idk2

bode.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+# Define the frequency range for the Bode plot
+omega = np.logspace(-2, 2, 1000)  # Frequency range from 0.01 to 100 rad/s
+
+# Define the transfer function parameters
+T_values = [0.2, 1, 5]
+
+# Create subplots
+fig, (ax_mag, ax_phase) = plt.subplots(2, 1, figsize=(10, 8))
+
+# Plot for each T value
+for T in T_values:
+    G_mag = 20 * np.log10(1 / np.sqrt(1 + (omega * T)**2))
+    G_phase = -np.degrees(np.arctan(omega * T))
+    
+    ax_mag.plot(omega, G_mag, label=f'T = {T}')
+    ax_phase.plot(omega, G_phase, label=f'T = {T}')
+
+# Magnitude plot settings
+ax_mag.set_xscale('log')
+ax_mag.set_title('Bode Magnitude Plot')
+ax_mag.set_ylabel('Magnitude (dB)')
+ax_mag.grid(True)
+ax_mag.legend()
+
+# Phase plot settings
+ax_phase.set_xscale('log')
+ax_phase.set_title('Bode Phase Plot')
+ax_phase.set_ylabel('Phase (degrees)')
+ax_phase.set_xlabel('Frequency (rad/s)')
+ax_phase.grid(True)
+ax_phase.legend()
+
+plt.tight_layout()
+plt.show()
+

nyquist.py

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+# Requires 'control' package:
+# pip install control
+import numpy as np
+import matplotlib.pyplot as plt
+import control as ctrl
+
+def nyquist_diagram(T):
+    # Define the numerator and denominator of the transfer function
+    numerator = [1]  # Numerator of the transfer function
+    den1 = [1, 1, 1]  # First part of the denominator
+    den2 = [T, 1]  # Second part of the denominator
+
+    # Convolve the two denominator parts
+    denominator = np.convolve(den1, den2)
+
+    # Create the transfer function
+    system = ctrl.TransferFunction(numerator, denominator)
+    
+    # Generate the Nyquist plot
+    ctrl.nyquist_plot(system)
+    
+    # Enhance plot appearance
+    plt.title('Nyquist Diagram')
+    plt.xlabel('Real')
+    plt.ylabel('Imaginary')
+    plt.grid(True)
+    plt.show()
+
+# Example usage
+T = 1  # Time constant
+nyquist_diagram(T)
+

step.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.signal import TransferFunction, step
+
+def step_rc(R, C, t_end, step_amplitude):
+    # Define the transfer function H(s) = 1 / (RCs + 1)
+    num = [1]
+    den = [R * C, 1]
+    system = TransferFunction(num, den)
+
+    # Generate time points
+    t = np.linspace(0, t_end, 1000)
+    
+    # Calculate the step response
+    t, response = step(system, T=t)
+    
+    # Scale the response by the step amplitude
+    response *= step_amplitude
+    
+    # Plot the step response
+    plt.plot(t, response)
+    plt.title('Step Response of RC Circuit')
+    plt.xlabel('Time (s)')
+    plt.ylabel('Response (V)')
+    plt.grid(True)
+    plt.show()
+    
+    return t, response
+
+# Example usage
+R = 1000  # Ohms
+C = 1e-6  # Farads
+t_end = 0.01  # seconds
+step_amplitude = 5  # Volts
+
+t, response = step_rc(R, C, t_end, step_amplitude)
+

step2.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.signal import TransferFunction, step
+
+def step_response(T, t_end):
+    # Define the transfer function H(s) = (-Ts + 1) / (s^3 + 3s^2 + 2s + 1)
+    num = [-T, 1]
+    den = [1, 3, 2, 1]
+    system = TransferFunction(num, den)
+
+    # Generate time points
+    t = np.linspace(0, t_end, 1000)
+    
+    # Calculate the step response
+    t, response = step(system, T=t)
+    
+    # Plot the step response
+    plt.plot(t, response)
+    plt.title('Step Response of the System')
+    plt.xlabel('Time (s)')
+    plt.ylabel('Response')
+    plt.grid(True)
+    plt.show()
+    
+    return t, response
+
+# Example usage
+T = 1  # Time constant
+t_end = 10  # seconds
+
+t, response = step_response(T, t_end)
+

step3.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.signal import TransferFunction, step, convolve
+
+def step_response(numerator, denominator, t_end, step_amplitude):
+    # Define the transfer function H(s) = numerator / denominator
+    system = TransferFunction(numerator, denominator)
+
+    # Generate time points
+    t = np.linspace(0, t_end, 1000)
+    
+    # Calculate the step response
+    t, response = step(system, T=t)
+    
+    # Scale the response by the step amplitude
+    response *= step_amplitude
+    
+    # Plot the step response
+    plt.plot(t, response)
+    plt.title('Step Response of the System')
+    plt.xlabel('Time (s)')
+    plt.ylabel('Response')
+    plt.grid(True)
+    plt.show()
+    
+    return t, response
+
+# Example usage
+T = 1  # Time constant
+numerator = [1]  # Numerator of the transfer function
+den1 = [1, 1, 1]  # First part of the denominator
+den2 = [T, 1]  # Second part of the denominator
+
+# Convolution of the two denominator parts
+denominator = convolve(den1, den2)
+
+t_end = 20  # Duration of the simulation
+step_amplitude = 0.1  # Step amplitude
+
+t, response = step_response(numerator, denominator, t_end, step_amplitude)
+