Write a MATLAB program that can be used to design the gain of a digital control system to meet a percent overshoot requirement. The program will be used for systems of the type represented in Figure P13.5 and meet the following requirements:

a. The user will input the desired percent overshoot.

b. MATLAB will convert G₁(s) cascaded with the sample-and-hold to G(z).

c. MATLAB will display the root locus on the z-plane along with an overlay of the percent overshoot curve.

d. The user will click with the mouse at the intersection of the root locus and percent overshoot overlay and MATLAB will respond with the value of gain followed by a display of the step response of the closed-loop system. 

Apply your program to Problem 17 and compare results.

                                 

Transcribed Image Text:

C(s) R(s) + G,(s) Sample- and-hold FIGURE P13.5