nyquist.ipynb

{
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  {
   "cell_type": "code",
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    {
     "output_type": "error",
     "ename": "IndentationError",
     "evalue": "unexpected indent (<ipython-input-6-c3ec908c3d5c>, line 5)",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-6-c3ec908c3d5c>\"\u001b[1;36m, line \u001b[1;32m5\u001b[0m\n\u001b[1;33m    diff\u001b[0m\n\u001b[1;37m    ^\u001b[0m\n\u001b[1;31mIndentationError\u001b[0m\u001b[1;31m:\u001b[0m unexpected indent\n"
     ]
    }
   ],
   "source": [
    "#%matplotlib widget\n",
    "from sympy import Symbol, Basic, denom, numer, plot as splot, Eq, Or, plot_implicit, \\\n",
    "                  latex, Rational as R, plot_parametric, I, atan, exp, arg, pi, conjugate, \\\n",
    "                  Piecewise, And, sin, cos, Or, Max, re, im, lambdify, Expr, solve, oo, tan, limit,\n",
    "                  diff\n",
    "from sympy.plotting.plot import plot3d_parametric_surface, plot_contour\n",
    "from functools import partial\n",
    "from IPython.display import display\n",
    "from sympy.abc import s, z\n",
    "from utils import f2zpk, zpk2f, f2nd, splot_multiple, reim\n",
    "from typeguard import typechecked\n",
    "smplot = partial(typechecked(splot_multiple), plotf=splot, random_colors=True)\n",
    "pmplot = partial(typechecked(splot_multiple), plotf=plot_parametric, random_colors=True)\n",
    "w = Symbol(\"omega\", real=True)\n",
    "k = Symbol(\"K\", real=True)\n",
    "# Conexión a lazo cerrado en sustracción\n",
    "def cls_connect(h: Basic, g: Basic):\n",
    "    return h / (1+g*h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
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    {
     "output_type": "display_data",
     "data": {
      "text/plain": "K*(s + 3)/(s*(s - 1)) + 1",
      "text/latex": "$\\displaystyle \\frac{K \\left(s + 3\\right)}{s \\left(s - 1\\right)} + 1$"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "(cos(omega), sin(omega))"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "(1 - exp(-sqrt(sin(omega)**2 + cos(omega)**2 + 6*cos(omega) + 9)/(sqrt(sin(omega)**2 + cos(omega)**2)*sqrt(sin(omega)**2 + cos(omega)**2 - 2*cos(omega) + 1))))*sqrt(sin(omega)**2 + cos(omega)**2)*(I*sin(omega) + cos(omega) + 3)*sqrt(sin(omega)**2 + cos(omega)**2 - 2*cos(omega) + 1)/((I*sin(omega) + cos(omega))*(I*sin(omega) + cos(omega) - 1)*sqrt(sin(omega)**2 + cos(omega)**2 + 6*cos(omega) + 9))",
      "text/latex": "$\\displaystyle \\frac{\\left(1 - e^{- \\frac{\\sqrt{\\sin^{2}{\\left(\\omega \\right)} + \\cos^{2}{\\left(\\omega \\right)} + 6 \\cos{\\left(\\omega \\right)} + 9}}{\\sqrt{\\sin^{2}{\\left(\\omega \\right)} + \\cos^{2}{\\left(\\omega \\right)}} \\sqrt{\\sin^{2}{\\left(\\omega \\right)} + \\cos^{2}{\\left(\\omega \\right)} - 2 \\cos{\\left(\\omega \\right)} + 1}}}\\right) \\sqrt{\\sin^{2}{\\left(\\omega \\right)} + \\cos^{2}{\\left(\\omega \\right)}} \\left(i \\sin{\\left(\\omega \\right)} + \\cos{\\left(\\omega \\right)} + 3\\right) \\sqrt{\\sin^{2}{\\left(\\omega \\right)} + \\cos^{2}{\\left(\\omega \\right)} - 2 \\cos{\\left(\\omega \\right)} + 1}}{\\left(i \\sin{\\left(\\omega \\right)} + \\cos{\\left(\\omega \\right)}\\right) \\left(i \\sin{\\left(\\omega \\right)} + \\cos{\\left(\\omega \\right)} - 1\\right) \\sqrt{\\sin^{2}{\\left(\\omega \\right)} + \\cos^{2}{\\left(\\omega \\right)} + 6 \\cos{\\left(\\omega \\right)} + 9}}$"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "K*(-sin(omega)*Heaviside(cos(omega)) + I*cos(omega))/((I*sin(omega) + Max(0, cos(omega)))*(r*(I*sin(omega) + Max(0, cos(omega))) - 1)) - K*(r*(I*sin(omega) + Max(0, cos(omega))) + 3)*(-sin(omega)*Heaviside(cos(omega)) + I*cos(omega))/((I*sin(omega) + Max(0, cos(omega)))*(r*(I*sin(omega) + Max(0, cos(omega))) - 1)**2) + K*(r*(I*sin(omega) + Max(0, cos(omega))) + 3)*(sin(omega)*Heaviside(cos(omega)) - I*cos(omega))/(r*(I*sin(omega) + Max(0, cos(omega)))**2*(r*(I*sin(omega) + Max(0, cos(omega))) - 1))",
      "text/latex": "$\\displaystyle \\frac{K \\left(- \\sin{\\left(\\omega \\right)} \\theta\\left(\\cos{\\left(\\omega \\right)}\\right) + i \\cos{\\left(\\omega \\right)}\\right)}{\\left(i \\sin{\\left(\\omega \\right)} + \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right)\\right) \\left(r \\left(i \\sin{\\left(\\omega \\right)} + \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right)\\right) - 1\\right)} - \\frac{K \\left(r \\left(i \\sin{\\left(\\omega \\right)} + \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right)\\right) + 3\\right) \\left(- \\sin{\\left(\\omega \\right)} \\theta\\left(\\cos{\\left(\\omega \\right)}\\right) + i \\cos{\\left(\\omega \\right)}\\right)}{\\left(i \\sin{\\left(\\omega \\right)} + \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right)\\right) \\left(r \\left(i \\sin{\\left(\\omega \\right)} + \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right)\\right) - 1\\right)^{2}} + \\frac{K \\left(r \\left(i \\sin{\\left(\\omega \\right)} + \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right)\\right) + 3\\right) \\left(\\sin{\\left(\\omega \\right)} \\theta\\left(\\cos{\\left(\\omega \\right)}\\right) - i \\cos{\\left(\\omega \\right)}\\right)}{r \\left(i \\sin{\\left(\\omega \\right)} + \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right)\\right)^{2} \\left(r \\left(i \\sin{\\left(\\omega \\right)} + \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right)\\right) - 1\\right)}$"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "(1 - exp(-sqrt(r**2*sin(omega)**2 + r**2*Max(0, cos(omega))**2 + 6*r*Max(0, cos(omega)) + 9)/(r*sqrt(sin(omega)**2 + Max(0, cos(omega))**2)*sqrt(r**2*sin(omega)**2 + r**2*Max(0, cos(omega))**2 - 2*r*Max(0, cos(omega)) + 1))))*(r*(I*sin(omega) + Max(0, cos(omega))) + 3)*sqrt(sin(omega)**2 + Max(0, cos(omega))**2)*sqrt(r**2*sin(omega)**2 + r**2*Max(0, cos(omega))**2 - 2*r*Max(0, cos(omega)) + 1)/((1 - exp(-1))*(I*sin(omega) + Max(0, cos(omega)))*(r*(I*sin(omega) + Max(0, cos(omega))) - 1)*sqrt(r**2*sin(omega)**2 + r**2*Max(0, cos(omega))**2 + 6*r*Max(0, cos(omega)) + 9))",
      "text/latex": "$\\displaystyle \\frac{\\left(1 - e^{- \\frac{\\sqrt{r^{2} \\sin^{2}{\\left(\\omega \\right)} + r^{2} \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right)^{2} + 6 r \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right) + 9}}{r \\sqrt{\\sin^{2}{\\left(\\omega \\right)} + \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right)^{2}} \\sqrt{r^{2} \\sin^{2}{\\left(\\omega \\right)} + r^{2} \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right)^{2} - 2 r \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right) + 1}}}\\right) \\left(r \\left(i \\sin{\\left(\\omega \\right)} + \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right)\\right) + 3\\right) \\sqrt{\\sin^{2}{\\left(\\omega \\right)} + \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right)^{2}} \\sqrt{r^{2} \\sin^{2}{\\left(\\omega \\right)} + r^{2} \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right)^{2} - 2 r \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right) + 1}}{\\left(1 - e^{-1}\\right) \\left(i \\sin{\\left(\\omega \\right)} + \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right)\\right) \\left(r \\left(i \\sin{\\left(\\omega \\right)} + \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right)\\right) - 1\\right) \\sqrt{r^{2} \\sin^{2}{\\left(\\omega \\right)} + r^{2} \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right)^{2} + 6 r \\max\\left(0, \\cos{\\left(\\omega \\right)}\\right) + 9}}$"
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "nan",
      "text/latex": "$\\displaystyle \\text{NaN}$"
     },
     "metadata": {}
    }
   ],
   "source": [
    "G_s = k\n",
    "H_s = (s+3)/(s*(s-1))\n",
    "D_s = 1 + G_s * H_s\n",
    "display(D_s)\n",
    "limit_abs_tan = lambda expr: 2/pi*atan(abs(expr))*exp(I*arg(expr))\n",
    "limit_abs_exp = lambda expr: (1-exp(-abs(expr)))*exp(I*arg(expr))\n",
    "limit_abs_exp = lambda expr: (1-exp(-abs(expr)))*expr/abs(expr)\n",
    "unlimit_abs_exp = lambda expr: (-ln(1-abs(expr)))*exp(I*arg(expr))\n",
    "\n",
    "rsemicircle=(Max(cos(w), 0)+I*sin(w))*1\n",
    "rsemicircle=(cos(w)+I*sin(w))\n",
    "display(reim(rsemicircle))\n",
    "display(limit_abs_exp((G_s * H_s).subs(s, rsemicircle)).subs(k, 1))\n",
    "\n",
    "#lambdified = tuple(map(lambda f: lambdify((w,), f, \"numpy\"),\n",
    "#    reim((G_s * H_s).subs(s, rsemicircle).subs(k, 1))))\n",
    "\n",
    "def nyquist_curve(tf: Expr, s: Symbol, w: Symbol, radius: Basic):\n",
    "    return tf.subs(s, (Max(cos(w), 0)+I*sin(w))*radius)\n",
    "\n",
    "def parametric_arrow(expr: Basic, param: Symbol):\n",
    "    df_dt = expr.diff(param)\n",
    "    return lambda t: (expr.subs(param, t), df_dt.subs(param, t))\n",
    "\n",
    "r = Symbol(\"r\", real=True, positive=True)\n",
    "curve = nyquist_curve(\n",
    "    limit_abs_exp((G_s * H_s).subs(k, 1))/limit_abs_exp(1),\n",
    "    s, w, r\n",
    ")\n",
    "\n",
    "display(nyquist_curve((G_s * H_s), s, w, r).diff(w))\n",
    "\n",
    "#plot_implicit(x > 0, x_var=x)\n",
    "\n",
    "#limit_abs_exp = lambda expr: expr\n",
    "#pmplot(\n",
    "#    #(reim(nyquist_curve(limit_abs_exp(s), s, w, 10)), {}),\n",
    "#    (reim(nyquist_curve(\n",
    "#        limit_abs_exp((G_s * H_s).subs(k, 1))/limit_abs_exp(1),\n",
    "#        s, w, 100)\n",
    "#    ), {}),\n",
    "#    (reim(nyquist_curve(\n",
    "#        limit_abs_exp((G_s * H_s).subs(k, 1).subs(s, s + .5))/limit_abs_exp(1),\n",
    "#        s, w, 100 - 1)\n",
    "#    ), {}),\n",
    "#    ((w, 0, 2*pi), None),\n",
    "#    ylim=(-2,2), xlim=(-2, 2)\n",
    "#)\n",
    "\n",
    "#%matplotlib inline\n",
    "#u = Symbol(\"u\", real=True, positive=True)\n",
    "#v = Symbol(\"v\", real=True)\n",
    "#plot3d_parametric_surface(\n",
    "#    (*reim((G_s * H_s).subs(k, 1).subs(s, tan(u)+I*tan(v))), tan(u), (u, 0, .9*pi/2), (v, -.9*pi/2, .9*pi/2)),\n",
    "#    #(*reim(tan(u)+I*tan(v)), tan(u), (u, 0, .9*pi/2), (v, -.9*pi/2, .9*pi/2))\n",
    "#)\n",
    "\n",
    "#def nyquist_area(tf: Expr, s: Symbol, z: Symbol):\n",
    "#    return Or(*(s_ + conjugate(s_) > 0 for s_ in solve(tf - z, s)))\n",
    "\n",
    "#x = Symbol('x', real=True)\n",
    "#y = Symbol('y', real=True)\n",
    "#display(nyquist_area((G_s * H_s).subs(k, 1), s, x+I*y))\n",
    "#func = lambdify((x, y), nyquist_area((G_s * H_s).subs(k, 1), s, x+I*y))\n",
    "#plot_implicit(func, x_var=x, y_var=y)\n",
    "\n",
    "#display(solve(Eq(limit_abs_exp(s), z), s))\n",
    "#pmplot(\n",
    "#    (reim(rsemicircle*10), {}),\n",
    "#    ((reim(limit_abs_exp((G_s * H_s).subs(s, rsemicircle)).subs(k, 1))+((w, -pi/2, pi/2),)), {}),\n",
    "#    legend=False, xlim=(-10, 10), ylim=(-10, 10)\n",
    "#)"
   ]
  },
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<sympy.plotting.plot.Plot at 0x1d9e3b3cd00>"
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "source": [
    "smplot(\n",
    "    *((s**k + R(\"1/3\"), {}) for k in range (-2, 3)),\n",
    "    legend=True, xlim=(-2, 2), ylim=(0, 3)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "interactive(children=(FloatSlider(value=1.0, description='x', max=3.0, min=-1.0), Output()), _dom_classes=('wi…",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "124afd7a9f5f4c9993e318d872fc0b2b"
      }
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "Text(value='Hello World!', disabled=True)",
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "44f488b7f28246018bdcff45ccc69467"
      }
     },
     "metadata": {}
    }
   ],
   "source": [
    "\n",
    "from ipywidgets import interact\n",
    "import ipywidgets as widgets\n",
    "interact(lambda x: print(x), x=1.0)\n",
    "widgets.Text(value='Hello World!', disabled=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.8.1 64-bit",
   "language": "python",
   "name": "python38164bit6787c890cc544958b8023ebdfd490516"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.1-final"
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 },
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}