{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 7"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"using ControlSystems\n",
"using Plots; gr()\n",
"using LinearAlgebra"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## オブザーバ"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"StateSpace{Continuous, Int64}\n",
"A = \n",
" 0 1\n",
" -4 5\n",
"B = \n",
" 0\n",
" 1\n",
"C = \n",
" 1 0\n",
"D = \n",
" 0\n",
"\n",
"Continuous-time state-space model\n",
"StateSpace{Continuous, Int64}\n",
"A = \n",
" 0 1\n",
" -4 5\n",
"B = \n",
" 0\n",
" 1\n",
"C = \n",
" 1 0\n",
" 0 1\n",
"D = \n",
" 0\n",
" 0\n",
"\n",
"Continuous-time state-space model\n"
]
}
],
"source": [
"A = [0 1; -4 5]\n",
"B = [0; 1]\n",
"C = [1 0]\n",
"D = 0\n",
"P = ss(A, B, C, D)\n",
"println(P)\n",
"\n",
"A = [0 1; -4 5]\n",
"B = [0; 1]\n",
"C = [1 0; 0 1]\n",
"D = [0; 0]\n",
"Ps = ss(A, B, C, D)\n",
"println(Ps)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### オブザーバゲインの設計（極配置）"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ComplexF64[-35.0 + 0.0im; -421.0 + 0.0im;;]\n"
]
}
],
"source": [
"# オブザーバ極\n",
"observer_poles=[-15+5im,-15-5im]\n",
"\n",
"# オブザーバゲインの設計（状態フィードバックの双対） \n",
"L = -place(P.A', P.C', observer_poles)'\n",
"println(L)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2-element Vector{Float64}:\n",
" -35.0\n",
" -421.0"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"L = [ convert(Float64, L[i]) for i in 1:length(L) ]"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2-element Vector{ComplexF64}:\n",
" -15.000000000000002 - 4.9999999999999964im\n",
" -15.000000000000002 + 4.9999999999999964im"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eigvals(P.A + L * P.C)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ComplexF64[-46.0 - 0.0im -15.0 - 0.0im]\n"
]
}
],
"source": [
"# レギュレータ極\n",
"regulator_poles = [-5+5im, -5-5im]\n",
"# 極配置\n",
"F = -place(P.A, P.B, regulator_poles)\n",
"println(F)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1×2 adjoint(::Vector{Float64}) with eltype Float64:\n",
" -46.0 -15.0"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"F = [ convert(Float64, F[i]) for i in 1:length(F) ]'"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"Gsf = ss(P.A + P.B*F, P.B, [1 0; 0 1], [0; 0]);\n",
"Obs = ss(P.A + L*P.C, [P.B -L], [1 0; 0 1], [0 0; 0 0]);"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Td = 0:0.01:3;\n",
"X0 = [-1, 0.5];\n",
"u(x,t) = 0;\n",
"y, t, x, uout = lsim(Gsf, u, Td, x0=X0);\n",
"\n",
"Ud = F*x;\n",
"y, t, xhat, uout = lsim(Obs, [Ud' y[1,:]]', Td, [0, 0]);\n",
"\n",
"p = [ plot(), plot()]\n",
"\n",
"for i=1:2\n",
"plot!(p[i], t, x[i,:],\n",
" xlabel=\"t\", #X軸のラベル\n",
" ylabel=\"x\", #Y軸のラベル\n",
" lw=2, #線幅\n",
" ls=:solid, #線種\n",
" label=\"x\",\n",
" size=(300,230) #プロットのサイズ \n",
")\n",
" \n",
"plot!(p[i], t, xhat[i,:],\n",
" xlabel=\"t\", #X軸のラベル\n",
" ylabel=\"x\", #Y軸のラベル\n",
" lw=2, #線幅\n",
" ls=:solid, #線種\n",
" label=\"x̂\",\n",
" size=(300,230) #プロットのサイズ \n",
")\n",
"end\n",
"\n",
"plot( p[1], p[2], layout=(1,2), size=(600,230) )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 出力フィードバック"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"K:\n",
"StateSpace{Continuous, Float64}\n",
"A = \n",
" -35.0 1.0\n",
" -471.0 -10.0\n",
"B = \n",
" 35.0\n",
" 421.0\n",
"C = \n",
" -46.0 -15.0\n",
"D = \n",
" 0.0\n",
"\n",
"Continuous-time state-space model\n",
"----------------\n",
"K(s)=\n",
"TransferFunction{Continuous, ControlSystems.SisoRational{Float64}}\n",
"-7925.000000000001s - 9215.999999997051\n",
"---------------------------------------\n",
" 1.0s^2 + 45.0s + 821.0\n",
"\n",
"Continuous-time transfer function model\n"
]
}
],
"source": [
"# 出力フィードバック（オブザーバ＋状態フィードバック）\n",
"K = ss(P.A+P.B*F+L*P.C, -L, F, 0)\n",
"println(\"K:\\n\", K)\n",
"println(\"----------------\")\n",
"println(\"K(s)=\\n\", tf(K))\n",
" \n",
"# フィードバック系\n",
"Gfb = feedback(P, K);"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"# Td = 0:0.01:3;\n",
"\n",
"# u(x,t) = 0;\n",
"# y, t, x, uout = lsim(Gfb, Td, u, [-1, 0.5, 0, 0])\n",
"\n",
"# plot(t, x',\n",
"# xlabel=\"t\", #X軸のラベル\n",
"# ylabel=\"x\", #Y軸のラベル\n",
"# lw=2, #線幅\n",
"# ls=:solid, #線種\n",
"# legend=false,\n",
"# size=(300,230) #プロットのサイズ \n",
"# )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 外乱オブザーバ"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"using ControlSystems\n",
"using Plots; gr()\n",
"using LinearAlgebra"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"StateSpace{Continuous, Int64}\n",
"A = \n",
" 0 1\n",
" -4 5\n",
"B = \n",
" 0\n",
" 1\n",
"C = \n",
" 1 0\n",
"D = \n",
" 0\n",
"\n",
"Continuous-time state-space model\n",
"StateSpace{Continuous, Int64}\n",
"A = \n",
" 0 1\n",
" -4 5\n",
"B = \n",
" 0\n",
" 1\n",
"C = \n",
" 1 0\n",
" 0 1\n",
"D = \n",
" 0\n",
" 0\n",
"\n",
"Continuous-time state-space model\n"
]
}
],
"source": [
"A = [0 1; -4 5]\n",
"B = [0; 1]\n",
"C = [1 0]\n",
"D = 0\n",
"P = ss(A, B, C, D)\n",
"println(P)\n",
"\n",
"A = [0 1; -4 5]\n",
"B = [0; 1]\n",
"C = [1 0; 0 1]\n",
"D = [0; 0]\n",
"Ps = ss(A, B, C, D)\n",
"println(Ps)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"出力に0.5の定値外乱が加わるとする"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# オブザーバ極\n",
"observer_poles=[-15+5im,-15-5im]\n",
"# オブザーバゲインの設計（状態フィードバックの双対） \n",
"L = -place(P.A', P.C', observer_poles)'\n",
"L = [ convert(Float64, L[i]) for i in 1:length(L) ]\n",
"\n",
"# レギュレータ極\n",
"regulator_poles = [-5+5im, -5-5im]\n",
"# 極配置\n",
"F = -place(P.A, P.B, regulator_poles)\n",
"F = [ convert(Float64, F[i]) for i in 1:length(F) ]'\n",
"\n",
"\n",
"Gsf = ss(P.A + P.B*F, P.B, [1 0; 0 1], [0; 0]);\n",
"Obs = ss(P.A + L*P.C, [P.B -L], [1 0; 0 1], [0 0; 0 0]);"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Td = 0:0.01:3;\n",
"d = 0.5\n",
"X0 = [-1, 0.5];\n",
"u(x,t) = 0;\n",
"y, t, x, uout = lsim(Gsf, u, Td, x0=X0);\n",
"\n",
"Ud = F*x;\n",
"y, t, xhat, uout = lsim(Obs, [Ud' y[1,:].+d]', Td, [0, 0]);\n",
"\n",
"p = [ plot(), plot()]\n",
"\n",
"for i=1:2\n",
"plot!(p[i], t, x[i,:],\n",
" xlabel=\"t\", #X軸のラベル\n",
" ylabel=\"x\", #Y軸のラベル\n",
" lw=2, #線幅\n",
" ls=:solid, #線種\n",
" label=\"x\",\n",
" size=(300,230) #プロットのサイズ \n",
")\n",
" \n",
"plot!(p[i], t, xhat[i,:],\n",
" xlabel=\"t\", #X軸のラベル\n",
" ylabel=\"x\", #Y軸のラベル\n",
" lw=2, #線幅\n",
" ls=:solid, #線種\n",
" label=\"x̂\",\n",
" size=(300,230) #プロットのサイズ \n",
")\n",
"end\n",
"\n",
"plot( p[1], p[2], layout=(1,2), size=(600,230) )"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[149.5, -526.0, -187.5]\n"
]
}
],
"source": [
"# オブザーバ極\n",
"observer_poles=[-15+5im,-15-5im, -3] \n",
"\n",
"# オブザーバゲインの設計（状態フィードバックの双対）\n",
"Abar = [ P.A zeros(2,1) ; 0 0 0 ] \n",
"Bbar = [ P.B; 0 ]\n",
"Cbar = [ P.C 1 ]\n",
"\n",
"Lbar = -place(Abar', Cbar', observer_poles)'\n",
"Lbar = [ convert(Float64, Lbar[i]) for i in 1:length(Lbar) ]\n",
"\n",
"println(Lbar)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"Fbar = [ F 0 ]\n",
"\n",
"Aob = Abar + Lbar*Cbar\n",
"Bob = [Bbar -Lbar]\n",
"Obs = ss(Aob, Bob, [1 0 0; 0 1 0; 0 0 1], [0 0; 0 0; 0 0] );"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3-element Vector{ComplexF64}:\n",
" -15.000000000000306 + 4.999999999999643im\n",
" -15.000000000000306 - 4.999999999999643im\n",
" -2.9999999999994746 + 0.0im"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pole(Obs)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Td = 0:0.01:3;\n",
"d = 0.5\n",
"X0 = [-1, 0.5];\n",
"u(x,t) = 0;\n",
"y, t, x, uout = lsim(Gsf, u, Td, x0=X0);\n",
"\n",
"Ud = F*x;\n",
"y, t, xhat, uout = lsim(Obs, [Ud' y[1,:].+d]', Td, [0, 0, 0]);\n",
"\n",
"p = [ plot(), plot()]\n",
"\n",
"for i=1:2\n",
"plot!(p[i], t, x[i,:],\n",
" xlabel=\"t\", #X軸のラベル\n",
" ylabel=\"x\", #Y軸のラベル\n",
" lw=2, #線幅\n",
" ls=:solid, #線種\n",
" label=\"x\",\n",
" size=(300,230) #プロットのサイズ \n",
")\n",
" \n",
"plot!(p[i], t, xhat[i,:],\n",
" xlabel=\"t\", #X軸のラベル\n",
" ylabel=\"x\", #Y軸のラベル\n",
" lw=2, #線幅\n",
" ls=:solid, #線種\n",
" label=\"x̂\",\n",
" size=(300,230) #プロットのサイズ \n",
")\n",
"end\n",
"\n",
"plot( p[1], p[2], layout=(1,2), size=(600,230) )"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(t, xhat[3,:],\n",
" xlabel=\"t\", #X軸のラベル\n",
" ylabel=\"d̂\", #Y軸のラベル\n",
" lw=2, #線幅\n",
" ls=:solid, #線種\n",
" legend=false,\n",
" size=(300,230) #プロットのサイズ \n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"外乱 0.5 が推定できている"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## ロバスト制御"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"using ControlSystems\n",
"using Plots; gr()\n",
"using LinearAlgebra"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"30"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"g = 9.81 # 重力加速度[m/s^2]\n",
"l = 0.2 # アームの長さ[m]\n",
"M = 0.5 # アームの質量[kg]\n",
"mu = 1.5e-2 # 粘性摩擦係数\n",
"J = 1.0e-2 # 慣性モーメント\n",
"\n",
"P = tf( [0,1], [J, mu, M*g*l] )\n",
"\n",
"ref = 30 # 目標角度 [deg]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 乗法的不確かさ"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 垂直駆動アームのノミナルモデル\n",
"Pn = tf( [0,1], [J, mu, M*g*l] )\n",
"\n",
"# 不確かさ\n",
"delta = LinRange(-1, 1, 100)\n",
"WT = tf( [10, 0], [1, 150])\n",
"\n",
"P = TransferFunction[ (1 + WT*delta[i])*Pn for i in 1:length(delta) ];\n",
"DT = TransferFunction[ WT*delta[i] for i in 1:length(delta) ];\n",
"\n",
"setPlotScale(\"dB\")\n",
"w = exp10.(LinRange(-2, 3, 1000))\n",
"bodeplot(P, w; lc=:black, lw=0.5, size=(450,400), legend=false, title=\"\" )"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"bodeplot(DT, w; lc=:black, lw=0.5, size=(450,400), legend=false, title=\"\" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 混合感度問題"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"確認中"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# from control import mixsyn\n",
"\n",
"# WS = tf( [0, 1], [1, 1, 0.25]) # 感度関数に対する重み関数 \n",
"# WU = tf(1, 1)\n",
"# WT = tf( [10, 0], [1, 150]) # 相補感度関数に対する重み関数\n",
"\n",
"# # 混合感度問題\n",
"# K, _, gamma = mixsyn(Pn, w1=WS , w2=WU, w3=WT) \n",
"\n",
"# print('K=', ss2tf(K))\n",
"# print('gamma =', gamma[0])\n",
"\n",
"# fig, ax = plt.subplots(1, 2, figsize=(6,2.3))\n",
"\n",
"# # 感度関数\n",
"# Ssys = feedback(1, Pn*K)\n",
"# gain, _, w = bode(Ssys, logspace(-3,3), plot=False)\n",
"# ax[0].semilogx(w, 20*np.log10(gain), ls= '-', lw =2, label='$S$', color='k')\n",
"\n",
"# gain, _, w = bode(1/WS, logspace(-3,3), plot=False)\n",
"# ax[0].semilogx(w, 20*np.log10(gain), ls= '-.', lw =1, label='$1/W_S$', color='k')\n",
"\n",
"# # 相補感度関数\n",
"# Tsys = feedback(Pn*K, 1)\n",
"# gain, _, w = bode(Tsys, logspace(-3,3), plot=False)\n",
"# ax[1].semilogx(w, 20*np.log10(gain), ls = '-', lw =2, label='$T$', color='k')\n",
"\n",
"# gain, _, w = bode(1/WT, logspace(-3,3), plot=False)\n",
"# ax[1].semilogx(w, 20*np.log10(gain), ls= '--', lw =1, label='$1/W_T$', color='k')\n",
"\n",
"# for i in range(2):\n",
"# ax[i].set_ylim(-40, 40)\n",
"# ax[i].legend()\n",
"# ax[i].grid(which=\"both\", ls=':')\n",
"# ax[i].set_ylabel('Gain [dB]')\n",
"# ax[i].set_xlabel('$\\omega$ [rad/s]')\n",
"\n",
"# fig.tight_layout()\n",
"# # fig.savefig(\"robust_design.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# fig, ax = plt.subplots(figsize=(3, 2.3))\n",
"\n",
"# for i in range(len(delta)):\n",
"# P = (1 + WT*delta[i])*Pn\n",
"# Gyr = feedback(P*K, 1)\n",
" \n",
"# y, t = step(Gyr, np.arange(0,5,0.01))\n",
"\n",
"# ax.plot(t, y*ref, color ='k', lw =0.3)\n",
"\n",
"# Gyr = feedback(Pn*K, 1)\n",
"# y, t = step(Gyr, np.arange(0,5,0.01))\n",
"# ax.plot(t, y*ref, lw =2, color='k')\n",
"\n",
"# plot_set(ax, 't', 'y')\n",
"# ax.set_xlim(0, 2)\n",
"# ax.set_ylim(0, 60)\n",
"\n",
"# # fig.savefig(\"robust_step.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### PID制御との比較"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"kp = 2\n",
"kd = 0.1\n",
"ki = 10\n",
"\n",
"plt = plot()\n",
"for i in 1:1:length(delta)\n",
" Kpid = tf([kd, kp, ki], [1, 0])\n",
" \n",
" P = (1 + WT*delta[i])*Pn\n",
" Gyr = feedback(P*Kpid, 1)\n",
" y, t = step(Gyr, 0:0.01:5 )\n",
" plot!(plt, t, y', lc=:black, lw =0.3)\n",
"end\n",
"\n",
"plot!(plt,\n",
" xlabel=\"t\", #X軸のラベル\n",
" ylabel=\"y\", #Y軸のラベル\n",
" ylim = (0,2),\n",
" lw=2, #線幅\n",
" ls=:solid, #線種\n",
" legend=false,\n",
" size=(300,230) #プロットのサイズ \n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"ナイキスト線図で不確かさの影響を確認する"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Kpid = tf([kd, kp, ki], [1, 0])\n",
"H = TransferFunction[ Kpid*(1 + WT*delta[i])*Pn for i in 1:length(delta) ];\n",
"nyquistplot(H, gaincircle=true, lc = :black, lw = 1, xlim=(-1.5,0.5), ylim=(-1.5,0.5), size=(300,300), legend=false)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## ディジタル実装"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"using ControlSystems\n",
"using Plots; gr()\n",
"using LinearAlgebra"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"連続時間システムTransferFunction{Continuous, ControlSystems.SisoRational{Float64}}\n",
" 1.0\n",
"----------\n",
"0.5s + 1.0\n",
"\n",
"Continuous-time transfer function model\n"
]
}
],
"source": [
"P = tf([0, 1], [0.5, 1])\n",
"println(\"連続時間システム\",P)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"離散時間システム（zoh）TransferFunction{Discrete{Float64}, ControlSystems.SisoRational{Float64}}\n",
" 0.3296799539643608\n",
"-------------------------\n",
"1.0z - 0.6703200460356393\n",
"\n",
"Sample Time: 0.2 (seconds)\n",
"Discrete-time transfer function model\n"
]
}
],
"source": [
"ts = 0.2\n",
"\n",
"Pd1 = c2d(P, ts, :zoh)\n",
"println(\"離散時間システム（zoh）\", Pd1)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"離散時間システム（tustin）TransferFunction{Discrete{Float64}, ControlSystems.SisoRational{Float64}}\n",
"0.16666666666666669z + 0.1666666666666667\n",
"-----------------------------------------\n",
" 1.0z - 0.6666666666666667\n",
"\n",
"Sample Time: 0.2 (seconds)\n",
"Discrete-time transfer function model"
]
}
],
"source": [
"Pd2 = c2d(P, ts, :tustin)\n",
"print(\"離散時間システム（tustin）\",Pd2)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Tc = 0:0.01:3\n",
"y, t = step(P, Tc)\n",
"\n",
"Td = 0:ts:3;\n",
"\n",
"p = [ plot(), plot()]\n",
"\n",
"plot!(p[1], t, y',\n",
" xlabel=\"t\", #X軸のラベル\n",
" ylabel=\"y\", #Y軸のラベル\n",
" lw=2, #線幅\n",
" ls=:solid, #線種\n",
" label=\"continuous\",\n",
" size=(300,230) #プロットのサイズ \n",
")\n",
"\n",
"y, t = step(Pd1, Td)\n",
"\n",
"plot!(p[1], t, y',\n",
" seriestype = :scatter,\n",
" xlabel=\"t\", #X軸のラベル\n",
" ylabel=\"y\", #Y軸のラベル\n",
" label=\"zoh\",\n",
" legend=:bottomright,\n",
" size=(300,230) #プロットのサイズ \n",
")\n",
" \n",
"plot!(p[2], t, y',\n",
" xlabel=\"t\", #X軸のラベル\n",
" ylabel=\"y\", #Y軸のラベル\n",
" lw=2, #線幅\n",
" ls=:solid, #線種\n",
" label=\"continuous\",\n",
" size=(300,230) #プロットのサイズ \n",
")\n",
"\n",
"y, t = step(Pd2, Td)\n",
"\n",
"plot!(p[2], t, y',\n",
" seriestype = :scatter,\n",
" xlabel=\"t\", #X軸のラベル\n",
" ylabel=\"y\", #Y軸のラベル\n",
" label=\"tustin\",\n",
" legend=:bottomright,\n",
" size=(300,230) #プロットのサイズ \n",
")\n",
" \n",
"\n",
"plot( p[1], p[2], layout=(1,2), size=(600,230) )"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Tc = 0:0.01:3\n",
"\n",
"u(x,t) = 0.5 * sin.(6*t) + 0.5 * cos.(8*t)\n",
"yc, tc, x, uout = lsim(P, u, Tc);\n",
"\n",
"Td = 0:ts:3;\n",
"\n",
"p = [ plot(), plot()]\n",
"\n",
"plot!(p[1], tc, yc',\n",
" xlabel=\"t\", #X軸のラベル\n",
" ylabel=\"y\", #Y軸のラベル\n",
" lw=2, #線幅\n",
" ls=:solid, #線種\n",
" label=\"continuous\",\n",
" size=(300,230) #プロットのサイズ \n",
")\n",
"\n",
"y, t, x, uout = lsim(Pd1, u, Td);\n",
"\n",
"plot!(p[1], t, y',\n",
" seriestype = :scatter,\n",
" xlabel=\"t\", #X軸のラベル\n",
" ylabel=\"y\", #Y軸のラベル\n",
" label=\"zoh\",\n",
" legend=:bottomleft,\n",
" size=(300,230) #プロットのサイズ \n",
")\n",
" \n",
"plot!(p[2], tc, yc',\n",
" xlabel=\"t\", #X軸のラベル\n",
" ylabel=\"y\", #Y軸のラベル\n",
" lw=2, #線幅\n",
" ls=:solid, #線種\n",
" label=\"continuous\",\n",
" size=(300,230) #プロットのサイズ \n",
")\n",
"\n",
"y, t, x, uout = lsim(Pd2, u, Td);\n",
"\n",
"plot!(p[2], t, y',\n",
" seriestype = :scatter,\n",
" xlabel=\"t\", #X軸のラベル\n",
" ylabel=\"y\", #Y軸のラベル\n",
" label=\"tustin\",\n",
" legend=:bottomleft,\n",
" size=(300,230) #プロットのサイズ \n",
")\n",
" \n",
"\n",
"plot( p[1], p[2], layout=(1,2), size=(600,230) )"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"setPlotScale(\"dB\")\n",
"bodeplot(P, lw=2, size=(450,400), legend=false, title=\"\" )"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"setPlotScale(\"dB\")\n",
"bodeplot([Pd1, Pd2], lw=2, size=(450,400), legend=false, title=\"\" )"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.7.0",
"language": "julia",
"name": "julia-1.7"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.7.0"
}
},
"nbformat": 4,
"nbformat_minor": 4
}