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the inverted pendulum has a transfer function given by eq. (2.31 ), which is similar to a. use bode plot sketches to design a lead compensator to achieve a pm of . then verify and refine your design by using matlab. b. sketch a root locus and correlate it with the bode plot of the system. c. could you obtain the frequency response of this system experimentally?

Answer :

The following code implements a phase-lead compensator C(s) in frequency response form (where a and T are defined).

We can then interface it with a plant P(s) by using the following code:  C lead = (1+aTs)/(1+Ts). At high frequencies, the lead compensator gives phase lead. By doing this, the root locus is moved to the left, improving the system's stability and responsiveness. The phase lag provided by the lag compensator at low frequencies lowers the steady state error. The control system is marginally stable if the gain margin (GM) and phase margin (PM) are both equal to zero. The control system is unstable if the gain margin (GM) and/or phase margin (PM) are negative.

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