Control Systems Assignment
Question 1. The block diagram of a feedback control system is shown in Figure 1.
![20_Figure.jpg](https://secure.tutorsglobe.com/CMSImages/20_Figure.jpg)
1) Find the closed-loop transfer function Y(s)/R(s).
2) Determine the poles and zeros of the closed-loop system.
3) Calculate the output response y(t) to a unit step input R(s) = 1/s.
Question 2. Consider the signal-flow graph in Figure 2. Applying Mason's gain formula, obtain the transfer function Z(s)/X(s).
(Note: you need to show the steps of your work)
![1558_Figure1.jpg](https://secure.tutorsglobe.com/CMSImages/1558_Figure1.jpg)
Question 3.
A control system has the transfer function
Y(s)/R(s) = (3(s+3)(s+4))/((s+1)(s+2)(s+5)) = (3s2 + 21s + 36)/(s3 + 8s2+ 17s +10)
(1) Draw the signal-flow graph state model in
(a) phase variable canonical form
(b) input feedforward canonical form
(c) diagonal canonical form
(2) Find the state space representation x.(t) = Ax(t) + Br(t), y(t) = Cx(t) + Dr(t) for each canonical form in (1).
Question 4. Consider the feedback control system in Figure 3, where R(s) is the reference input and D(s) represents the disturbance.
![773_Figure2.jpg](https://secure.tutorsglobe.com/CMSImages/773_Figure2.jpg)
(a) Derive the transfer function Y(s)/D(s).
(b) Assume the reference input r(t) = 0 and that the parameter K operates within the range that ensures closed-loop stability. Use the final value theorem to find the steady-state response of y(t) to a unit step disturbance.
(c) Let the disturbance d (t) = 0. Find the steady-state error ess to a unit ramp input r(t) = t.
(d) Let the disturbance d (t) = 0. Determine the sensitivity of the closed-loop system to the parameter K.
(e) Let the disturbance d (t) = 0. Using the Routh-Hurwitz criterion, determine the range of K such that the closed-loop system is stable.