\n",
    "f1 = x2\n",
    "f2 = G - (k / m) * x2 - L0 * a * x3 ** 2 / (2 * m * (a + x1) ** 2)\n",
    "f3 = (1 / L(x1)) * (-R * x3 + L0 * a * x2 * x3 / (a + x1) ** 2)\n",
    "f = Matrix([f1, f2, f3])\n",
    "g = Matrix([0, 0, 1 / L(x1)])\n",
    "x_prime = f + g * u\n",
    "x = Matrix([x1, x2, x3])\n",
    "\n",
    "# Set state so that we assume we've reached constant yD = 0.05. Also recompute Jacobian.\n",
    "J = x_prime.jacobian(x)\n",
    "J = J.subs([(x1, 0.05), (x2, 0.00)])\n",
    "\n",
    "# Solve for s.s. current and input voltage at yD. Check if solution exists and makes sense.\n",
    "print('Set state to desired and solve for i_ss, v_ss, checking if solution makes sense:')\n",
    "x_prime = x_prime.subs([(x1 , 0.05), (x2, 0.00)])\n",
    "ss = solve(x_prime, x3, u)[1]  # (solves x' = 0), takes first/second (negative/positive) solution.\n",
    "display(ss)\n",
    "i_ss, v_ss = ss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion 1(a)\n",
    "We have shown that $x_3 = i_{ss} = 1.981$ A, and $u = v_{ss} = R \\cdot i_{ss} = 19.81$ V as Ohm's Law predicts. Since a solution to $f(x, u) = 0$ exists, we know $y$ identically 0.05 m is an equilibrium."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1(b): Show instability of above equilibrium."
   ]
  },
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   "execution_count": 4,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Jacobian evaluated at equilibrium:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}0 & 1.0 & 0\\\\196.2 & -0.1 & -9.905\\\\0 & 4.952 & -500.0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡  0     1.0     0   ⎤\n",
       "⎢                    ⎥\n",
       "⎢196.2  -0.1   -9.905⎥\n",
       "⎢                    ⎥\n",
       "⎣  0    4.952  -500.0⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left \\{ -499.903347144138 : 1, \\quad -14.1079533207851 : 1, \\quad 13.9097379649227 : 1\\right \\}$$"
      ],
      "text/plain": [
       "{-499.903347144138: 1, -14.1079533207851: 1, 13.9097379649227: 1}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "J_at_eq = J.evalf(4, subs={x3 : i_ss, u: v_ss}, chop=True)\n",
    "print('Jacobian evaluated at equilibrium:')\n",
    "display(J_at_eq)\n",
    "print('Eigenvalues:')\n",
    "J_at_eq.berkowitz_eigenvals() "
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1(b) Discussion\n",
    "The eigenvalues of the Jacobian evaluated at the equilibrium (-499.9, -14.1, 13.9) do not all lie in the open left half plane, so the equilibrium is unstable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1(c): Design a state feedback control law to stabilize the ball at desired position $y_D = 0.05$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "System dynamics with parameter values substituted:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}x_{2}\\\\- 0.1 x_{2} - \\frac{0.025 x_{3}^{2}}{\\left(x_{1} + 0.05\\right)^{2}} + 9.81\\\\\\frac{u}{0.01 + \\frac{0.02}{20.0 x_{1} + 1}} + \\frac{\\frac{0.0005 x_{2} x_{3}}{\\left(x_{1} + 0.05\\right)^{2}} - 10.0 x_{3}}{0.01 + \\frac{0.02}{20.0 x_{1} + 1}}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡                    x₂                     ⎤\n",
       "⎢                                           ⎥\n",
       "⎢                          2                ⎥\n",
       "⎢                  0.025⋅x₃                 ⎥\n",
       "⎢       -0.1⋅x₂ - ──────────── + 9.81       ⎥\n",
       "⎢                            2              ⎥\n",
       "⎢                 (x₁ + 0.05)               ⎥\n",
       "⎢                                           ⎥\n",
       "⎢                     0.0005⋅x₂⋅x₃          ⎥\n",
       "⎢                     ──────────── - 10.0⋅x₃⎥\n",
       "⎢                                2          ⎥\n",
       "⎢        u            (x₁ + 0.05)           ⎥\n",
       "⎢────────────────── + ──────────────────────⎥\n",
       "⎢           0.02                   0.02     ⎥\n",
       "⎢0.01 + ───────────     0.01 + ───────────  ⎥\n",
       "⎣       20.0⋅x₁ + 1            20.0⋅x₁ + 1  ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Output:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}x_{1}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "[x₁]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Dynamic equations (with parameters set).\n",
    "f1 = x2\n",
    "f2 = G - (k / m) * x2 - L0 * a * x3 ** 2 / (2 * m * (a + x1) ** 2)\n",
    "f3 = (1 / L(x1)) * (-R * x3 + L0 * a * x2 * x3 / (a + x1) ** 2)\n",
    "f = Matrix([f1, f2, f3])\n",
    "g = Matrix([0, 0, 1 / L(x1)])\n",
    "x_prime = f + g * u\n",
    "x = Matrix([x1, x2, x3])\n",
    "\n",
    "print('System dynamics with parameter values substituted:')\n",
    "display(x_prime)\n",
    "\n",
    "# Output\n",
    "y = Matrix([x1]) # Want to regulate output to 0.05 m.\n",
    "def h(x):\n",
    "    return y.subs(x, x)\n",
    "\n",
    "print('Output:')\n",
    "display(h(x))\n",
    "\n",
    "# Lie derivative helper functions.\n",
    "def gradient(scalar_function, variables):\n",
    "    # gradient multivar scalar function (row vector of partial derivaties)\n",
    "    matrix_scalar_function = Matrix([scalar_function])\n",
    "    return matrix_scalar_function.jacobian(variables)\n",
    "\n",
    "\n",
    "def LieD(func, along_trajectories_of, with_variables):\n",
    "    # Computes the Lie derivative (wrt time) of func (always scalar?) along trajectories of a vector field.\n",
    "    return gradient(func, with_variables).dot(along_trajectories_of)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Differentiate output $h$ until input $u$ appears."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative degree is: 3\n"
     ]
    }
   ],
   "source": [
    "def find_relative_degree(f, g, x, h):\n",
    "    # of SISO system: x' = f(x) + g(x) * u, y = h(x).\n",
    "    # Assuming h is not already a function of the input.\n",
    "    r = 0\n",
    "    L_prev_f_h = h\n",
    "    while True:\n",
    "        L_cur_f_h        =   LieD(L_prev_f_h, f, x)\n",
    "        L_g_L_prev_f_h   =   LieD(L_prev_f_h, g, x)\n",
    "        r += 1\n",
    "        if L_g_L_prev_f_h != 0: # good: input has shown up in rth derivative of output\n",
    "                                # (Note to self: shouldn't I be checking if magnitude bounded\n",
    "                                # away from 0 in some nbhd of the eq. pt?)\n",
    "            \n",
    "            # Uncomment below three lines to view final Lie derivatives.\n",
    "            # print \"L_cur_f_h, L_g_L_prev_f_h:\"\n",
    "            # display(L_cur_f_h)\n",
    "            # display(L_g_L_prev_f_h)\n",
    "            break\n",
    "        if L_cur_f_h == 0: # bad: if happens would never terminate.\n",
    "            print 'Error!'\n",
    "            return -1\n",
    "        L_prev_f_h = L_cur_f_h\n",
    "    return r\n",
    "\n",
    "print 'Relative degree is: ' + str(find_relative_degree(f, g, x, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion 1(c)\n",
    "It has been shown the relative degree of the system is $3$. Thus LgLf2_h = $\\frac{0.05 x_3}{(0.01 + \\frac{0.02}{20.0 x_1 + 1}) (x_1 + 0.05)^{2}}$, and choosing $u$ according to lecture 22-1 with coefficients ensuring poles in OLHP will let us regulate output to $y_D$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1(d): Discuss how the DOA of the desired equilibrium using this control law would compare to that using a standard linear control law, computed from a Jacobian linearization of the maglev system.\n",
    "\n",
    "### Discussion\n",
    "Since the relative degree is $\\gamma = n = 3$, the system is **full state linearizable**, and thus minimum phase (trivial zero dynamics). With the above feedback linearizing control law, we can achieve globally asymptotically stable tracking of $y_D$ (by Lecture 22-1), so the DOA is $\\mathbb{R}^3$\n",
    "\n",
    "With a standard linear control law using the Jacobian linearization, we would be linearizing highly nonlinear dynamics about an unstable equilibrium point, so we would expect the DOA to be a small neighborhood."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 2: Conventional Take-Off and Landing (CTOL) Aircraft Control\n",
    "### Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Add variables to namespace\n",
    "# Notation: (...)_kp = kth time derivative of (...)\n",
    "from sympy.abc import alpha, gamma, epsilon, theta\n",
    "var('x z x_p z_p x_2p z_2p theta_p theta_2p u1 u2 a_L a_D L D c')\n",
    "\n",
    "gamma = atan(z_p / x_p)\n",
    "alpha = theta - gamma\n",
    "L = a_L * (x_p ** 2 + z_p ** 2) * (1 + c * alpha)\n",
    "D = a_D * (x_p ** 2 + z_p ** 2)\n",
    "theta_2p = u2\n",
    "\n",
    "# Rotation matrix\n",
    "def R(theta):\n",
    "    Rot = Matrix([\n",
    "        [cos(theta),-sin(theta)],\n",
    "        [sin(theta), cos(theta)]])\n",
    "    return Rot\n",
    "\n",
    "# We'll define full state: s = (x', x, z', z, theta', theta).\n",
    "s = Matrix([x_p, x, z_p, z, theta_p, theta])\n",
    "f_pre = R(theta) * R(alpha).T * Matrix([-D, L]) + Matrix([0, -1])\n",
    "g1_pre = R(theta) * Matrix([1, 0])\n",
    "g2_pre = R(theta) * Matrix([0, epsilon])\n",
    "\n",
    "# System dynamics\n",
    "f  = Matrix([  f_pre[0],   x_p,   f_pre[1],   z_p,   0,   theta_p ])\n",
    "g1 = Matrix([ g1_pre[0],     0,  g1_pre[1],     0,   0,         0 ])\n",
    "g2 = Matrix([ g2_pre[0],     0,  g2_pre[1],     0,   1,         0 ])\n",
    "\n",
    "s_p = f + g1 * u1 + g2 * u2\n",
    "\n",
    "# Output\n",
    "def h1(s):\n",
    "    M = Matrix([0, 1, 0, 0, 0, 0])\n",
    "    return M.dot(s)\n",
    "    \n",
    "def h2(s):\n",
    "    M = Matrix([0, 0, 0, 1, 0, 0])\n",
    "    return M.dot(s)    \n",
    "\n",
    "y1 = h1(s)\n",
    "y2 = h2(s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 2 continued.\n",
    "#### Linearize the system from the inputs u1, u2 to the outputs y1 = x, y2 = z. Give the linearizing control law. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Add auxiliary variables v1, v2 to namespace (used to set control law u).\n",
    "var('v1 v2')\n",
    "\n",
    "def find_vector_relative_degree(f, g1, g2, s, h1, h2):\n",
    "    # of MIMO (TITO) system: s' = f(s) + g1(s) * u1 + g2(s) * u2; y1 = h1(s), y2 = h2(s).\n",
    "    # Assuming h1, h2 not already functions of the inputs.\n",
    "\n",
    "    # We'll test singularity of a matrix A to determine if the systems has vector relative degree (r1, r2).\n",
    "    A00, A01, A02, A03 = -1,-1,-1,-1 # See EE 222 lecture notes 18 page 13.\n",
    "    L_r1_f_h1, L_r2_f_h2 = None, None # Will set later.\n",
    "    \n",
    "    # Do one at a time. Start with differentiating y1 until u1 OR u2 appears.\n",
    "    L_prev_f_h = h1\n",
    "    r1 = 0\n",
    "    while True:\n",
    "        L_cur_f_h        =   LieD(L_prev_f_h,  f, s)\n",
    "        L_g1_L_prev_f_h  =   LieD(L_prev_f_h, g1, s)\n",
    "        L_g2_L_prev_f_h  =   LieD(L_prev_f_h, g2, s)\n",
    "        r1 += 1\n",
    "        if L_g1_L_prev_f_h != 0 or L_g2_L_prev_f_h != 0: # good: input has shown up in r1-th derivative of output\n",
    "                                # (Note to self: shouldn't I be checking if magnitude bounded\n",
    "                                # away from 0 in some nbhd of the eq. pt?)\n",
    "            print \"u appeared! (1)\"\n",
    "            A00, A01 = L_g1_L_prev_f_h, L_g2_L_prev_f_h\n",
    "            L_r1_f_h1 = L_cur_f_h # r1-th Lie derivative of h1 along f.\n",
    "            break\n",
    "        if L_cur_f_h == 0: # bad: if happens and previous conditions failed, alg would never terminate.\n",
    "            print 'Error! ' + str(r1)\n",
    "            r1 = -1\n",
    "            break\n",
    "        L_prev_f_h = L_cur_f_h\n",
    "    \n",
    "    # Now, differentiate y2 until u1 OR u2 appears.\n",
    "    L_prev_f_h = h2\n",
    "    r2 = 0\n",
    "    while True:\n",
    "        L_cur_f_h        =   LieD(L_prev_f_h,  f, s)\n",
    "        L_g1_L_prev_f_h  =   LieD(L_prev_f_h, g1, s)\n",
    "        L_g2_L_prev_f_h  =   LieD(L_prev_f_h, g2, s)\n",
    "        r2 += 1\n",
    "        if L_g1_L_prev_f_h != 0 or L_g2_L_prev_f_h != 0: # good: input has shown up in r2-th derivative of output\n",
    "            print \"u appeared! (2)\"\n",
    "            A10, A11 = L_g1_L_prev_f_h, L_g2_L_prev_f_h\n",
    "            L_r2_f_h2 = L_cur_f_h # r2-th Lie derivative of h2 along f.\n",
    "            break\n",
    "        if L_cur_f_h == 0: # bad: if happens and previous conditions failed, alg would never terminate.\n",
    "            print 'Error! ' + str(r2)\n",
    "            r2 = -1\n",
    "            break\n",
    "        L_prev_f_h = L_cur_f_h\n",
    "\n",
    "    assert r1 != -1 and r2 != -1, 'Error! (3)'\n",
    "    \n",
    "    print('A(s):')\n",
    "    A = Matrix([[A00, A01],[A10, A11]])\n",
    "    display(A)\n",
    "    \n",
    "    print(\"Determinant of A(s):\")\n",
    "    display(A.det())\n",
    "    \n",
    "    print(\"Inverse of A(s):\")\n",
    "    display(Inverse(A))\n",
    "    \n",
    "    iA = Inverse(A)\n",
    "    u = -iA * Matrix([L_r1_f_h1, L_r2_f_h2]) + iA * Matrix([v1, v2])\n",
    "    \n",
    "    return r1, r2, u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "u appeared! (1)\n",
      "u appeared! (2)\n",
      "A(s):\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}\\cos{\\left (\\theta \\right )} & - \\epsilon \\sin{\\left (\\theta \\right )}\\\\\\sin{\\left (\\theta \\right )} & \\epsilon \\cos{\\left (\\theta \\right )}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡cos(θ)  -ε⋅sin(θ)⎤\n",
       "⎢                 ⎥\n",
       "⎣sin(θ)  ε⋅cos(θ) ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Determinant of A(s):\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\epsilon \\sin^{2}{\\left (\\theta \\right )} + \\epsilon \\cos^{2}{\\left (\\theta \\right )}$$"
      ],
      "text/plain": [
       "     2           2   \n",
       "ε⋅sin (θ) + ε⋅cos (θ)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inverse of A(s):\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left(\\left[\\begin{matrix}\\cos{\\left (\\theta \\right )} & - \\epsilon \\sin{\\left (\\theta \\right )}\\\\\\sin{\\left (\\theta \\right )} & \\epsilon \\cos{\\left (\\theta \\right )}\\end{matrix}\\right]\\right)^{-1}$$"
      ],
      "text/plain": [
       "                     -1\n",
       "⎛⎡cos(θ)  -ε⋅sin(θ)⎤⎞  \n",
       "⎜⎢                 ⎥⎟  \n",
       "⎝⎣sin(θ)  ε⋅cos(θ) ⎦⎠  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vector relative degree is: (2, 2)\n"
     ]
    }
   ],
   "source": [
    "r1, r2, u = find_vector_relative_degree(f, g1, g2, s, h1(s), h2(s))\n",
    "print 'Vector relative degree is: ' + str((r1, r2))\n",
    "\n",
    "# Note to self: Didn't bother with putting in normal form. Why?\n",
    "# Vector rel. deg. was needed to compute the fbk linearzing control law.\n",
    "# Should I have put into normal form?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion\n",
    "Since the above $A$ matrix is nonsingular, we'll derive the feedback linearizing control law per EE 222 lecture notes 18 page 13."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 2 continued\n",
    "#### Assume that the zero dynamics of the aircraft correspond to the aircraft flying at a constant altitude and constant horizontal velocity x' = v with v constant (trim). Derive the zero dynamics of the system. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Zero dynamics in symbolic form:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}0\\\\v\\\\0\\\\0\\\\- \\frac{a_{D} v^{2}}{\\epsilon} \\sin{\\left (\\theta \\right )} - \\frac{1}{\\epsilon} \\left(a_{L} v^{2} \\left(c \\theta + 1\\right) - 1\\right) \\cos{\\left (\\theta \\right )}\\\\\\theta_{p}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡                       0                       ⎤\n",
       "⎢                                               ⎥\n",
       "⎢                       v                       ⎥\n",
       "⎢                                               ⎥\n",
       "⎢                       0                       ⎥\n",
       "⎢                                               ⎥\n",
       "⎢                       0                       ⎥\n",
       "⎢                                               ⎥\n",
       "⎢       2          ⎛     2              ⎞       ⎥\n",
       "⎢  a_D⋅v ⋅sin(θ)   ⎝a_L⋅v ⋅(c⋅θ + 1) - 1⎠⋅cos(θ)⎥\n",
       "⎢- ───────────── - ─────────────────────────────⎥\n",
       "⎢        ε                       ε              ⎥\n",
       "⎢                                               ⎥\n",
       "⎣                      θ_p                      ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute leftover dynamics after setting variables to zero dynamics values below:\n",
    "v = Symbol('v') # constant horizontal velocity\n",
    "alt = Symbol('alt') # constant vertical altitude\n",
    "\n",
    "# Set aux input v1,v2 to zero since we're looking at zero dynamics (but not u=0).\n",
    "# (First applied fbk linearizing control law, then set v1,v2 to zero.)\n",
    "# (Doing a whole bunch of substitutions to see what's leftover.)\n",
    "# (Vector relative degree (2, 2) so we expect 6 - 4 = 2 dimensional zero dynamics.)\n",
    "\n",
    "substitutions = {x_2p : 0., x_p : v,\n",
    "                 z_2p : 0., z_p : 0., z : alt,\n",
    "                 v1 : 0, v2 : 0} \n",
    "u_subbed = u.subs(substitutions)\n",
    "substitutions = {x_2p : 0., x_p : v,\n",
    "                 z_2p : 0., z_p : 0., z : alt,\n",
    "                 v1 : 0, v2 : 0,\n",
    "                 u1 : u_subbed[0], u2 : u_subbed[1]}\n",
    "\n",
    "print 'Zero dynamics in symbolic form:'\n",
    "leftover = s_p.subs(substitutions)\n",
    "leftover = trigsimp(leftover) # essential!!!\n",
    "display(leftover)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Full 6 dimensional system dynamics evaluated for given parameters:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}0\\\\0.17\\\\0\\\\0\\\\- 10.0 \\left(5.202 \\theta - 0.133\\right) \\cos{\\left (\\theta \\right )} - 0.578 \\sin{\\left (\\theta \\right )}\\\\\\theta_{p}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡                      0                      ⎤\n",
       "⎢                                             ⎥\n",
       "⎢                    0.17                     ⎥\n",
       "⎢                                             ⎥\n",
       "⎢                      0                      ⎥\n",
       "⎢                                             ⎥\n",
       "⎢                      0                      ⎥\n",
       "⎢                                             ⎥\n",
       "⎢-10.0⋅(5.202⋅θ - 0.133)⋅cos(θ) - 0.578⋅sin(θ)⎥\n",
       "⎢                                             ⎥\n",
       "⎣                     θ_p                     ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 dimensional zero dynamics:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}\\theta_{p}\\\\- 10.0 \\left(5.202 \\theta - 0.133\\right) \\cos{\\left (\\theta \\right )} - 0.578 \\sin{\\left (\\theta \\right )}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡                     θ_p                     ⎤\n",
       "⎢                                             ⎥\n",
       "⎣-10.0⋅(5.202⋅θ - 0.133)⋅cos(θ) - 0.578⋅sin(θ)⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "substitutions = {epsilon : 0.1, v : 0.17, a_D : 2., a_L : 30., c : 6.}\n",
    "leftover2 = leftover.subs(substitutions)\n",
    "print('Full 6 dimensional system dynamics evaluated for given parameters:')\n",
    "display(leftover2)\n",
    "\n",
    "# As expected, two dimensional dynamics leftover (theta , theta').\n",
    "lo = Matrix([leftover2[5], leftover2[4]])\n",
    "print('2 dimensional zero dynamics:')\n",
    "display(lo)\n",
    "\n",
    "# Lambda-fied vector field (fast!)\n",
    "lf = lambdify((theta, theta_p), lo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Plot zero dynamics phase portrait\n",
    "from scipy.integrate import odeint\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.ticker as tck\n",
    "\n",
    "def leftover_dynamics_DFE(x, t=0.0):\n",
    "    theta1 = x[0]\n",
    "    theta2 = x[1]\n",
    "    return lf(theta1, theta2).squeeze() # results in change from a 2x1 matrix to 2 dim vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OWYNTV14ZUHBq6p9TfQan/nnonxIVnAKICIvIts1DvhvC2CVjsz/4nXe8NjOv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\nVPzxxx+c+/dfcKAuZt3sERjdarU6G6eCDe0D18x9+x/fT53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IUYbHuC/8p6FsI0a40lk2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+MzJKlq2ovnD3Qoa2iSyi89837WbrijY4HIpEUQk1Bg9P17M1QXmwnuNrEIdh8Ga6dXukIoYm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\nTjh8GEixBZ5RozIca1G/RW7l7CapapSpQZNr3J9s63AYYmO3pdPDd6VOTo3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H6Lphg8dr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      "text/plain": [
       "<matplotlib.figure.Figure at 0x107d0d610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Simulation of zero dynamics.\n",
    "\n",
    "t = np.linspace(0, 20, 1000)\n",
    "n = 24\n",
    "random_initial_conditions = np.random.uniform(low=-pi, high=pi, size=(n, 2))\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(20,10))\n",
    "ax.xaxis.set_major_formatter(tck.FormatStrFormatter('%g $\\pi$'))\n",
    "ax.xaxis.set_major_locator(tck.MultipleLocator(base=1.0))\n",
    "ax.yaxis.set_major_formatter(tck.FormatStrFormatter('%g $\\pi$'))\n",
    "ax.yaxis.set_major_locator(tck.MultipleLocator(base=1.0))\n",
    "ax.set_xlabel('$\\Theta $', fontsize=24)\n",
    "ax.set_ylabel('$\\Theta$\\'', fontsize=24)\n",
    "ax.grid()\n",
    "\n",
    "for ic in random_initial_conditions:\n",
    "    trajectory = odeint(leftover_dynamics_DFE, ic, t) / pi # divide values by pi because of axis formatting\n",
    "    ax.plot(trajectory[:,0], trajectory[:,1], lw=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion\n",
    "#### Can you predict from the zero dynamics what would actually happen if you used this control law for tracking for $\\epsilon$ values greater than 0?\n",
    "The zero dynamics suggest that the airplane would still maintain a constant altitude and horizontal velocity while tipping its nose up and down. For some initial conditions, the oscillations are of such large amplitude that the plane may break (and even loop around), which is not predicted by the zero dynamics.\n",
    "\n",
    "#### Can you suggest an alternative approximate control law (no need to derive it in functional form, just suggest how you would derive it)?\n",
    "A PID controller that compensates based on deviations from and accumulations of error (away from constant altitude and horizontal velocity)."
   ]
  }
 ],
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   "language": "python",
   "name": "python2"
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   "codemirror_mode": {
    "name": "ipython",
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