Consider the PID position control system shown in Figure

Chapter , Problem 10.49

(choose chapter or problem)

Consider the PID position control system shown in Figure 10.7.3, where I = 10 and c = 2. The desired time constant is \(\tau = 2\).

a. Compute the required values of the gains for the following two sets of root locations.

1. \(s = −0.5, s = −5 \pm 5 j\)

2. s = −0.5, s = −1, s = −2.

b. For both cases, use a computer method to plot the command response to a unit step. Discuss the effects of the root separation factor on the response. Compare the results with those of Example 10.7.4, where the roots are s = −5 and \(s = −0.5 \pm 0.5 j\).

c. For both cases, use a computer method to plot the disturbance frequency response. Discuss the effects of the root separation factor on the frequency response. Compare the results with those of Example 10.7.4.