1) A power amplifier model is described by the transfer function: G(s) = 1/(s+1)(s+4)(s+8).
a) Perform root locus design of a compensator to achieve: ζ≈ 0.7, ωn ≈ 5√2 rad/s
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.
2) 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 ζ = 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.
3) The model of an automobile is given as: G(s) =28s+120/ s2 +7s+ 14.
a) Use frequency domain methods to design a lead-lag/PID compensator for the following specs:
ωB≥ 10rad/s, Kp = ∞, Kv = 20, Mp≤ 1dB (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.
4) The state-space model of a dc motor is given as:
Consider he following parameter values: J = .01, b = .1, R = .5, L = .001, kt = kb = .025.
a) Find a linear trans ormation 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.