P3. Consider the closed-loop system given by 2 C(s) 0,4 52 + 26@ns + m2 R(S) Determine the values of S and on so that th

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P3 Consider The Closed Loop System Given By 2 C S 0 4 52 26 Ns M2 R S Determine The Values Of S And On So That Th 1 (410.47 KiB) Viewed 26 times

P3. Consider the closed-loop system given by 2 C(s) 0,4 52 + 26@ns + m2 R(S) Determine the values of S and on so that the system responds to a step unit with approximately 5% overshoot and with a settling time of 2 sec. (Use the 2% criterion.). Using MATLAB make the plot of c(t) VS t. a. Determine the values of the damping ration and the undamped natural frequency for the given values of maximum overshoot and settling time (7.5 pts). Determine also the damped natural frequency (2.5 pts). b. Which is the closed-loop transfer function of the system? Write this equation explicitly. (2.5 pts). Specify the type of the closed-loop system. i.e., first-order, second-order, etc. (2.5 pts) c. According to the value of the damping ratio obtained in (a), specify the type of system. Then, write the general form of the response signal c(t). (2.5 pts) d. Write a program in Matlab to plot the input signal r(t) and the response signal c(t) as a function of time (2.5 pts). Sketch/draw this plot on a blank paper and specify/label on it the rise time, the peak time, the maximum overshoot, and the settling times (2% criterion) and (5% criterion). (5 pts) e. Explain the physical behavior of a second-order system for its four cases (1) undamped, (2) underdamped, (3) critically damped, and (4) overdamped. In other words, how does behave the response signal for each case? (5 pts)