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P6.1. Figure P6.1 shows a simple negative feedback control system with a variable gain, K, in...
b) The Nyquist plot of a unity feedback control system is as shown in Figure Q5(b)....
b) The Nyquist plot of a unity feedback control system is as shown in Figure Q5(b). Nyqulst Diagram x 10 1.5 1- System: N Real: -9.08e-005 0.5- Imag: -5.62e-006 Frequency (rad/sec): -104 -0.5 -15 -1.5 0.5 0.5 1.5 1 2.5 3.5 Real Axis x 10 Figure Q5(b) K If the transfer function of the system is given as G(s) (s+10)(s+50)(s+150) determine the following: The closed loop stability of the system using Nyquist Stability Criterion. i) ii) Gain margin and phase...
1. Consider the usual unity-feedback closed-loop control system with a proportional-gain controll...
1. Consider the usual unity-feedback closed-loop control system with a proportional-gain controller Sketch (by hand) and fully label a Nyquist plot with K-1 for each of the plants listed below.Show all your work. Use the Nyquist plot to determine all values of K for which the closed-loop system is stable. Check your answers using the Routh-Hurwitz Stability Test. [15 marks] (a) P(s)-2 (b) P(s)-1s3 (c) P(s) -4-8 s+2 (s-2) (s+10)
1. Consider the usual unity-feedback closed-loop control system with a...
A unity feedback control system has the following open loop transfer function, K L(s) .If K 10, evaluate the stability...
A unity feedback control system has the following open loop transfer function, K L(s) .If K 10, evaluate the stability condition of the system using the s(s-1) Nyquist stability criterion.
A unity feedback control system has the following open loop transfer function, K L(s) .If K 10, evaluate the stability condition of the system using the s(s-1) Nyquist stability criterion.
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...
Find a & b Figure 1 shows a closed-loop control system in which G(S)-40/1 (S+2) (S+3)],...
Find a & b
Figure 1 shows a closed-loop control system in which G(S)-40/1 (S+2) (S+3)], and H(S)-1/(S+4) Y(s) H(s) 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 in dB that makes the system marginally stable? (25 points)
3. For the feedback control system shown in Figure Q3 below, the forward-path transfer function given...
3. For the feedback control system shown in Figure Q3 below, the forward-path transfer function given by G(s) and the sensor transfer function is given by H(s). R(s) C(s) G(s) H(s) Figure Q3 It is known that G(s) -- K(+20) S(+5) H(s) = and K is the proportional gain. (S+10) i. Determine the closed-loop transfer function and hence the characteristic equation of the system. [6 marks] ii. Using the Routh-Hurwitz criterion, determine the stability of the closed-loop system. Determine the...
Question 5 or a unity feedback system in Figure 4 C(s) (s+40%s +100) Figure 4 a) Find the value o...
Question 5 or a unity feedback system in Figure 4 C(s) (s+40%s +100) Figure 4 a) Find the value of gain, K, to yield a closed-loop response with 20% overshoot when the system is under a step input. Check the system stability at this gain value (use either Nyquist criterion or Margins). Assume the system is under a unity step input. Use Simulink to obtain and compare the time responses with and without gain adjustment and discuss how the response...
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...
1- [a] For positive values of K, plot the root locus for a unity negative feedback...
1- [a] For positive values of K, plot the root locus for a unity negative feedback control system having the following open-loop transfer function: K G(s)= (5 + 1)(8 + 4)(8 + 7) For what values of gain K does the system become unstable? Find also the value of k at which the damping ratio is 0.5 and the closed loop poles. (25%) [b] The characteristic equations of linear control systems are given below. Apply Routh-Hurwitz criterion to determine the...
Discuss the mathematical requirements for stability in a linear feedback system and state the Rou...
Discuss the mathematical requirements for stability in a linear feedback system and state the Routh Stability criterion. (6 marks) (a) The open loop transfer function of a control system with unity feedback is given by: (b) 35 s(1 + Ts) (1 +0.25s) G(s) - Use Routh's criterion to determine the value of T for which the closed loop system is marginally stable. (8 marks) i Use the Nyquist criterion to confirm the values obtained in (i). (8 marks) ii Sketch...
b) The Nyquist plot of a unity feedback control system is as shown in Figure Q5(b). Nyqulst Diagram x 10 1.5 1- System: N Real: -9.08e-005 0.5- Imag: -5.62e-006 Frequency (rad/sec): -104 -0.5 -15 -1.5 0.5 0.5 1.5 1 2.5 3.5 Real Axis x 10 Figure Q5(b) K If the transfer function of the system is given as G(s) (s+10)(s+50)(s+150) determine the following: The closed loop stability of the system using Nyquist Stability Criterion. i) ii) Gain margin and phase...
1. Consider the usual unity-feedback closed-loop control system with a proportional-gain controller Sketch (by hand) and fully label a Nyquist plot with K-1 for each of the plants listed below.Show all your work. Use the Nyquist plot to determine all values of K for which the closed-loop system is stable. Check your answers using the Routh-Hurwitz Stability Test. [15 marks] (a) P(s)-2 (b) P(s)-1s3 (c) P(s) -4-8 s+2 (s-2) (s+10)
1. Consider the usual unity-feedback closed-loop control system with a...
A unity feedback control system has the following open loop transfer function, K L(s) .If K 10, evaluate the stability condition of the system using the s(s-1) Nyquist stability criterion.
A unity feedback control system has the following open loop transfer function, K L(s) .If K 10, evaluate the stability condition of the system using the s(s-1) Nyquist stability criterion.
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...
Find a & b
Figure 1 shows a closed-loop control system in which G(S)-40/1 (S+2) (S+3)], and H(S)-1/(S+4) Y(s) H(s) 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 in dB that makes the system marginally stable? (25 points)
3. For the feedback control system shown in Figure Q3 below, the forward-path transfer function given by G(s) and the sensor transfer function is given by H(s). R(s) C(s) G(s) H(s) Figure Q3 It is known that G(s) -- K(+20) S(+5) H(s) = and K is the proportional gain. (S+10) i. Determine the closed-loop transfer function and hence the characteristic equation of the system. [6 marks] ii. Using the Routh-Hurwitz criterion, determine the stability of the closed-loop system. Determine the...
Question 5 or a unity feedback system in Figure 4 C(s) (s+40%s +100) Figure 4 a) Find the value of gain, K, to yield a closed-loop response with 20% overshoot when the system is under a step input. Check the system stability at this gain value (use either Nyquist criterion or Margins). Assume the system is under a unity step input. Use Simulink to obtain and compare the time responses with and without gain adjustment and discuss how the response...
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...
1- [a] For positive values of K, plot the root locus for a unity negative feedback control system having the following open-loop transfer function: K G(s)= (5 + 1)(8 + 4)(8 + 7) For what values of gain K does the system become unstable? Find also the value of k at which the damping ratio is 0.5 and the closed loop poles. (25%) [b] The characteristic equations of linear control systems are given below. Apply Routh-Hurwitz criterion to determine the...
Discuss the mathematical requirements for stability in a linear feedback system and state the Routh Stability criterion. (6 marks) (a) The open loop transfer function of a control system with unity feedback is given by: (b) 35 s(1 + Ts) (1 +0.25s) G(s) - Use Routh's criterion to determine the value of T for which the closed loop system is marginally stable. (8 marks) i Use the Nyquist criterion to confirm the values obtained in (i). (8 marks) ii Sketch...
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