我习惯于在MatLab中进行离散时间控制系统的仿真，现在我正在尝试使用Python和NumPy。
因此，我下面的代码是有效的，但我想迭代数字向量，而不是将值追加到列表中。有可能吗？
换句话说，与其使用

xl.append(xt)
ul.append(uc)

我想使用一些与MatLab等价的代码，比如x[：，k+1]=np.dot(Ad，x[：，k])+Bd*uc，但它在我的代码上不起作用。如果我这样做，我没有得到预期的两行列向量，而是得到了一个2x2矩阵和一个错误。
另一个问题：为什么必须使用plt.lot(tk，u[：，0]，Label=‘u’)而不是plt.lot(tk，u，Label=‘u’)？

from control.matlab import *

import math
import numpy as np

import matplotlib.pyplot as plt

Ts = 0.1

N = 50

#x = np.zeros((2, N+1))
tk = np.zeros(N)
u = np.zeros(N)

v = np.random.randn(N)/86.6 #% measurement noise

wn = 1.12
wn2 = pow(wn, 2)

A = [[0, 1], [-1.5, -1.4]]
B = [[0], [1.5]]
C = [[1, 0]]
D = 0

# Control gains
K = np.array([2.64, 3.41071429])

# Now build a feedback with control law u = -K*x
Ad = np.eye(2) + np.multiply(A, Ts)
Bd = np.multiply(B, Ts)
Cd = C

xt = [[1.0], [0.12]]   # initial states
xl = []
ul = []

for k in range(0, N):
    tk[k] = k*Ts
    uc = -K.dot(xt)
    xt = np.dot(Ad, xt) + Bd*uc
    
    xt[1, 0] += v[k]
    
    xl.append(xt)
    ul.append(uc)
    
x = np.array(xl)
u = np.array(ul)

#x = np.delete(x, N, 1) # delete the last position of x

#s = TransferFunction.s
#Gs  = wn2/(s**2 + 0*s + wn2) # This is the KF solution
#yout, T = step(Gs)

plt.rcParams["figure.figsize"] = (10, 7)

plt.figure()
#plt.plot(T, yout, label='Open loop')
plt.plot(tk, x[:, 0], label='x_0')
plt.plot(tk, x[:, 1], label='x_1')
plt.plot(tk, u[:, 0], label='u')
plt.legend()
plt.title('Pendulum ex. 7.14 Franklin book')
plt.xlabel('Time')
plt.ylabel('amp.')
plt.show()

我想要的是这样的代码：

from control.matlab import *

import math
import numpy as np

import matplotlib.pyplot as plt

Ts = 0.1

N = 50

x = np.zeros((2, N+1))
tk = np.zeros(N)
u = np.zeros(N)

v = np.random.randn(N)/86.6 #% measurement noise

wn = 1.12
wn2 = pow(wn, 2)

A = [[0, 1], [-1.5, -1.4]]
B = [[0], [1.5]]
C = [[1, 0]]
D = 0

# Control gains
K = np.array([2.64, 3.41071429])

# Now build a feedback with control law u = -K*x
Ad = np.eye(2) + np.multiply(A, Ts)
Bd = np.multiply(B, Ts)
Cd = C

for k in range(0, N):
    tk[k] = k*Ts
    u[k] = -K.dot(x[:, k])

    x[1, k] += v[k]
    x[:, k+1] = np.dot(Ad, x[:, k]) + Bd*u[k]
    

x = np.delete(x, N, 1) # delete the last position of x

#s = TransferFunction.s
#Gs  = wn2/(s**2 + 0*s + wn2) # This is the KF solution
#yout, T = step(Gs)

plt.rcParams["figure.figsize"] = (10, 7)

plt.figure()
#plt.plot(T, yout, label='Open loop')
plt.plot(tk, x[:, 0], label='x_0')
plt.plot(tk, x[:, 1], label='x_1')
plt.plot(tk, u[:, 0], label='u')
plt.legend()
plt.title('Pendulum ex. 7.14 Franklin book')
plt.xlabel('Time')
plt.ylabel('amp.')
plt.show()

但它会导致以下错误：

Traceback (most recent call last):
  File "C:\Users\ ... \np_matrices_v1.py", line 46, in <module>
    x[:, k+1] = np.dot(Ad, x[:, k]) + Bd*u[k]
ValueError: could not broadcast input array from shape (2,2) into shape (2,)