41) A power amplifier model is described by the transfer function: G(s) (54.1)(s4.4Xsi.e)
a) Perform root locus design of a compensator to achieve: < a 0.7, ton a 5f =ab) 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 < = 0.8; then, design the outer loop for < = 0.7. Plot the step response.
Q2) 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 < = 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. 28ss 120 Ca) The model of an automobile is given as: G(s) — 5-4.75+14′ a) Use frequency domain methods to design a lead-lag/PID compensator for the following specs: eon > 10TI = co, K, = 20,14p < 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.
Q4) The state-space model of a dc motor is given as: cri itetai =—kalL +IT] va, I w = 10 11 Pal Consider he following parameter values:/ = .01, b = .1 R = .5, L = .001,kt = kb = .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.