Reference no: EM131227811
CONTROL SYSTEMS
Solve all questions and show your step by step working
Q1: A system with unity feedback is shown in figure (1).
Use the Routh-Hurwitz stability criterion, determine if closed-loop system with
G(s) = 100(s +8)/(s +3)(s' +15s +10)(s +1) is stable or not.
Q2:
A closed-loop feedback system is shown in Figure. For what range of values of the parameters and p is the system stable?
FIGURE. Closed-loop system with parameters K and p.
Q3:
A closed-loop control system is shown in figure (3). where G(s) is the transfer function of the system. eG(s) is the transfer function of the controller, D(s) is a disturbance. R(s) and 17(r) are the input and output. respectively. The open-loop system is unstable with a transfer function of G(s) = 2/s-2
The objectives of the controller. G(s) are to make the closed-loop system stable and at the same thue to minimize the effect of the disturbance.
Consider a proportional-integral (P1) controller with a transfer function Gc(s) = (ks + 1)/s.
Answer the following questions:
(a) Determine the value of K so that the closed-loop system is stable and has a critically damped response
(b) Find the steady-state error for the case where R(s) = 1/s and D(s)= 0.
(c) Find the steady-state output of the system when R(s)= 0 and D(s)= 1/s.
(d) Base on the above analysis. explain whether the objectives of the controller have been met.
Q4:
A control system as shown in figure (4) has a transfer function of G(s) = 1/s(s-1)
(a) Let Gc(s) = K.By sketching the root-locus, show that the closed-loop system is always unstable.
(b) Let Gc(s)= K(s +2). Sketch the root-locus and show that the closed-loop system can be stabilized. Determine the range of K for the closed-loop system to remain stable.
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