Redo Problem 6 using MATLAB in the following way:

a. MATLAB will generate the root locus for the uncompensated system along with the 0.707 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 %OS, 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 PD compensator zero 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 PD compensator 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.

Data From Problem 6:

The unity feedback system shown in Figure P9.1 with

is operating with a dominant-pole damping ratio of 0.707. Design a PD controller so that the settling time is reduced by a factor of 2. Compare the transient and steady-state performance of the uncompensated and compensated systems. Describe any problems with your design.

Transcribed Image Text:

K(s+ 6) (s+ 2)(s + 3)(s+ 5) G(s) =