Skip to content

Instantly share code, notes, and snippets.

@dsaint31x
Last active April 19, 2019 05:23
Show Gist options
  • Save dsaint31x/5ddc7c37d828d51a4ff0411d104de843 to your computer and use it in GitHub Desktop.
Save dsaint31x/5ddc7c37d828d51a4ff0411d104de843 to your computer and use it in GitHub Desktop.
SS_Laplace_Pole_Stability
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Pole에 따른 impulse response의 형태.\n",
"\n",
"* pole이 s 평면의 우반면에 있으면 impulse res.는 발산 → 시스템 불안정\n",
"* 공액 복소극(imaginary component가 있는 경우)의 경우에는 진동이 발생\n",
"* pole이 허축에서 멀리 떨어질수록 impulse res.의 감소(증가) 속도 빠름\n",
"* 실축에서 멀리 떨어질수록 impulse res.의 진동 속도(freq.)가 빨라짐 \n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import sympy as sym\n",
"from sympy.abc import s,t,x,y,z\n",
"from sympy.integrals import inverse_laplace_transform\n",
"\n",
"#sym.init_printing(use_latex='mathjax')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Pole=0\n",
"pole이 0인 경우로 단일근, 중근, 삼중근 일때의 Impulse Response를 살펴본 결과임."
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<sympy.plotting.plot.Plot at 0x7f44582e8f98>"
]
},
"execution_count": 87,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Transfer function\n",
"H = 1/(s)\n",
"\n",
"# Impulse Response\n",
"h = inverse_laplace_transform(H,s,t)\n",
"\n",
"# plot graph\n",
"sym.plot(h)"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<sympy.plotting.plot.Plot at 0x7f4458201ba8>"
]
},
"execution_count": 88,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Transfer function\n",
"H = 1/(s*s)\n",
"\n",
"# Impulse Response\n",
"h = inverse_laplace_transform(H,s,t)\n",
"\n",
"# plot graph\n",
"sym.plot(h)"
]
},
{
"cell_type": "code",
"execution_count": 105,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Transfer function\n",
"H0 = 1/(s**3)\n",
"H1 = 1/(s**4)\n",
"\n",
"# Impulse Response\n",
"h0 = inverse_laplace_transform(H0,s,t)\n",
"h1 = inverse_laplace_transform(H1,s,t)\n",
"\n",
"# plot graph\n",
"p0 = sym.plot(h0,line_color='blue', show=False)\n",
"p1 = sym.plot(h1,line_color='red', show=False)\n",
"\n",
"p0.append(p1[0])\n",
"\n",
"p0.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## pole is located on the left side\n",
"\n",
"* real number\n",
"* complex number"
]
},
{
"cell_type": "code",
"execution_count": 126,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Transfer function\n",
"H0 = 1/(s+1)\n",
"H1 = 1/(s+2)\n",
"H2 = 3/((s+2+10j)*(s+2-10j))\n",
"\n",
"\n",
"# Impulse Response\n",
"h0 = inverse_laplace_transform(H0,s,t)\n",
"h1 = inverse_laplace_transform(H1,s,t)\n",
"h2 = inverse_laplace_transform(H2,s,t)\n",
"\n",
"names = ['p=-1','p=-2','p=-1-10j']\n",
"\n",
"# plot graph\n",
"p0 = sym.plot(h0,line_color='blue', show=False)\n",
"p1 = sym.plot(h1,line_color='red', show=False)\n",
"p2 = sym.plot(h2,line_color='orange', show=False)\n",
"\n",
"p0.append(p1[0])\n",
"p0.append(p2[0])\n",
"\n",
"p0.show()"
]
},
{
"cell_type": "code",
"execution_count": 127,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Transfer function\n",
"H0 = 1/((s+1+10j)*(s+1-10j))\n",
"H1 = 1/((s+2+10j)*(s+2-10j))\n",
"\n",
"# Impulse Response\n",
"h0 = inverse_laplace_transform(H0,s,t)\n",
"h1 = inverse_laplace_transform(H1,s,t)\n",
"\n",
"# plot graph\n",
"p0 = sym.plot(h0,line_color='blue', show=False)\n",
"p1 = sym.plot(h1,line_color='red', show=False)\n",
"\n",
"p0.append(p1[0])\n",
"p0.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## pole is located on the right side\n",
"\n",
"* real number\n",
"* complex number"
]
},
{
"cell_type": "code",
"execution_count": 128,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Transfer function\n",
"H0 = 1/(s-.1)\n",
"H1 = 1/(s-.2)\n",
"H2 = 3/((s-.2+10j)*(s-.2-10j))\n",
"\n",
"\n",
"# Impulse Response\n",
"h0 = inverse_laplace_transform(H0,s,t)\n",
"h1 = inverse_laplace_transform(H1,s,t)\n",
"h2 = inverse_laplace_transform(H2,s,t)\n",
"\n",
"# plot graph\n",
"p0 = sym.plot(h0,line_color='blue', show=False)\n",
"p1 = sym.plot(h1,line_color='red', show=False)\n",
"p2 = sym.plot(h2,line_color='orange', show=False)\n",
"\n",
"p0.append(p1[0])\n",
"p0.append(p2[0])\n",
"\n",
"p0.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## pole is imaginary number"
]
},
{
"cell_type": "code",
"execution_count": 130,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Transfer function\n",
"H0 = 1/((s+1j)*(s-1j))\n",
"H1 = 1/((s+10j)*(s-10j))\n",
"\n",
"# Impulse Response\n",
"h0 = inverse_laplace_transform(H0,s,t)\n",
"h1 = inverse_laplace_transform(H1,s,t)\n",
"\n",
"# plot graph\n",
"p0 = sym.plot(h0,line_color='blue', show=False)\n",
"p1 = sym.plot(h1,line_color='red', show=False)\n",
"\n",
"p0.append(p1[0])\n",
"p0.show()"
]
},
{
"cell_type": "code",
"execution_count": 141,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(s - 10*I)**2*(s + 10*I)**2\n"
]
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Transfer function\n",
"H0 = 1/((s+10j)*(s-10j))\n",
"den = ((s+10j)*(s-10j))**2\n",
"den = sym.nsimplify(den) # 이게 빠지면 PolynomialDivisionFailed발생. 반드시 해줄것\n",
"print(den)\n",
"H1 = 1/(den)\n",
"\n",
"# Impulse Response\n",
"h0 = inverse_laplace_transform(H0,s,t)\n",
"h1 = inverse_laplace_transform(H1,s,t)\n",
"\n",
"# plot graph\n",
"p0 = sym.plot(h0,line_color='blue', show=False)\n",
"p1 = sym.plot(h1,line_color='red', show=False)\n",
"\n",
"p0.append(p1[0])\n",
"p0.show()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.7"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment