P13.11

(a) For the system described in Problem P13.10,

design a lag compensator G s c ( ) to achieve a per

cent overshoot P O. . ≤ 30% and a steady-state error of ess = 0.01 for a ramp input. Assume a con

tinuous nonsampled system with G s p( ).

(b) Determine a suitable D(z) to satisfy the require

ments of part

(a) with a sampling period T = 0.1 s.

Assume a zero-order hold and sampler, and use the G s c ( )-to-D z( ) conversion method.

(c) Plot the step response of the system with the continuous-time compensator G s c( ) of part (a)

and of the digital system with the D(z) of part

(b). Compare the results.

(d) Repeat part

(b) for T = 0.01 s and then repeat part (c).

(e) Plot the ramp response for D(z) with T = 0.1 s and compare it with the continuous-system response.