8.2-4. Consider the system of Problem 8.2-2. The plant frequency response (Gleft(j omega_{w}ight)) is given in Table
Question:
8.2-4. Consider the system of Problem 8.2-2. The plant frequency response \(G\left(j \omega_{w}ight)\) is given in Table P8.2-2.
(a) Let the digital controller realize a gain \(K\), that is, \(D(z)=K\). Find \(K\) such that the system phase margin is \(45^{\circ}\).
(b) Obtain the system step response of part (a) using MATLAB, and find the rise time \(t_{r}\) and the percent overshoot.
Problem 8.2-2
Table P8.2-2
Transcribed Image Text:
Consider the system of Fig. P8.2-2 with T = 0.2. (a) Show that the pulse transfer function of the plant is given by 1 G(z) T = 1 [36+D] [s (s + D(z) = (b) The frequency response for G(z) is given in Table P8.2-2. From this frequency response, sketch the Bode and the Nyquist diagrams for the uncompensated system, indicating the gain and phase margins. (c) Calculate the value of G(jo) as w. It is not necessary to find G(w) to calculate this value. (d) Use the results of part (b) to estimate the overshoot in the unit-step response. (e) Based on the results in part (d), are the zeros of the uncompensated system characteristic equation real or complex? Why? (f) Use MATLAB to find the rise time t,. The step response will show a 21 percent overshoot. 0.01873z + 0.01752 (z - 1)(z- 0.8187) 1--Ts S m(t) 1 s(s+1) C(s)
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To solve this problem we need to find the gain K for the digital controller such that the system phase margin is 45 Then well obtain the system step response using MATLAB and find the rise time t r an...View the full answer
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Related Book For
Digital Control System Analysis And Design
ISBN: 9780132938310
4th Edition
Authors: Charles Phillips, H. Nagle, Aranya Chakrabortty
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