5. Consider the system given in (a) is marginally stable. X + 4. 10/( s (0.1...
Wis) R(s u(s) 14 Gl(s) H(s) Given a system as in the diagram above, where K is an adjustable parameter pl(s) Dal(sKp+ g) Assuming W-0, find the transfer function Y(s)/R(s) h) Assuming R-0, find the transfer function Y(s)/W(s) i) What is the type of the system (with respect to steady-state error)? j) What is the steady-state error when rt)u(t) (unit-step) and w(t)-0 k) What is the s.s. error when r(t) t u(t) and w(t)-0 ) Assume r(t)-0, what is the...
1. Consider a feedback system given below: T(s) Disturbance Controller Dynamics R(S) + Gc(s) G.(s) U(s) Sensor H(s) IMs) Sensor noise where the input and transfer functions are given as follows: R(s) = –,7,(s) = 0, N(s) = 0, G, - 15,6, -_- , and H(s) = 1. s's + 3) a. Derive the system transfer function Y(s)/R(s) = G,, poles, $, On, and, from the response function y(t), the performance measures: rise time Tr, peak time Tp, percent overshoot...
The transfer function of the given physical system is 2500 Gp(s)-T-1000 Part 3 1. Frequency response (a) Draw the bode plot of open-loop transfer function when K (b) Use bode plot of open-loop transfer function to determine the type of system (do not use transfer function) (c) For what input the system will have constant steady-state error (d) for the unit input in item (c) calculate the constant steady-state error.(Use bode plot to calculate the error.) (e) Design a lead...
Consider the unity feedback system is given below R(S) C(s) G() with transfer function: G(s) = K s(s + 1)(s + 2)(8 + 6) a) Find the value of the gain K, that will make the system stable. b) Find the value of the gain K, that will make the system marginally stable. c) Find the actual location of the closed-loop poles when the system is marginally stable.
(30%) Consider a system with the transfer function Y(s) s+6-k (a) Determine the range of parameter k so that the system G(s) is stable. (b) Determine the value of k for which the system becomes marginally stable. (c) Assuming parameter k has the value in part(b) and hence the system is marginally stable, find a bounded input r(t) that results in unbounded output y(t). For this part, specifying the bounded input signal r(t) and a justification is enough Finding v(t)...
The below system given by G(s) = 1/[s(s2 + 5s + 4)] is None Marginally stable Unstable Stable
Q.3(a) Transfer function model of a plant is, G(s) The controller is Ge(s)-K, where K is a constant. Find the value of K such that steady-state error for unit ramp input is 0.1. Find the gain margin and the phase mar gin (6 marks) (b) What are the effects on gain margin, phase margin and steady-state error, if the gain K is increased? (3 marks (c) Can the closed loop be unstable if the controller of Q.3(a) is implemented digi...
5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sketch the it step response (a) G (s) = (c) G(s)-t 2+68+ (d) G (s) = 36 6. The equation of motion of a rotational mechanical system is given by where θ° and θί are respectively, output and input angular displace- ments. Assuming that all initial conditions are zero, determine (a) the transfer function model. (b) the natural frequency, w natural frequency,...
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...
5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sketch the it step response (a) G (s) = (c) G(s)-t 2+68+ (d) G (s) = 36 6. The equation of motion of a rotational mechanical system is given by where θ° and θί are respectively, output and input angular displace- ments. Assuming that all initial conditions are zero, determine (a) the transfer function model. (b) the natural frequency, w natural frequency,...