Question

Design a Pl or PDcontroller for the system Go)+ 10 to meet the following specifications Zero steady state error for unit step reference input ·4 < 0.12s . %OS < 10%. (a) Determine the low frequency gain, crossover frequency and phase margin necessary to meet the (b) Decide if C() needs an integrator. Plot the Bode plot of either G(s) or G(o)/s, depending on (c) Use sisotool (or iteration) to choose a gain and place a zero to meet the specifications specifications. your choice (d) Write the transfer function of the resulting controller C(s), where C(s) includes the integrator, if used. State whether this is a PI or PD controller. (e) Plot the bode plot of the loop gain C(s)G(s), the Bode plot of the closed loop transfer function, and the closed loop step response.

Answer all parts and show all work.

Answer 1

Given that Design PI PD controller for the system G(C) = 1/S(S + 10) Here, meet following specification zero steady state error unit step input R(S) = 1/s for unit step input Now ess = lim_s rightarrow 0 S > R (S)/1 + G(S) H(S) implies ess = lim_s rightarrow 0 S 1/ S /1 + 1/ S (S + 10) ess = lim_s rightarrow 0 S(S + 10)/S(S + 10) + 1 implies ess = lim_s rightarrow 0 S^2 + 10 S/S^2 + 10S + 1 put S = 0 ess = 0 Now ess is zero for unit step Reference I/P so, G(S) = 1/S^2 + 10 S Compare with wn^2/s^2 + z & w_n + wn^2 of II nd order eq.. \r\n Rise time tr = pi - phi/wn squareroot 1 - xi^2 tr = pi - phi/w_n squareroot 1 - xi^2 w_n = 1 xi w_n = 10^5 implies xi times 1 = 5 implies xi times 1 = 5