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4. The Nyquist Diagram (for z-ear with 0 < ??< ?) of the open-loop gain, G(z)H(z),...
The open loop transfer function of an electro-mechanical system with unity feedback is: 24K G(s) S(s+2)(s +6) The Nyquist diagram of G(s) has a shape similar to the one shown below Nyquist diagram Cl...
The open loop transfer function of an electro-mechanical system with unity feedback is: 24K G(s) S(s+2)(s +6) The Nyquist diagram of G(s) has a shape similar to the one shown below Nyquist diagram Cl When K -1, calculate both the frequency and the gain at which the plot crosses the real axis Hence state the gain margin or critical gain Kc for this system. If K is chosen as K-0.2Kc, show that the gain G(jo) l at a frequency ω-1.308...
(i)Apply the Nyquist criterion to find the gain Kp at which the closed loop system becomes...
(i)Apply the Nyquist criterion to find the gain Kp at which the
closed loop system becomes marginally stable and the practical
range of safe operating gains for the proportional controller.
(ii) Find the gain margin of the system when the operating gain
of the controller Kp = 2. Use Fig. 2 to read the required values
off the plot.
Proportional Controller Process R(S) Y() Figure 1: Unity Feedback Systems Consider again the system in Fig. 1. The plant transfer function...
A closed-loop unity feedback system has the loop gain G(z) given below. (a) Show that the...
A closed-loop unity feedback system has the loop gain G(z) given below. (a) Show that the system is unstable using the Routh-Hurwitz criterion. (b) Show that the system is unstable by examining its Nyquist plot. (c) Use MATLAB to determine the gain margin of the system. (d) Now decrease the gain of the system by approximately 1 dB by setting G(z) 3. equal to Gn(z) as given below and show that the resulting system is stable by repeating steps (a)...
. S3 G(s) H (s) = K s2 + s-4 For the closed loop system use a Nyquist plot to, a. Classify the st...
. S3 G(s) H (s) = K s2 + s-4 For the closed loop system use a Nyquist plot to, a. Classify the stability of the system. b. Find the range of K for a stable system. (analytic by hand) c. Find the value of K for a marginally stable system. (analytic by hand)
. S3 G(s) H (s) = K s2 + s-4 For the closed loop system use a Nyquist plot to, a. Classify the stability of the...
2. The Nyquist diagram of a system's loop transfer function is shown in Figure 2. Assume...
2. The Nyquist diagram of a system's loop transfer function is shown in Figure 2. Assume that H(s) 1 and G(s) has no poles in the right half plane. Now suppose a gain K is cascaded with G(s) Find the range of positive K for which the system is stable. Im Re 18 0.5 Figure 2
A2. (a) Explain how the open-loop polar plot can be used to assess closed-loop stability by...
A2. (a) Explain how the open-loop polar plot can be used to assess closed-loop stability by applying Nyquist's stability criterion. Apply Nyquist's stability criterion to determine the stability condition for a closed-loop system that is unstable in the open-loop. [30%] = K (b) An unstable system has transfer function given by G(S) in which the gain K is S(S-2) positive. A derivative compensator H(s) = 0.5s + 1 is inserted in the negative feedback path to form a control loop....
(9) Draw a Nyquist plot of the following open-loop transfer function, and determine whether the closed-loop system is stable by using the Nyquist stability criterion. (12 points) Go)HG)(45+8)...
(9) Draw a Nyquist plot of the following open-loop transfer function, and determine whether the closed-loop system is stable by using the Nyquist stability criterion. (12 points) Go)HG)(45+8)
(9) Draw a Nyquist plot of the following open-loop transfer function, and determine whether the closed-loop system is stable by using the Nyquist stability criterion. (12 points) Go)HG)(45+8)
Figure 1 shows a closed-loop control system in which G(S)=40/[ (S+2) (S+3)], and H(S)=1/(S+4) R(3) +...
Figure 1 shows a closed-loop control system in which G(S)=40/[ (S+2) (S+3)], and H(S)=1/(S+4) R(3) + E(S) Y() G(s) H(S) Figure 2 shows the Nyquist plot for the open-loop transfer function. Nywist Diagram Systems imag: 2.5606 FC-56 THVL AM On RAH System: sys Real: -0.187 Imag: 2.56e-05 Frequency: (rad/s): -5.16 Figure 2 shows the Nyquist plot for the open-loop transfer function. Nyulat Diagram 05 Systems imag: 250 os ghar Axle 5.10 05 System: sys Real: -0.187 Imag: 2.56e-05 Frequency: (rad/s):...
Figure 1 shows a closed-loop control system in which G(S)=40/[ (S+2) (S+3)], and H(S)=1/(S+4) R(S) E(S)...
Figure 1 shows a closed-loop control system in which G(S)=40/[ (S+2) (S+3)], and H(S)=1/(S+4) R(S) E(S) Y(s) G(S) HS) Figure 2 shows the Nyquist plot for the open-loop transfer function. Figure 2 shows the Nyquist plot for the open-loop transfer function System: sys Real: -0.187 Imag: 2.56e-05 Frequency: (rad/s): -5.16 Using the Nyquist criterion: a) Find out the gain margin expressed in dB. Is the system stable or unstable? (25 points) b) What is the value of the gain expressed...
A feedback control system with adjustable gain K is shown as in Figure 4.1. Here, Q4 1 and H (s) where b 2a bs +a G(s)=...
A feedback control system with adjustable gain K is shown as in Figure 4.1. Here, Q4 1 and H (s) where b 2a bs +a G(s)= 3(s+a) Y(s) R(s) G(s) К H(s) Figure 4.1 A feedback control system with adjustable gain Sketch Nyquist plot for G(s)H(s) for 0.9 <a < 1.1. (a) (18 marks) (b) Discuss the stability of closed-loop system with open-loop function as in (a) if K 10b (7 marks)
A feedback control system with adjustable gain K...
The open loop transfer function of an electro-mechanical system with unity feedback is: 24K G(s) S(s+2)(s +6) The Nyquist diagram of G(s) has a shape similar to the one shown below Nyquist diagram Cl When K -1, calculate both the frequency and the gain at which the plot crosses the real axis Hence state the gain margin or critical gain Kc for this system. If K is chosen as K-0.2Kc, show that the gain G(jo) l at a frequency ω-1.308...
(i)Apply the Nyquist criterion to find the gain Kp at which the
closed loop system becomes marginally stable and the practical
range of safe operating gains for the proportional controller.
(ii) Find the gain margin of the system when the operating gain
of the controller Kp = 2. Use Fig. 2 to read the required values
off the plot.
Proportional Controller Process R(S) Y() Figure 1: Unity Feedback Systems Consider again the system in Fig. 1. The plant transfer function...
A closed-loop unity feedback system has the loop gain G(z) given below. (a) Show that the system is unstable using the Routh-Hurwitz criterion. (b) Show that the system is unstable by examining its Nyquist plot. (c) Use MATLAB to determine the gain margin of the system. (d) Now decrease the gain of the system by approximately 1 dB by setting G(z) 3. equal to Gn(z) as given below and show that the resulting system is stable by repeating steps (a)...
. S3 G(s) H (s) = K s2 + s-4 For the closed loop system use a Nyquist plot to, a. Classify the stability of the system. b. Find the range of K for a stable system. (analytic by hand) c. Find the value of K for a marginally stable system. (analytic by hand)
. S3 G(s) H (s) = K s2 + s-4 For the closed loop system use a Nyquist plot to, a. Classify the stability of the...
2. The Nyquist diagram of a system's loop transfer function is shown in Figure 2. Assume that H(s) 1 and G(s) has no poles in the right half plane. Now suppose a gain K is cascaded with G(s) Find the range of positive K for which the system is stable. Im Re 18 0.5 Figure 2
A2. (a) Explain how the open-loop polar plot can be used to assess closed-loop stability by applying Nyquist's stability criterion. Apply Nyquist's stability criterion to determine the stability condition for a closed-loop system that is unstable in the open-loop. [30%] = K (b) An unstable system has transfer function given by G(S) in which the gain K is S(S-2) positive. A derivative compensator H(s) = 0.5s + 1 is inserted in the negative feedback path to form a control loop....
(9) Draw a Nyquist plot of the following open-loop transfer function, and determine whether the closed-loop system is stable by using the Nyquist stability criterion. (12 points) Go)HG)(45+8)
(9) Draw a Nyquist plot of the following open-loop transfer function, and determine whether the closed-loop system is stable by using the Nyquist stability criterion. (12 points) Go)HG)(45+8)
Figure 1 shows a closed-loop control system in which G(S)=40/[ (S+2) (S+3)], and H(S)=1/(S+4) R(3) + E(S) Y() G(s) H(S) Figure 2 shows the Nyquist plot for the open-loop transfer function. Nywist Diagram Systems imag: 2.5606 FC-56 THVL AM On RAH System: sys Real: -0.187 Imag: 2.56e-05 Frequency: (rad/s): -5.16 Figure 2 shows the Nyquist plot for the open-loop transfer function. Nyulat Diagram 05 Systems imag: 250 os ghar Axle 5.10 05 System: sys Real: -0.187 Imag: 2.56e-05 Frequency: (rad/s):...
Figure 1 shows a closed-loop control system in which G(S)=40/[ (S+2) (S+3)], and H(S)=1/(S+4) R(S) E(S) Y(s) G(S) HS) Figure 2 shows the Nyquist plot for the open-loop transfer function. Figure 2 shows the Nyquist plot for the open-loop transfer function System: sys Real: -0.187 Imag: 2.56e-05 Frequency: (rad/s): -5.16 Using the Nyquist criterion: a) Find out the gain margin expressed in dB. Is the system stable or unstable? (25 points) b) What is the value of the gain expressed...
A feedback control system with adjustable gain K is shown as in Figure 4.1. Here, Q4 1 and H (s) where b 2a bs +a G(s)= 3(s+a) Y(s) R(s) G(s) К H(s) Figure 4.1 A feedback control system with adjustable gain Sketch Nyquist plot for G(s)H(s) for 0.9 <a < 1.1. (a) (18 marks) (b) Discuss the stability of closed-loop system with open-loop function as in (a) if K 10b (7 marks)
A feedback control system with adjustable gain K...
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