Redo Problem 11 using MATLAB in the following way:

a. MATLAB will generate the root locus for the uncompensated system along with the 0.8 damping ratio line. You will interactively select the operating point. MATLAB will then inform you of the coordinates of the operating point, the gain at the operating point, as well as the estimated %O_S,T_s, T_p, ζ, ω_n, and K_p represented by a second order approximation at the operating point.

b. MATLAB will display the step response of the uncompensated system.

c. Without further input, MATLAB will calculate the compensated design point and will then ask you to input a value for the lead compensator pole from the keyboard. MATLAB will respond with a plot of the root locus showing the compensated design point. MATLAB will then allow you to keep changing the lead compensator pole value from the keyboard until a root locus is plotted that goes through the design point.

d. For the compensated system, MATLAB will inform you of the coordinates of the operating point,the gain at the operating point,as well as the estimated %O_S, T_s, T_p, ζ, ω_n, and K_p represented by a second-order approximation at the operating point.

e. MATLAB will then display the step response of the compensated system.

f. Change the compensator’s zero location a few times and collect data on the compensated system to see if any other choices of compensator zero yield advantages over the original design.

Data from Problem 11:

Given the unity feedback system of Figure P9.1, with

do the following:

a. Sketch the root locus.

b. Find the coordinates of the dominant poles for which ζ = 0.8.

c. Find the gain for which ζ = 0.8.

d. If the system is to be cascade-compensated so that T_s = 1 second and ζ = 0.8, find the compensator pole if the compensator zero is at -4.5.

e. Discuss the validity of your second-order approximation.

f. Use MATLAB or any other computer program to simulate the compensated and uncompensated systems and compare the results to
those expected.

Transcribed Image Text:

K(s + 6) G(s) (s +3(s +4)(s+ 7)(s +9)