How to use numpy in matrices iterations like Matlab

I am used to make my discrete time control systems simulations in Matlab and now I’m trying python and numpy.

So, my code bellow is working, but I would like to iterate over the numpy vector instead appending values into a list. Is it possible?

In other words, instead of using

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

I would like to use some Matlab equivalent like x[:, k+1] = np.dot(Ad, x[:, k]) + Bd*uc, but it’s not working on my code. If I do that, instead of obtaining a two line column vector that is the expected, I got a 2×2 matrix and an error.

Another question: Why it’s neccessary to use plt.plot(tk, u[:, 0], label=’u’) instead plt.plot(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()

what I want is the code like this:

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()

But it results in a following error:

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,)