Actuation and Feedback Delay It turns out we can\'t instantaneously sense and ac

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Actuation and Feedback Delay

It turns out we can't instantaneously sense and actuate our system. Who knew! We now consider a 2ms delay for actuation dynamics in our controller, and a variable delay of Delta seconds in the feedback loop for sensing. These additions are displayed in Figure 0.1. Fig. 0.1. Feedback structure with output noise, disturbances and delay. Delays have the effect of not just making performance poor, but actually destabilizing the closed loop. First, plot a step response with Delta = 0 using your best controller from Homeworks 5/6. Is this response noticeably poorer already due to simply the actuation delay? Next, let Delta > 0. and find the value Delta max(C) for your particular controller where the closed-loop from r(s) to theta2(s) becomes unstable. Hint: You can just do this using a for loop. If you are having problems with your MATLAB code, try a Pade approximation for the delay. What was the phase margin of your original loop gain C(s)G1(s)e-0.002s? Modify your controller C(s) to a new controller C-(s) to increase this phase margin. Now, as in Part (a), find the value Delta max(C-). Based on your findings in (b), what is the qualitative relationship between phase margin and delay tolerance (i.e.. Delta max)? Explain this in terms of the Nyquist plot, then repeat the explanation using the Bode plot.

Explanation / Answer

See this link..

http://paginas.fe.up.pt/~larocha/articles/MB11.pdf

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