Prob 4 For each of the open-loop transfer functions of unity negative feedback systems given below,...
A unity gain negative feedback system has an open-loop transfer function given by 4. s) = s(1 + 10s)(1 + 10s)? Draw a Bode diagram for this system and determine the loop gain K required for a phase margin of 20 deg. What is the gain margin? 5. We are given the closed-loop transfer function 10(s + 1) T(s) = 82+98+10 for a "unity feedback" system and asked to find the open-loop transfer function, generate a log-magnitude-phase plot for both...
3. The open loop transfer function of a unity feedback system is given by \(G(S)=\frac{K}{S(1+S T)}\) Where Tand \(\mathrm{K}\) are constants having positive values. By what factor the amplifier gain be reduced so that (a) peak overshoot of unit step response of the system is reduced from \(75 \%\) to \(25 \% .\) b) The damping ratio increases from \(0.1\) to \(0.6\).
Problem 5. (20pts) The open-loop transfer function of a unity feedback system G(8) -- +2) a) Locate open-loop zeros and open-loop poles. b) Construct the root-locus diagram as 0 <K <oo. Mark the portions of the real axis that belong to the root locus - Mark with K =0 the point where the root locus bra O the point where the root locus branches start and with K = oo the point where the branches end. - Find break-away and/or...
1 Sketch the root locus for the unity feedback systems that have an open-loop transfer function of: 6. G(S) = k(s? +1) (s - 1)(8 + 2)(8+3)
please solve If a system has the open-loop transfer function G(s) s(s+25n) with unity feedback, then the closed-loop transfer function is given b T(s) s2+20ns+wf Verify the values of the PM shown in Fig. 6.36 for = 0.1,0.4, and 0.7. Figure 6.36 Damping ratio versus 1.0 0.8 PM 2 0.6 0,4 0.2 0 0° 10° 20° 30° 40° 50 60° 70° 80° Phase margin Damping ratio, If a system has the open-loop transfer function G(s) s(s+25n) with unity feedback, then...
2. Given a unity feedback system with open-loop transfer function s+40s-I) a) For K-1, derive the expressions for the real and imaginary parts of G(jo). b) What happen to the real and imaginary parts of G(jo) for ω 0 and for Are there values of ω that either the real or imaginary part goes to zero? If not, compute Gijo) for some ovalue, say,, or 2, to help you sketch the Polar plot of Gja). c) d) Use Matlab to...
Question# 1 (25 points) For a unity feedback system with open loop transfer function K(s+10)(s+20) (s+30)(s2-20s+200) G(s) = Do the following using Matlab: a) Sketch the root locus. b) Find the range of gain, K that makes the system stable c) Find the value of K that yields a damping ratio of 0.707 for the system's closed-loop dominant poles. d) Obtain Ts, Tp, %OS for the closed loop system in part c). e) Find the value of K that yields...
4) A unity feedback control system shown in Figure 2 has the following controller and process with the transfer functions: m(60100c Prs(s +10(s+7.5) a) Obtain the open- and closed-loop transfer functions of the system. b) Obtain the stability conditions using the Routh-Hurwitz criterion. e) Setting by trial-and-error some values for Kp, Ki, and Ko, obtain the time response for minimum overshoot and minimum settling time by Matlab/Simulink. Y(s) R(s) E(s) Fig. 2: Unity feedback control system 4) A unity feedback...
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...
Spring 2019 3. Given a closed-loop control system with unity feedback is shown in the block diagram. G(s) is the open-loop transfer function, and the controller is a gain, K. 1. (20) Calculate the open-loop transfer function tar →Q--t G(s) (10) Calculate the steady-state error to a step input of the open-loop system. 7. (in Bode Form) from the Bode plot. (10) Calculate the shortest possible settling time with a percentage overshoot of 5% or less. 8. 2. (10)Plot the...