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1. Consider the standard unity feedback system with the feedforward transfer function K(a+3) 82-2 KG(s) Using...
4. (20%) For the unity-feedback system whose feedforward transfer function is K(sub) i K>0, b>a >...
4. (20%) For the unity-feedback system whose feedforward transfer function is K(sub) i K>0, b>a > 3 (s + a)(s* +45 + 5) (a) (10%) Sketch the root-locus plot. (b) (5%) Determine center and angle of asymptotes. (c) (5%) If a > 0 and b>0, what is the constraint on values of a and b to guarantee that the closed-loop system is stable?
Question# 1 (25 points) For a unity feedback system with open loop transfer function K(s+10)(s+20) (s+30)(s2-20s+2...
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...
Consider the following unity feedback system for Problems 2-3 R(9) —tqKAG YIS) Figure 1 Problem 2...
Consider the following unity feedback system for Problems 2-3 R(9) —tqKAG YIS) Figure 1 Problem 2 Consider the system shown in the above figure, where G(s) = s(8+1128+1) a) Draw a Bode diagram of the open-loop transfer function G(s) when K=1. b) On your plot, indicate the crossover frequencies, PM, and GM. Is the closed-loop system stable with K=1? c) Determine the range of K for which the closed-loop systems will be stable. d) Verify your answer in (c) using...
Consider the unity feedback system is given below R(S) C(s) G(s) with transfer function: G() =...
Consider the unity feedback system is given below R(S) C(s) G(s) with transfer function: G() = K(+2) s(s+ 1/s + 3)(+5) a) Sketch the root locus. Clearly indicate any asymptotes. b) Find the value of the gain K, that will make the system marginally stable. c) Find the value of the gain K, for which the closed-loop transfer function will have a pole on the real axis at (-0.5).
A unity gain negative feedback system has an open-loop transfer function given by 4. s) =...
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...
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)...
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...
Consider a unity feedback control system with open loop transfer function KG(G) s(s+2)(s + 6) 1....
Consider a unity feedback control system with open loop transfer function KG(G) s(s+2)(s + 6) 1. Write the characteristic equation of the system 2. Determine the open loop poles and open loop zeros of the system 3. Are there any zeros in infinity? If yes, how many? 4. Sketch the segments of root locus on real axis 5. Determine and sketch the center and the angles of the asymptotes
Problem 3: Consider a unity feedback system with a plant model given by 10(s- 5) and a controller...
Problem 3: Consider a unity feedback system with a plant model given by 10(s- 5) and a controller given by s + p for K 0 and some real z and p. a) Use the root-locus technique to determine the sign of z and p so that the closed-loop system is stable for all K E (0, K) for some Ku> 0. b) Sketch the possible forms of the root-locus in terms of the pole and zero locations of Ge(s)....
Consider the following controller in a unity feedback configuration: (s + 10) C(s) = k· (s...
Consider the following controller in a unity feedback configuration: (s + 10) C(s) = k· (s + 5) (a) (by hand) Using an approximation for the plant P(s) a 11 S +2)(s2 + 5s + 25) determine the proper L(s) and sketch an accurate Root Locus plot (b) (by hand) Once you have established the Root Locus, determine the range of k values that guarantees closed-loop stability using the L(jw) method along with the Root Locus plot.
7. Consider a unity feedback control system with open-loop transfer function G(s) = k 5 s...
7. Consider a unity feedback control system with open-loop transfer function G(s) = k 5 s + 2)(52 + 4s + 5) Find the value of gain K > 0 for which the root locus crosses the imaginary axis.
4. (20%) For the unity-feedback system whose feedforward transfer function is K(sub) i K>0, b>a > 3 (s + a)(s* +45 + 5) (a) (10%) Sketch the root-locus plot. (b) (5%) Determine center and angle of asymptotes. (c) (5%) If a > 0 and b>0, what is the constraint on values of a and b to guarantee that the closed-loop system is stable?
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...
Consider the following unity feedback system for Problems 2-3 R(9) —tqKAG YIS) Figure 1 Problem 2 Consider the system shown in the above figure, where G(s) = s(8+1128+1) a) Draw a Bode diagram of the open-loop transfer function G(s) when K=1. b) On your plot, indicate the crossover frequencies, PM, and GM. Is the closed-loop system stable with K=1? c) Determine the range of K for which the closed-loop systems will be stable. d) Verify your answer in (c) using...
Consider the unity feedback system is given below R(S) C(s) G(s) with transfer function: G() = K(+2) s(s+ 1/s + 3)(+5) a) Sketch the root locus. Clearly indicate any asymptotes. b) Find the value of the gain K, that will make the system marginally stable. c) Find the value of the gain K, for which the closed-loop transfer function will have a pole on the real axis at (-0.5).
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...
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...
Consider a unity feedback control system with open loop transfer function KG(G) s(s+2)(s + 6) 1. Write the characteristic equation of the system 2. Determine the open loop poles and open loop zeros of the system 3. Are there any zeros in infinity? If yes, how many? 4. Sketch the segments of root locus on real axis 5. Determine and sketch the center and the angles of the asymptotes
Problem 3: Consider a unity feedback system with a plant model given by 10(s- 5) and a controller given by s + p for K 0 and some real z and p. a) Use the root-locus technique to determine the sign of z and p so that the closed-loop system is stable for all K E (0, K) for some Ku> 0. b) Sketch the possible forms of the root-locus in terms of the pole and zero locations of Ge(s)....
Consider the following controller in a unity feedback configuration: (s + 10) C(s) = k· (s + 5) (a) (by hand) Using an approximation for the plant P(s) a 11 S +2)(s2 + 5s + 25) determine the proper L(s) and sketch an accurate Root Locus plot (b) (by hand) Once you have established the Root Locus, determine the range of k values that guarantees closed-loop stability using the L(jw) method along with the Root Locus plot.
7. Consider a unity feedback control system with open-loop transfer function G(s) = k 5 s + 2)(52 + 4s + 5) Find the value of gain K > 0 for which the root locus crosses the imaginary axis.
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