G(s) = K(s + 2) (s2 + 9)/(s-2)(s+6) For the system above, find the following through calculations:
G(s) = K(s + 2) (s2 + 9)/(s-2)(s+6)
For the system above, find the following through calculations:
a) Sketch the root locus by hand, labeling all relevant points on your plot.
a. Open Loop Poles and Zeros.
b. Centroid (if there are any)
c. Asymptotes (if there are any)
d. Break away points (if there are any).
e. Location where the poles cross into the Right Half Plane
b) Discuss the stability of the system as the gain changes (i.e. does the system ever become unstable?). Find the specific range of K for which the system is Stable.
c) Use Matlab/Simulink to validate your hand drawing.
Homework Answers
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G(s) = K(s + 2) (s2 + 9)/(s-2)(s+6) For the system above, find the following through calculations:
Problem 3: (30) Consider the following systen where K is a proportional gain (K>0). s-2 (a) Sketch the root locus us...
Problem 3: (30) Consider the following systen where K is a proportional gain (K>0). s-2 (a) Sketch the root locus using the below procedures. (1) find poles and zeros and locate on complex domain (2) find number of branches (3) find asymptotes including centroid and angles of asymptotes (4) intersection at imaginary axis (5) find the angle of departure (6) draw the root migration (b) Find the range of K for which the feedback system is asymptotically stable.
Problem 3:...
QUESTION 2: Again, for the feedback control system from Question 1, Let G(S) 3 +27 s2 +218 s+504 ...
QUESTION 2: Again, for the feedback control system from Question 1, Let G(S) 3 +27 s2 +218 s+504 s2 +6s+34 Part a) What are the poles and zeroes of G(s)? Part b) Plot the root-locus using RLOCUS.M - Refer to the MATLAB notes in the back of this handout. - Be sure to indicate the direction of "increasing K" on each branch Part c) Comment on this root-locus plot How it pertains to poles and zeros of G(s), etc. Are...
Root Locus: Consider the following system
Root Locus: Consider the following system (a) What are the poles of the open loop system (locations of the open loop poles)? What are zeros of the open loop system (locations of the zeros)? (b) What is the origin of the asymptotes? (c) What are the angles of asymptotes? (d) Find the break-away and break-in points. (e) Find the angles of departure for all the poles. (f) Draw the root locus plot of G(s). (g) For what values of K is the closed loop system stable?
Sketch the root locus of the given system above with respect to k
Sketch the root locus of the given system above with respect to k [Find the asymptotes and their angles, the break-away or break-in points, the angle of arrival or departure for the complex poles and zeros imaginary axis crossing points, respectively (if any).]
Theroot-locus design method (d) Gos)H(s)2) 5.5 Complex poles and zeros. For the systems with an open-loop transfer function given below, sketch the root locus plot. Find the asymptotes and their angle...
Theroot-locus design method
(d) Gos)H(s)2) 5.5 Complex poles and zeros. For the systems with an open-loop transfer function given below, sketch the root locus plot. Find the asymptotes and their angles. the break-away or break-in points, the angle of arrival or departure for the complex poles and zeros, respectively, and the range of k for closed-loop stability 5 10ん k(s+21
(d) Gos)H(s)2) 5.5 Complex poles and zeros. For the systems with an open-loop transfer function given below, sketch the root...
Problem S Consider the control system shown in Figure 4 let Cand G,() -K and Gc...
Problem S Consider the control system shown in Figure 4 let Cand G,() -K and Gc (s) K (s-1) (s+2) (s+3) (a) Determine the open-loop system (i.e., G (s)) poles and zeros. (b) Determine the number of asymptotes and the angles of asymptotes. (c) Determine the break-in/break-out points (if any) (d) Sketch the root locus (e) Determine the value of K (if any) for which the system is marginally stable
Consider proportional feedback control as shown below. r(t) For each G(s) in the following problems A....
Consider proportional feedback control as shown below. r(t) For each G(s) in the following problems A. Sketch the root locus. Clearly show the open-loop poles and zeros, and the high-gain asymptotes on your sketch. Calculate the centroid to assure that the high gain asymptotes are accurate. B. If your sketch reveals any break-in or break-away points, calculate those location C. Does your sketch reveal a jo- crossing? If so, stability may be an issue. D. A damping ratio of 7-...
The characteristic equation (denominator of the closed-loop transfer function set equal to zero) is given s3 + 2s2 + (20K +7)s+ 100K Sketch the root locus of the given system above with respect to...
The characteristic equation (denominator of the closed-loop transfer function set equal to zero) is given s3 + 2s2 + (20K +7)s+ 100K Sketch the root locus of the given system above with respect to K. [ Find the asymptotes and their angles, the break-away or break-in points, the angle of arrival or departure for the complex poles and zeros, imaginary axis crossing points, respectively (if any).
The characteristic equation (denominator of the closed-loop transfer function set equal to zero) is...
Problem 2 For the unity feedback system below in Figure 2 G(s) Figure 2. With (8+2) G(s) = (a) Sk...
Problem 2 For the unity feedback system below in Figure 2 G(s) Figure 2. With (8+2) G(s) = (a) Sketch the root locus. 1. Draw the finite open-loop poles and zeros. ii. Draw the real-axis root locus iii. Draw the asymptotes and root locus branches. (b) Find the value of gain that will make the system marginally stable. (c) Find the value of gain for which the closed-loop transfer function will have a pole on the real axis at s...
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...
Problem 3: (30) Consider the following systen where K is a proportional gain (K>0). s-2 (a) Sketch the root locus using the below procedures. (1) find poles and zeros and locate on complex domain (2) find number of branches (3) find asymptotes including centroid and angles of asymptotes (4) intersection at imaginary axis (5) find the angle of departure (6) draw the root migration (b) Find the range of K for which the feedback system is asymptotically stable.
Problem 3:...
QUESTION 2: Again, for the feedback control system from Question 1, Let G(S) 3 +27 s2 +218 s+504 s2 +6s+34 Part a) What are the poles and zeroes of G(s)? Part b) Plot the root-locus using RLOCUS.M - Refer to the MATLAB notes in the back of this handout. - Be sure to indicate the direction of "increasing K" on each branch Part c) Comment on this root-locus plot How it pertains to poles and zeros of G(s), etc. Are...
Theroot-locus design method
(d) Gos)H(s)2) 5.5 Complex poles and zeros. For the systems with an open-loop transfer function given below, sketch the root locus plot. Find the asymptotes and their angles. the break-away or break-in points, the angle of arrival or departure for the complex poles and zeros, respectively, and the range of k for closed-loop stability 5 10ん k(s+21
(d) Gos)H(s)2) 5.5 Complex poles and zeros. For the systems with an open-loop transfer function given below, sketch the root...
Problem S Consider the control system shown in Figure 4 let Cand G,() -K and Gc (s) K (s-1) (s+2) (s+3) (a) Determine the open-loop system (i.e., G (s)) poles and zeros. (b) Determine the number of asymptotes and the angles of asymptotes. (c) Determine the break-in/break-out points (if any) (d) Sketch the root locus (e) Determine the value of K (if any) for which the system is marginally stable
Consider proportional feedback control as shown below. r(t) For each G(s) in the following problems A. Sketch the root locus. Clearly show the open-loop poles and zeros, and the high-gain asymptotes on your sketch. Calculate the centroid to assure that the high gain asymptotes are accurate. B. If your sketch reveals any break-in or break-away points, calculate those location C. Does your sketch reveal a jo- crossing? If so, stability may be an issue. D. A damping ratio of 7-...
The characteristic equation (denominator of the closed-loop transfer function set equal to zero) is given s3 + 2s2 + (20K +7)s+ 100K Sketch the root locus of the given system above with respect to K. [ Find the asymptotes and their angles, the break-away or break-in points, the angle of arrival or departure for the complex poles and zeros, imaginary axis crossing points, respectively (if any).
The characteristic equation (denominator of the closed-loop transfer function set equal to zero) is...
Problem 2 For the unity feedback system below in Figure 2 G(s) Figure 2. With (8+2) G(s) = (a) Sketch the root locus. 1. Draw the finite open-loop poles and zeros. ii. Draw the real-axis root locus iii. Draw the asymptotes and root locus branches. (b) Find the value of gain that will make the system marginally stable. (c) Find the value of gain for which the closed-loop transfer function will have a pole on the real axis at s...
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...
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