Modern Control System Theory and Design, 2nd Edition

7.11.  ILLUSTRATIVE PROBLEMS AND SOLUTIONS

This section provides a set of illustrative problems and their solutions to supplement the material presented in Chapter 7.

I7.1. A closed-loop unity–feedback control system used to position a load has a forward transfer function given by

The time constant of the open-loop process is 2 sec. Determine the time constant of the closed-loop control system.

SOLUTION:

Therefore,

So, the time constant of the closed-loop control system is 0.1818 sec.

I7.2. We wish to analyze the performance of a unity-feedback second-order control system whose forward transfer function represents a process, G_p(s), given by:

(a)  Determine the gain crossover frequency, ω_c, analytically without using the graphical Bode plot.

(b)  Determine the phase margin and gain margin of this control system analytically without using the graphical Bode plot.

(c)  A phase-lead network compensation, G_c(s), given by

is to be added in series with the process’ transfer function, G_p(