Consider the Bode plot in Figure 1: i) Determine/Estimate the systems open loop transfer GH(s) ii) Recommend a suitable controller/compensator that can be applied to this system. Clearly state your objective(s) and assumptions.
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The magnitude plot shows a slope of -20dB/decade after the gain crossover frequency. This indicates a single pole in the open-loop transfer function. Show more…
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Problem-1 (25p). Suppose that you as a Control Engineer are called-in to consult on a control system in a piece of equipment in the field. No one could find the design report or test results from the original design of the control system. Therefore, you needed to take the frequency response of the control system by opening the feedback loop. You realized that the system has just a unit feedback and obtained the Bode plots below. (a) Estimate the open-loop transfer function. (b) Determine the system type and the steady-state error from the plots. Make sure that you obtain the same steady-state error using the result of (a).
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Q2. Consider an open-loop system shown below: (i) When input is a unit step input (r(t) = 1(t), t > 0), the output of the system is y(t) = 0.5t + 0.25e^-2t - 0.25. Calculate the transfer function of the open-loop system. (ii) Consider the system in (i) is closed by a negative unity feedback, determine whether the closed-loop system is stable or not. (iii) Consider the system in (ii) is controlled by a phase lead compensator Dc(s) shown as below: Design the phase lead compensator which satisfies: 1) Steady state error of the closed-loop system is ess ≤ 0.02 for unit ramp input; 2) Phase margin PM ≥ 45°.
(e) Estimate the percent overshoot, rise time, and settling time of the step response. (f) Estimate the bandwidth of the closed-loop frequency response. (g) Estimate the peak amplitude and peak frequency of the closed-loop frequency response. (h) Replace G(s) by KG(s) with K > 0. Find the range of K for stability. (i) Replace G(s) by e^-TsG(s) with T > 0. Find the range of T for stability.
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