P5.2 A specific closed-loop control system is to be designed for an underdamped response to a step input. The specifications for the system are as follows: 10% < P.O. < 20%, T_s < 0.6 s. (a) Identify the desired area for the dominant roots of the system. (b) Determine the smallest value of a third root r_3 if the complex conjugate roots are to represent the dominant response. (c) The closed-loop system transfer function T(s) is third-order, and the feedback has a unity gain. Determine the loop transfer function G(s) = Y(s)/E(s) when the settling time to within 2% of the final value is T_s = 0.6 s and the percent overshoot is P.O. = 20%.
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The problem is about designing a closed-loop control system with an underdamped response to a step input. The system specifications include a percent overshoot (P.O.) less than 20% and a settling time (Ts) less than 0.6 seconds. Show more…
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