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