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Python Equivalent/Chapter 7/6_9.py

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+import numpy as np
+import control as ctrl
+
+# Define the system matrices
+A = np.array([[-2, -1, 2],
+              [-1, -2, 2],
+              [-2, 0, 2]])
+
+B = np.array([[0, 0],
+              [0, 1],
+              [1, 0]])
+
+f = np.array([[1],
+              [1]])
+
+# Calculate b = B*f
+b = B @ f
+
+# Compute the controllability matrix
+C = ctrl.ctrb(A, b)
+
+# Given matrices
+Psi = np.array([[1, 2, -1],
+                [0, 1, 2],
+                [0, 0, 1]])
+
+delta = np.array([4, 13, 10])
+
+# Compute M matrix
+M = delta @ np.linalg.inv(C @ Psi)
+
+# Compute K1
+K1 = f * M
+
+# Desired closed-loop poles
+pd = np.array([-2, -2, -2])
+
+# Compute the state feedback gain using pole placement
+k = ctrl.acker(A, B, pd)
+
+# Compute K2
+K2 = f * k
+
+# Compute the closed-loop system matrix Ac
+Ac = A - B @ K1
+
+# Compute eigenvalues of Ac
+eigvals_Ac = np.linalg.eigvals(Ac)
+
+print("State feedback gain K1:")
+print(K1)
+print("\nState feedback gain k (pd = [-2, -2, -2]):")
+print(k)
+print("\nState feedback gain K2:")
+print(K2)
+print("\nEigenvalues of Ac:")
+print(eigvals_Ac)