QUESTION ONE (a) Determine the stability of the system whose overall transfer function is given below;...
Q2. Fig Q2 shows the block diagram of an unstable system with transfer function G(s) - under the control of a lead compensator (a) Using the Routh's stability criterion, determine the conditions on k and a so that the closed-loop system is stable, and sketch the region on the (k, a)- plane where the conditions are satisfied. Hence, determine the minimum value of k for the lead compensator to be a feasible stabilizing controller. (10 marks) (b) Suppose α-2. Given...
3. For the feedback control system shown in Figure Q3 below, the forward-path transfer function given by G(s) and the sensor transfer function is given by H(s). R(s) C(s) G(s) H(s) Figure Q3 It is known that G(s) -- K(+20) S(+5) H(s) = and K is the proportional gain. (S+10) i. Determine the closed-loop transfer function and hence the characteristic equation of the system. [6 marks] ii. Using the Routh-Hurwitz criterion, determine the stability of the closed-loop system. Determine the...
(10 pts) 2. Determine the range of K for stability of a unity feedback control system whose open-loop transfer function is: K(2s +1) G(s)= s(s-1)(s+2)
A robot force control system with unity feedback has a loop transfer function [6 7.11 Tood transfer function (6l K(s +2.5) (s2 + 2s 2) (s2 + 4s + 5) (a) Find the gain K that results in dominant roots with a damping ratio of 0.707. Sketch the root locus. (b) Find the actual percent overshoot and peak time for the gain K of part (a)
A robot force control system with unity feedback has a loop transfer function [6...
Sketch the root loci for a unity control system, whose open-loop
transfer function is given by
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Sketch the root loci for a unity control system, whose open-loop transfer function is given by G(s) = K/s(s^2 + 4s + 5)
A2. (a) Explain how the open-loop polar plot can be used to assess closed-loop stability by applying Nyquist's stability criterion. Apply Nyquist's stability criterion to determine the stability condition for a closed-loop system that is unstable in the open-loop. [30%] = K (b) An unstable system has transfer function given by G(S) in which the gain K is S(S-2) positive. A derivative compensator H(s) = 0.5s + 1 is inserted in the negative feedback path to form a control loop....
1) Plot the root locus of the system whose characteristic equation is 2) Plot the root locus of the closed loop system whose open-loop transfer function is given as 2s + 2 G(S)H(S)+7s3 +10s2 3) Plot root locus of the closed-loop system for which feedforward transfer function is s + 1 G(S) s( ) St(s - and feedback transfer function is H(S)2 +8s +32
1) Plot the root locus of the system whose characteristic equation is 2) Plot the root...
A. Consider the characteristic equations below, comment on their system stability? 1. D(s)=s4 +253 +852 + 4s + 3 2. D(s)=s5 +54 +353 +352 + 6s + 4 B. Find the range of values of K for the closed loop system to remain stable? R(s) C(s) K s(s? +5 +1)(8+3)(s+4)
Discuss the mathematical requirements for stability in a linear feedback system and state the Routh Stability criterion. (6 marks) (a) The open loop transfer function of a control system with unity feedback is given by: (b) 35 s(1 + Ts) (1 +0.25s) G(s) - Use Routh's criterion to determine the value of T for which the closed loop system is marginally stable. (8 marks) i Use the Nyquist criterion to confirm the values obtained in (i). (8 marks) ii Sketch...
Question 6 The open-loop transfer function G(s) of a control system is given as G(8)- s(s+2)(s +5) A proportional controller is used to control the system as shown in Figure 6 below: Y(s) R(s) + G(s) Figure 6: A control system with a proportional controller a) Assume Hp(s) is a proportional controller with the transfer function H,(s) kp. Determine, using the Routh-Hurwitz Stability Criterion, the value of kp for which the closed-loop system in Figure 6 is marginally stable. (6...