Question
If the transfer functions of the plant and controller are given as Plant: P(s)=1/s, (e.g., a normalized description of car velocity with force as the
If the transfer functions of the plant and controller are given as
Plant: P(s)=1/s, (e.g., a normalized description of car velocity with force as the input; this can represent a cruise control system.)
Controller:C(s)=K((s+z)/s) , where K and z are constants.
Design a controller (select values of K and z) such that the following specifications are met:
Target crossover frequency = 1 rad/s (approximately equal to the closed-loop bandwidth).
Target phase margin is 60.
Show all your work and demonstrate your design meets these specifications by the use of allmargin command on the open-loop transfer function L(s) = P(s)C(s). (hint: help allmargin in Matlab). Include MATLAB code and results.
Plot the closed-loop frequency and step responses from the reference input r to the output y. Show the achieved bandwidth by marking on the Bode plot with a data cursor. Comment on how different, if so, it is from the specified bandwidth. Include MATLAB code and plots. (Read http://www.mathworks.com/help/matlab/creating_plots/data-cursor-displaying-data-values-interactively.html on how to use the data cursor.)
Plot the closed-loop frequency and step responses from the disturbance d to the output y. Does the steady state error e become 0 when a step disturbance d is applied to this closed loop transfer function? Include MATLAB code and plots.
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