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(a) (i) Show that the sensitivity of the closed-loop transfer function T(s) to variations in the...
Determine: 1. The transfer function C(s)/R(s). Also find the closed-loop poles of the system. 2. The values of the undamped natural frequency ωN and damping ratio ξ of the closed-loop poles. 3. The expressions of the rise time, the peak time, the maximum overshoot, and the 2% settling time due to a unit-step reference signal. For the open-loop process with negative feedback R(S) Gp(S) C(s) H(s) 103 Go(s) = 1 , Gp(s)- s(s + 4) Determine: 1. The transfer function...
Determine the proportioanl gain constant Kp and T such that the bandwidth of the closed-loop system is around 0.55 rad/sec and an overshoot of around 9%. Note that the closed-loop bandwidth is close to the gain crossover (cut-off) frequency. Check your design in both frequency and time domain and comment. Determine the maximum overshoot and settling time. Determine as well, using a Bode diagram, the expression of the stead state closed loop output for a sinusodial input with 0 deg...
question b or the control system in Figure 1: C(s) Find the closed-loop transfer function T(s)-- R(s) a) b) Find a value of Kp that will yield less than 15% overshoot for the closed-loop system. (Note: ignore the zero dynamics to calculate Kp initially). c IIsing vour K from nart h) write a MATI AR scrint that calculates the closedloon Motor Plant R(s)+ C(s) Controller 10 Kp (s+9) s2 +6s15 12 Figure 1: Unity feedback with PD control or the...
Q.4 A position control system is shown in Figure Q4. Assume that K(s) = K, the plant 50 s(0.2s +1) transfer function is given by G(s) s02s y(t) r(t) Figure Q4: Feedback control system. (a) Design a lead compensator so that the closed-loop system satisfies the following specifications (i) The steady-state error to a unit-ramp input is less than 1/200 (ii) The unit-step response has an overshoot of less than 16% Ts +1 Hint: Compensator, Dc(s)=aTs+ 1, wm-T (18 marks)...
A system with a closed-loop transfer function of the form: T(S) = 10(s + 7) (s + 10)(s + 20) has a(n) ......... .... response. critically damped overdamped undamped underdamped
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...
Closed-loop system response and characteristics, Proportional gain 10 < paste transfer function Ts as output from Matlab here> clear all: close all: ls J = 0.022R = 0.11;K = 0.02;R 1.5;L= 0.6; Closed loop Transfer function T(s) Cs-10; RRA pole (Tg) 22T zero (Tg) figure ; figure ; teS) characteristics natural frequency damping ratio Dr-abs(real (RpT (2)) ) / ettling time peak time ER忌 overshoot 032=100 rise time Step response of open-loop system: Pole-zero map: easte,pole-zero plot here> Pole-Zero Map...
Y(s) C(s) G(s) R(S) Figure 1: Closed-loop system Q2 Consider the setup in Figure 1 with S s1 (i) Design a K,τ, α in the lead compensator 1TOS so that the closed-loop system shown in Figure 1 has a steady state error of.0 for a unit ramp reference input at R and a phase margin of about 45 degrees K, α, τ without Bode plots. When you add phase with the lead compensator add an additional 10 degrees of phase....
For the given closed loop system, where: C(s)= 9.43 s+ 9.56 G(s)= 87.84 / ( s2+ 2.94 s+ 9.00 ) Part A: Obtain the rise time of the step response of the plant transfer function G(s). Part B: Obtain the overshoot of the step response of the plant transfer function G(s). Part C: Obtain the 1% settling time of the step response of the plant transfer function G(s). Part D: Obtain the natural frequency ωn of the characteristic polynomial of...
Q3. Consider a single loop unity feedback control system of the open loop transfer function (a) Find the range of values of the gain K and the parameter p so that: (i) The overshoot is less than 10%. (ii)The settling time is less than 4 seconds Note: , 4.6 M. = exp CO 40% (b)What are the three elements in a PID controller? Considering each in turn, explain the main ways in which varying the parameters affects the closed-loop system...