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

Consider the PID position control system shown in Figure 10.7.3, where I = 10 and c = 2. The desired time constant is τ = 2.
a. Compute the required values of the gains for the following two sets of root locations.
1. s = -0.5, s = -5 ± 5 j
2. s = -0.5, s = -1, .v = -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 arc
s = -5 and s = -6.5 ±0.5j.
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.

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