Farbod02 patch 1

Python Equivalence/Chapter 3/DCmotor.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.signal import lsim
+
+# Define system matrices
+A = np.array([[0, 1, 0], [0, 0, 4.438], [0, -12, -24]])
+b1 = np.array([[0], [0], [20]])
+b2 = np.array([[0], [-7.396], [0]])
+B = np.hstack((b1, b2))
+C = np.array([[1, 0, 0], [0, 1, 0]])
+D = 0
+
+# Time vector
+t = np.arange(0, 4, 0.01)
+
+# Define the input signal
+u1 = 3 - 6 * square(2 * np.pi * 4 * t)
+
+# Perform simulation
+t, y, x = lsim((A, B, C, D), U=u1, T=t)
+
+# Plot the results
+plt.plot(t, x[:, 0], 'k', label='theta')
+plt.plot(t, x[:, 1], 'k-.', label='omega')
+plt.plot(t, x[:, 2], 'k:', label='i')
+plt.grid(True)
+plt.xlabel('Time (sec)')
+plt.ylabel('State variable')
+plt.legend()
+plt.show()

Python Equivalence/Chapter 3/DCmotor_transfun.py

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+import numpy as np
+import control as ctrl
+
+
+# Define system matrices
+A = np.array([[0, 1, 0], [0, 0, 4.438], [0, -12, -24]])
+b1 = np.array([[0], [0], [20]])
+b2 = np.array([[0], [-7.396], [0]])
+B = np.hstack((b1, b2))
+C = np.array([[1, 0, 0]])
+D = np.array([[0, 0]])
+
+# Create state-space system
+DCM = ctrl.ss(A, B, C, D)
+
+# Convert to transfer function
+DCM_tf = ctrl.ss2tf(DCM)
+
+# Convert to zero-pole-gain
+DCM_zpk = ctrl.ss2zpk(DCM)
+
+# Print the results
+print("Transfer Function:")
+print(DCM_tf)
+print("\nZero-Pole-Gain:")
+print(DCM_zpk)

Python Equivalent/Chapter 5_6/exp5_3.py

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+import numpy as np
+A = np.array([[-3/2, 1/2], [1/2, -3/2]])
+B = np.array([[1/2], [1/2]])
+C = np.array([[1, -1]])
+def ctrb(A, B):
+    n = A.shape[0]
+    m = B.shape[1]
+    C = np.hstack([np.linalg.matrix_power(A, i) @ B for i in range(n)])
+    return C
+def obsv(A, C):
+    n = A.shape[0]
+    m = C.shape[1]
+    O = np.vstack([C @ np.linalg.matrix_power(A, i) for i in range(n)])
+    return O
+def null_space(A, tol=1e-15):
+    u, s, vh = np.linalg.svd(A)
+    null_mask = (s <= tol)
+    null_space = np.compress(null_mask, vh, axis=0)
+    return null_space.T
+Cn = ctrb(A, B)
+print("Controllability Matrix:")
+print(Cn)
+print("Rank of Controllability Matrix:", np.linalg.matrix_rank(Cn))
+print("Null space of Controllability Matrix:")
+print(null_space(Cn))
+On = obsv(A, C)
+print("\nObservability Matrix:")
+print(On)
+print("Rank of Observability Matrix:", np.linalg.matrix_rank(On))
+print("Null space of Observability Matrix:")
+print(null_space(On))

Python Equivalent/Chapter 5_6/exp5_4.py

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+import numpy as np
+num = [[1, 2], [-1, 1]]
+den = [[1, 1], [1, 2], [1, 1], [1, 3]]
+def nested_lists_to_arrays(nested_list):
+    return [np.array(coeff) for coeff in nested_list]
+num_np = nested_lists_to_arrays(num)
+den_np = nested_lists_to_arrays(den)
+def tf(num, den):
+    num_poly = np.poly1d(num)
+    den_poly = np.poly1d(den)
+    return num_poly, den_poly
+num_tf, den_tf = tf(num_np[0], den_np[0])
+print("Transfer Function (num/den):")
+print(num_tf)
+print("---")
+print(den_tf)
+A = np.array([[-1]])
+B = np.array([[1], [2]])
+C = np.array([[1, 2]])
+D = np.array([[0]])
+def ss2tf(A, B, C, D):
+    return np.linalg.inv(s*np.eye(A.shape[0]) - A) @ B + D
+s = np.array([[0, 1], [-1, 0]])
+my_sys = np.array([[1/(s+1), 2/(s+2)], [-1/(s+1), 1/(s+3)]])
+A_ss = np.array([[0, 1], [-1, -4]])
+B_ss = np.array([[0], [0], [1]])
+C_ss = np.array([[1, 2]])
+D_ss = np.array([[0]])
+print("\nState-Space Matrices:")
+print("A_ss:\n", A_ss)
+print("B_ss:\n", B_ss)
+print("C_ss:\n", C_ss)
+print("D_ss:\n", D_ss)

Python Equivalent/Chapter 5_6/exp_5_6.py

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+import numpy as np
+from scipy.linalg import solve_continuous_lyapunov
+A = np.array([[-1, -2], [1, -4]])
+Q = np.eye(2)
+P = solve_continuous_lyapunov(A.T, -Q)
+det_P = np.linalg.det(P)
+print("Matrix P (Lyapunov equation solution):")
+print(P)
+print("\nDeterminant of P:", det_P)