{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Especificações para projeto de compensadores SISO" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib widget\n", "\n", "import numpy as np\n", "import control as ct" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Paleta de cores\n", "cp = {\n", " 'red': (1.0, 0.349, 0.369, 1.0),\n", " 'green': (0.541, 0.788, 0.149, 1.0),\n", " 'blue': (0.098, 0.510, 0.769, 1.0),\n", " 'lred': (1.0, 0.588, 0.6, 1.0),\n", " 'lgreen': (0.722, 0.894, 0.443, 1.0),\n", " 'lblue': (0.369, 0.706, 0.918, 1.0),\n", " 'orange': (1.0, 0.506, 0.227, 1.0),\n", " 'yellow': (1.0, 0.792, 0.227, 1.0),\n", " 'pink': (1.0, 0.349, 0.611, 1.0),\n", " 'purple': (0.416, 0.298, 0.576, 1.0),\n", " 'turquoise': (0.098, 0.761, 0.769, 1.0),\n", " 'brown': (0.576, 0.380, 0.298, 1.0)\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1. Especificações de polos dominantes para projeto via lugar das raízes\n", "\n", "#### 1.1. Aproximação por sistema de primeira ordem em malha fechada\n", "\n", "Caso o *sistema em malha fechada* possua um único polo dominante localizado em $\\bar p_1 = \\displaystyle - \\frac{1}{\\tau}$, seu comportamento pode ser aproximado por uma função de transferência equivalente de *primeira ordem*:\n", "$$\n", "T(s) \\approx \\frac{1}{1 + \\tau s}\n", "$$\n", "em que $\\tau$ é a *constante de tempo*. \n", "\n", "Em termos de resposta a degrau, $5 \\tau$ deve ser o tempo necessário para que a resposta $y(t)$ se aproxime com erro inferior a 1% da referência escolhida." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "abce38eb9cf34986bc6c7bd75b8a6753", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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Aproximação por sistema de segunda ordem em malha fechada\n", "\n", "Caso o *sistema em malha fechada* possua apenas um par de polos complexos conjugados dominantes\n", "$\n", "\\bar p_{1,2} = - \\sigma \\pm \\mathsf{j} \\omega\n", "$, \n", "seu comportamento *em malha fechada* pode ser aproximado por uma função de transferência equivalente de *segunda ordem*:\n", "$$\n", "T(s) \\approx \\frac{\\omega_n^2}{s^2 + 2 \\zeta \\omega_n s + \\omega_n^2}\n", "$$\n", "em que $\\omega_n = \\displaystyle \\sqrt{\\sigma^2 + \\omega^2}$ é a *frequência natural* (não-amortecida) e $\\zeta = \\displaystyle \\frac{\\sigma}{\\omega_n}$ é a *razão de amortecimento*." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "1d83337aa0ec420abd0f5d1a52d8f1e6", "version_major": 2, "version_minor": 0 }, "image/png": 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\n", " \n", "
\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "T_2 = ct.tf([1], [1, np.sqrt(2), 1])\n", "t_2, y_2 = ct.step_response(T_2)\n", "\n", "fig, (state) = plt.subplots(\n", " 1, 1, figsize=(5, 4), sharex=True)\n", "\n", "state.plot(t_2, np.ones(len(t_2)),\n", " color=cp['yellow'], label=r'$r(t)$', linewidth=2)\n", "# state.plot(t, y_PI, color=cp['green'], label='PI', linewidth=2)\n", "state.plot(t_2, y_2, color=cp['red'], label=r'$y(t)$', linewidth=2)\n", "state.set_xlabel(r'$t$')\n", "state.legend()\n", "state.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A resposta de um sistema de segunda ordem a uma referência degrau pode ser caracterizada por:\n", "\n", "**(a) tempo de subida ($t_r$)** – tempo requerido para que a resposta a um degrau unitário suba de $y = 0.1$ a $y = 0.9$:\n", "$$\n", "t_r \\approx \\frac{1 + 1.1 \\zeta + 1.4 \\zeta^2}{\\omega_n}\n", "$$\n", "\n", "Para um sistema linear em geral (não necessariamente de segunda ordem), o tempo de subida (*rise time*) é inversamente proprocional à largura de banda (*bandwidth*).\n", "\n", "**(b) tempo de acomodação ($t_s$)** – tempo requerido para que a resposta a um degrau unitário atinja e permaneça em um intervalo $1 - f < y < 1 + f$ com $f$ sendo uma fração, cujos valores típicos são $f = 0.05$ (5%) ou $f = 0.02$ (2%).\n", "$$\n", " t_s = - \\frac{1}{\\zeta \\omega_n} \\ln \\left(f \\sqrt{1-\\zeta^2} \\right)\n", "$$\n", "\n", "Em particular, para $\\zeta \\ll 1$ e $f = 0.02$, uma boa aproximação consiste em tomar:\n", "$$\n", "t_s \\approx \\frac{4}{\\zeta \\omega_n}\n", "$$\n", "\n", "\n", "**(c) tempo de pico ($t_p$)** – tempo necessário para que a resposta a um degrau unitário atinja seu valor máximo.\n", "$$\n", " t_p = \\frac{\\pi}{\\omega_n \\sqrt{1 - \\zeta^2}}\n", "$$\n", "\n", "**(d) sobressinal ou *overshoot* ($M_p$)** – quanto o valor máximo observado para a saída excede o degrau unitário\n", "$$\n", " M_p = y(t_p) - 1 = \\exp \\left( {\\frac{-\\zeta \\pi}{\\sqrt{1 - \\zeta^2}}} \\right)\n", "$$\n", "\n", "A partir desta equação, podemos expressar a *razão de amortecimento* como:\n", "$$\n", " \\zeta = \\frac{-\\ln \\left( M_{p} \\right)}{\\sqrt{\\pi^2 + \\ln^2 \\left( M_{p} \\right)}}\n", "$$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "1bc0dcf7f896492381cc45a060c57fbe", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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\n", " Figure\n", "
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\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "ζ = np.linspace(0, 0.99, 100)\n", "M_p = np.exp(-ζ * np.pi/np.sqrt(1 - ζ**2))\n", "plt.plot(ζ, M_p, color=cp['blue'], linewidth=2)\n", "plt.xlabel(r'$\\zeta$')\n", "plt.ylabel(r'$M_p$')\n", "plt.title('Overshoot vs. razão de amortecimento (sist. de segunda ordem)')\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Retornando à função de transferência do tipo $m=1$ do exemplo A-6-19 do livro: \n", "> OGATA, K. (2001) Modern Control Engineering, 4th ed., Pearson.\n", "\n", "que visa representar um *piloto automático para o modo longitudinal (pitch) de um avião*:\n", "\n", "\\begin{align*}\n", " L(s) = G(s)H(s) = \\frac{K(s+a)}{s(s-b)(s^2 + 2\\zeta \\omega_n s + \\omega_n^2)} = K \\frac{N(s)}{D(s)}\n", "\\end{align*}\n", "\n", "Adotando $a=b=1$, $\\zeta=0.5$ e $\\omega_n=4$:\n", "\n", "\\begin{align*}\n", " L(s) = \\frac{K(s+1)}{s(s-1)(s^2 + 4s + 16)}\n", "\\end{align*}\n", "\n", "tem-se um zero em $z_1 = -1$ e quatro polos em $p_0=0$ (multiplicidade algébrica 1), $p_1=+1$ e $p_{2,3}=-2 \\pm 2\\sqrt{3} \\mathsf{j}$.\n", "\n", "Vimos que, nestas condições, a planta é *condicionalmente estável*, ou seja, é possível ter um comportamento estável em malha fechada com controlador *proporcional* ($K$) se, e somente se: $$23.32 < K < 35.68$$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{s + 1}{s^4 + 3 s^3 + 12 s^2 - 16 s}$$" ], "text/plain": [ "TransferFunction(array([1., 1.]), array([ 1., 3., 12., -16., 0.]))" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zeros = np.array([-1])\n", "poles = np.array([0, +1, -2 + (2j * np.sqrt(3)), -2 - (2j * np.sqrt(3))])\n", "\n", "N = ct.tf(np.poly(zeros), [1])\n", "D = ct.tf(np.poly(poles), [1])\n", "\n", "L_0 = N/D\n", "L_0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Também projetamos para este sistema, via *método do lugar das raízes* um compensador PID:\n", "$$\n", "G_c(s) = K_c \\left( 1+ \\frac{1}{\\tau_i s} + \\tau_d s \\right)\n", "$$\n", "com: $\\tau_i = 12$ s, $\\tau_d = 3.6667$ s e $K_c = 15$. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{55 s^2 + 15 s + 1.25}{s}$$" ], "text/plain": [ "TransferFunction(array([55.0005, 15. , 1.25 ]), array([1, 0]))" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "τ_i = 12.0\n", "τ_d = 3.6667\n", "G_c_PID = 15 * ct.tf([τ_d, 1, 1/τ_i], [1, 0])\n", "G_c_PID" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Verifiquemos então a resposta a degrau do sistema em malha fechada considerando a introdução do compensador PID no canal direto:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{55 s^3 + 70 s^2 + 16.25 s + 1.25}{s^5 + 3 s^4 + 12 s^3 - 16 s^2}$$" ], "text/plain": [ "TransferFunction(array([55.0005, 70.0005, 16.25 , 1.25 ]), array([ 1., 3., 12., -16., 0., 0.]))" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Malha aberta\n", "L_c = G_c_PID * L_0\n", "L_c" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{55 s^3 + 70 s^2 + 16.25 s + 1.25}{s^5 + 3 s^4 + 67 s^3 + 54 s^2 + 16.25 s + 1.25}$$" ], "text/plain": [ "TransferFunction(array([55.0005, 70.0005, 16.25 , 1.25 ]), array([ 1. , 3. , 67.0005, 54.0005, 16.25 , 1.25 ]))" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Malha fechada\n", "T_c = ct.feedback(L_c)\n", "T_c" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "e1c8bd2640b944d089fd70d903b54ec7", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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Especificações de margem de estabilidade para projeto via diagrama de Bode\n", "\n", "#### 2.1. Compensador de avanço de fase\n", "$$\n", "G_c(s) = \\frac{1 + \\tau_c s}{1 + \\alpha \\tau_c s} = \\frac{1}{\\alpha} \\frac{s + \\frac{1}{\\tau_c}}{s + \\frac{1}{\\alpha \\tau_c}}, \\quad 0 < \\alpha < 1\n", "$$\n", "\n", "Passo-a-passo do projeto:\n", "\n", "**PASSO 1 –** determinar a margem de fase do sistema não-compensado\n", "\n", "Voltando ao exemplo, consideremos como sistema não-compensando a função de transferência de malha aberta original com ganho proporcional $K = 32$, o que garante um $\\displaystyle K_1 = \\lim_{s \\to 0} s L(s) = -2$." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "e0c0cc7cbca14450874e8f2dcb114b6c", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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{}, "outputs": [ { "data": { "text/plain": [ "0.09941332626855381" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "φ_m = 55 * np.pi/180\n", "α = (1 - np.sin(φ_m))/(1 + np.sin(φ_m))\n", "α" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**PASSO 3 –** Determine a frequência $ω_m$ no gráfico do sistema não-compensado, onde se observa uma magnitude de $\\sqrt{\\alpha}$ (ou $- 10 |\\log_{10} \\alpha| \\ \\text{dB}$)." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.3152987888789835, -10.025553949087868)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(np.sqrt(α), 10*np.log10(α))" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4.860292686423012" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# obtendo o valor de ω_m por interpolação linear\n", "i_m = np.where((mag[:-1] > np.sqrt(α)) & (mag[1:] < np.sqrt(α)))[0][0]\n", "ω_m = omega[i_m] + (np.sqrt(α) - mag[i_m]) * (omega[i_m+1] - omega[i_m]) / (mag[i_m+1] - mag[i_m])\n", "ω_m" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**PASSO 4 –** Calcule $\\tau_c$ e conclua o projeto do compensador." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.6525522241125327" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "τ_c = 1/(ω_m * np.sqrt(α))\n", "τ_c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### ANÁLISE DO COMPENSADOR PROJETADO\n", "\n", "Substituindo os valores obtidos para $\\alpha$ e $\\tau_c$ a seguinte expressão para o compensador de avanço de fase $G_c(s)$:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{0.6526 s + 1}{0.06487 s + 1}$$" ], "text/plain": [ "TransferFunction(array([0.65255222, 1. ]), array([0.06487239, 1. ]))" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G_c_lead = ct.tf([τ_c, 1], [α * τ_c, 1])\n", "G_c_lead" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Abaixo, o diagrama de Bode de $G_c(s)$:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "0ed02f973fda433da1e253ac34da8402", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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\n", " Figure\n", "
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\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "mag_lead, phase_lead, omega_lead = ct.bode_plot(\n", " [G_c_lead], color=cp['orange'], linewidth=2.5, dB=True, omega_limits=(1e-2, 1000), initial_phase=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Considerando a presença do compensador, a nova função de transferência de malha aberta se torna:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{20.88 s^2 + 52.88 s + 32}{0.06487 s^5 + 1.195 s^4 + 3.778 s^3 + 10.96 s^2 - 16 s}$$" ], "text/plain": [ "TransferFunction(array([20.88167117, 52.88167117, 32. ]), array([ 0.06487239, 1.19461716, 3.77846865, 10.96204181,\n", " -16. , 0. ]))" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "L_1 = 32 * G_c_lead * L_0\n", "L_1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A partir do diagrama de Bode, verificamos os novos valores obtidos para margem de ganho e margem de fase:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "cbb22df0c52042e79424956d8c77cf71", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "mag_1, phase_1, omega_1 = ct.bode_plot(\n", " L_1, color=cp['blue'], linewidth=2.5, dB=True, margins=True, omega_limits=(1e-1, 10), initial_phase=-270)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Abaixo analisamos a função de trasnferência em malha fechada $T_1(s)$, por meio de seu diagrama de Bode, largura de banda e resposta a degrau:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{20.88 s^2 + 52.88 s + 32}{0.06487 s^5 + 1.195 s^4 + 3.778 s^3 + 31.84 s^2 + 36.88 s + 32}$$" ], "text/plain": [ "TransferFunction(array([20.88167117, 52.88167117, 32. ]), array([ 0.06487239, 1.19461716, 3.77846865, 31.84371298, 36.88167117,\n", " 32. ]))" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_1 = ct.feedback(L_1)\n", "T_1" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "67882f4b148841169dec234eeed5c78d", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# diagrama de Bode\n", "plt.figure()\n", "mag_T1, phase_T1, omega_T1 = ct.bode_plot(\n", " [T_1], color=cp['green'], linewidth=2.5, dB=True, omega_limits=(1e-2, 1000), initial_phase=0)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "7.181258019059842" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# largura de banda\n", "T_1.bandwidth()" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "f9f4114a27d74212b956ac0b3249df9c", "version_major": 2, "version_minor": 0 }, "image/png": 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", "text/html": [ "\n", "
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'Peak': 1.8597486415313942,\n", " 'PeakTime': 0.7501569229454528,\n", " 'SteadyStateValue': 1.0}" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ct.step_info(T_1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Podemos também avaliar a respectiva função de transferência de sensibilidade $S_1(s) = 1 - T_1(s)$:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{0.06487 s^5 + 1.195 s^4 + 3.778 s^3 + 10.96 s^2 - 16 s}{0.06487 s^5 + 1.195 s^4 + 3.778 s^3 + 31.84 s^2 + 36.88 s + 32}$$" ], "text/plain": [ "TransferFunction(array([ 0.06487239, 1.19461716, 3.77846865, 10.96204181,\n", " -16. , 0. ]), array([ 0.06487239, 1.19461716, 3.77846865, 31.84371298, 36.88167117,\n", " 32. ]))" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S_1 = 1 - T_1\n", "S_1" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, 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\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# diagrama de Bode\n", "plt.figure()\n", "mag_S1, phase_S1, omega_S1 = ct.bode_plot(\n", " [S_1], color=cp['red'], linewidth=2.5, dB=True, omega_limits=(1e-2, 1000), initial_phase=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2.2. Compensador de atraso de fase\n", "\n", "$$ G_g(s) = \\frac{1 + \\tau_g s}{1 + \\beta \\tau_g s} = \\frac{1}{\\beta} \\frac{s + \\frac{1}{\\tau_g}}{s + \\frac{1}{\\beta \\tau_g}}, \n", "\\quad \\beta >1\n", "$$\n", "\n", "Para o exemplo anterior observamos que a margem de fase ainda é pequena, pois o valor de $\\omega_c$ está acima da faixa de frequências em que se observa o maior valor de $180^\\circ + \\phase{L_1(\\mathsf{j} \\omega)}$. O compensador de atraso neste caso, vai atuar reduzindo o valor de $\\omega_c$, com o objetivo de colocá-lo nesta faixa de frequências, o que maximizaria o valor da margem de fase $\\text{PM} = 180^\\circ + \\phase{L_1(\\mathsf{j} \\omega_c)}$.\n", "\n", "**PASSO 1 –** Avaliar o diagrama de Bode da malha aberta ainda sem compensador de atraso:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "079cddd11f2a47349deb5539c07bd3f7", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "mag_1, phase_1, omega_1 = ct.bode_plot(\n", " L_1, color=cp['blue'], linewidth=2.5, dB=True, margins=True, omega_limits=(1e-1, 10), initial_phase=-270)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**PASSO 2 –** A partir da margem de fase desejada, admitindo uma margem de segurança (tipicamente $+5^\\circ$), encontre o valor da nova frequência de corte.\n", "\n", "Para o exemplo, admitamos que seja desejável uma margem de fase $\\text{PM} = 45^\\circ + 5^\\circ = 50^\\circ$." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.4866866541213115" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# obtendo o valor de ω_c por interpolação linear\n", "i_c = np.where((phase_1[:-1] > (-1 + 50/180)*np.pi) & (phase_1[1:] < (-1 + 50/180)*np.pi))[0][0]\n", "ω_c = omega_1[i_c] + ((-1 + 50/180)*np.pi - phase_1[i_c]) * (omega_1[i_c+1] - omega_1[i_c]) / (phase_1[i_c+1] - phase_1[i_c])\n", "ω_c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**PASSO 3 –** Obter $\\tau_g$ considerando que o zero do compensador esteja, em módulo, uma década abaixo de $\\omega_c$, ou seja:\n", "$$\\frac{1}{\\tau_g} = 0.1 \\omega_c$$" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4.021415397644288" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "τ_g = 1 / (0.1 * ω_c)\n", "τ_g" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**PASSO 4 –** Obter $\\beta$ considerando que na freqûencia de corte $\\omega_c$, $|G_g(\\omega_c) L_1(\\omega_c)| = 1$, ou seja:\n", "$$\\left|\\frac{1}{\\beta} L_1(\\mathsf{j} \\omega_c) \\right| = 1\n", "\\quad \\Rightarrow \\quad \\beta = | L_1(\\mathsf{j} \\omega_c)|\n", "\\quad \\text{($20 \\log_{10} \\beta = 20 \\log_{10} | L_1(\\mathsf{j} \\omega_c)|$)}\n", "$$" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.7329357994898436" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "β = mag_1[i_c]\n", "β" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### ANÁLISE DO COMPENSADOR PROJETADO\n", "\n", "Considerando os valores de $\\beta$ e $\\tau_g$ calculados, obtém-se o seguinte compensador de atraso $G_g(s)$:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{4.021 s + 1}{6.969 s + 1}$$" ], "text/plain": [ "TransferFunction(array([4.0214154, 1. ]), array([6.96885471, 1. ]))" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G_g = ct.tf([τ_g, 1], [β * τ_g, 1])\n", "G_g" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Abaixo, o diagrama de Bode de $G_g(s)$:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "788559fea42e40699aa129a67df65096", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "mag_lead, phase_lead, omega_lead = ct.bode_plot(\n", " [G_g], color=cp['pink'], linewidth=2.5, dB=True, omega_limits=(1e-3, 100), initial_phase=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A nova função de transferência de malha aberta $L_2(s)$, considerando agora a associação de ambos os compensadores projetados, se torna:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{83.97 s^3 + 233.5 s^2 + 181.6 s + 32}{0.4521 s^6 + 8.39 s^5 + 27.53 s^4 + 80.17 s^3 - 100.5 s^2 - 16 s}$$" ], "text/plain": [ "TransferFunction(array([ 83.97387398, 233.54083787, 181.5669639 , 32. ]), array([ 0.45208624, 8.38998582, 27.52621617, 80.17134528,\n", " -100.53963351, -16. , 0. ]))" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "L_2 = G_g * L_1\n", "L_2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Abaixo, o diagrama de Bode de $L_2(s)$, mostrando as margens de ganho e de fase obtidas ao final do projeto:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "f2bf034879e14f37812eb1c61fcfe70c", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "mag_2, phase_2, omega_2 = ct.bode_plot(\n", " L_2, color=cp['brown'], linewidth=2.5, dB=True, margins=True, omega_limits=(1e-1, 10), initial_phase=-270)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Abaixo analisamos a função de trasnferência em malha fechada $T_2(s)$, por meio de seu diagrama de Bode, largura de banda e resposta a degrau:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{83.97 s^3 + 233.5 s^2 + 181.6 s + 32}{0.4521 s^6 + 8.39 s^5 + 27.53 s^4 + 164.1 s^3 + 133 s^2 + 165.6 s + 32}$$" ], "text/plain": [ "TransferFunction(array([ 83.97387398, 233.54083787, 181.5669639 , 32. ]), array([ 0.45208624, 8.38998582, 27.52621617, 164.14521926,\n", " 133.00120436, 165.5669639 , 32. ]))" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_2 = ct.feedback(L_2)\n", "T_2" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "b0517ad7dc0944d1be75e13b3ddec455", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# diagrama de Bode\n", "plt.figure()\n", "mag_T2, phase_T2, omega_T2 = ct.bode_plot(\n", " [T_2], color=cp['green'], linewidth=2.5, dB=True, omega_limits=(1e-2, 1000), initial_phase=0)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.709063584002731" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# largura de banda\n", "T_2.bandwidth()" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "fd7bb54596ef4b2fbafa16035e6eeaf2", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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'Peak': 1.7576703284347084,\n", " 'PeakTime': 1.0374202421891288,\n", " 'SteadyStateValue': 1.0}" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ct.step_info(T_2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finalmente, para a função de sensibilidade $S_2(s) = 1 - T_2(s)$:" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{0.4521 s^6 + 8.39 s^5 + 27.53 s^4 + 80.17 s^3 - 100.5 s^2 - 16 s}{0.4521 s^6 + 8.39 s^5 + 27.53 s^4 + 164.1 s^3 + 133 s^2 + 165.6 s + 32}$$" ], "text/plain": [ "TransferFunction(array([ 0.45208624, 8.38998582, 27.52621617, 80.17134528,\n", " -100.53963351, -16. , 0. ]), array([ 0.45208624, 8.38998582, 27.52621617, 164.14521926,\n", " 133.00120436, 165.5669639 , 32. ]))" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S_2 = 1 - T_2\n", "S_2" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "35294ff968234c979045ac1ca4394b37", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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