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July 5, 2016 15:49
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| # coding: utf-8 | |
| # In[1]: | |
| import numpy as np | |
| import scipy as sp | |
| # matplotlib: | |
| from matplotlib.pylab import plt | |
| get_ipython().magic('matplotlib inline') | |
| # In[2]: | |
| # 単純な二階微分方程式の状態空間： | |
| # In[3]: | |
| # 微分方程式： y'' = ay' + by | |
| # 一階微分化： x2' = a*x2 + b*x1; x1=y, x2=y', x2=x1' | |
| # 状態： [x1', x2'] = [[0,1], [a,b]] * [x1, x2] | |
| # 出力： y = [1,0]*[x1, x2] | |
| a,b = 0.2, 1.3 | |
| x1, x2 = 1.3, 0.6 | |
| vec = np.array([x1, x2]) | |
| mat = np.array([[0,1], [a,b]]) # x2が次期にx1に行く。今のx2にはax1+bx2。 | |
| y = [] | |
| for i in range(10): | |
| vec = mat.dot(vec) | |
| y.append(vec[0]) #x1をyとして出力。 | |
| plt.plot(y) | |
| # In[4]: | |
| # クラス化： | |
| class SpaceState(object): | |
| def __init__(self): | |
| self.a = 0.2 | |
| self.b = 1.3 | |
| self.x1 = 1.3 | |
| self.x2 = 0.6 | |
| def calc(self): | |
| vec = np.array([self.x1, self.x2]) | |
| mat = np.array([[0,1], [self.a, self.b]]) # x2が次期にx1に行く。今のx2にはax1+bx2。 | |
| y = [] | |
| for i in range(10): | |
| vec = mat.dot(vec) | |
| y.append(vec[0]) #x1をyとして出力。 | |
| return y | |
| # In[5]: | |
| aho1 = SpaceState() | |
| plt.plot(aho1.calc()) | |
| aho2 = SpaceState() | |
| aho2.x2 = 2.3 | |
| plt.plot(aho2.calc()) | |
| # In[6]: | |
| # バネの振動： | |
| # In[7]: | |
| # 微分方程式： my’’(t) = -cy’(t) -ky(t) + u(t) | |
| # 一階微分化： x2' = -c/m*x2 + -k/m*x1; x2=x1' | |
| # 状態： [x1’,x2’] = [[0,1], [-k/m,-c/m]]*[x1,x2] + [0,1/m]*u | |
| # 出力： y = [1,0]*[x1,x2] | |
| k = 0.2 | |
| c = 1.3 | |
| m = 3 | |
| x1, x2 = 1.3, 0.6 | |
| vec = np.array([x1, x2]) | |
| u = 2.3 | |
| mat = np.array([[0,1], [-k/m, -c/m]]) | |
| u_mat = np.array([0, 1/m]) | |
| y = [] | |
| for i in range(10): | |
| vec = mat.dot(vec) + u_mat.dot(u) | |
| y.append(vec[0]) | |
| plt.plot(y) | |
| # In[8]: | |
| # クラス化： | |
| class Spring(object): | |
| def __init__(self): | |
| self.time = 10 | |
| self.k = 0.2 | |
| self.c = 1.3 | |
| self.m = 3 | |
| self.x1 = 1.3 | |
| self.x2 = 0.6 | |
| self.u = 2.3 | |
| def calc(self): | |
| vec = np.array([self.x1, self.x2]) | |
| mat = np.array([[0,1], [-self.k/self.m, -self.c/self.m]]) | |
| u_mat = np.array([0, 1/self.m]) | |
| y = [] | |
| for i in range(self.time): | |
| vec = mat.dot(vec) + u_mat.dot(self.u) | |
| y.append(vec[0]) | |
| return y | |
| # In[9]: | |
| aho1 = Spring() | |
| aho1.m = 1.3 | |
| plt.plot(aho1.calc()) | |
| aho2 = Spring() | |
| aho2.x2 = 2.1 | |
| plt.plot(aho2.calc()) | |
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