01) A power amplifier model is described by the transfer function:

a)   Perform root locus design of a compensator to achieve:

b)   Modify the design to achieve zero steady-state error to a step input.

c)   Consider a tachometer feedback for the amplifier and design a rate feedback compensator: design the minor loop for ζ = 0.8; then, design the outer loop for ζ = 0.7. Plot the step response.

02) Consider the power amplifier model above.

a)   Choose a sample time T and obtain the pulse transfer function G(z).

b)   Use root locus plot with 'grid' to design a static compensator for 1 = 0.7. Plot the step response.

c)    Modify the compensator to achieve zero steady-state error to a step input. Plot the step response. Give the update rule for computer implementation of the compensator.

03) The model of an automobile is given as: G(s) - 28s+120_{s / S²} +7s +14

a)  Use frequency domain methods to design a lead-lag/PID compensator for the following specs:

(open loop frequency response peak)

b) Choose a sample time T, and use bilinear transform to obtain an equivalent digital compensator. Plot and compare the step response for both compensators.

04) The state-space model of a dc motor is given as:

Consider the following parameter values:J = .01, b = .1,R = .5 , L= .001, K_t = k_b = .025.

a)  Find a linear transformation to transform the model into controller form.

b)  Design a state feedback controller for closed-loop eigenvalues at -100, -500. Plot the step response of the compensated system.

c)  Design an integral controller for perfect tracking of the model. Choose the third eigenvalue at -0.1. Find the transfer function of the closed-loop system and plot the step response.