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EEL 4652 Control Systems 1 (Fall 2018) Homework 4 Nyquist Stability Criterion + Frequency Domain Design...
Question 2 System Stability in the s-Domain and in the Frequency Domain: Bode Plots, Root Locus...
Question 2 System Stability in the s-Domain and in the Frequency Domain: Bode Plots, Root Locus Plots and Routh- Hurwitz Criterion ofStability A unit feedback control system is to be stabilized using a Proportional Controller, as shown in Figure Q2.1. Proportional Controller Process The process transfer function is described as follows: Y(s) G(s) s2 +4s 100 s3 +4s2 5s 2 Figure Q2.1 Your task is to investigate the stability of the closed loop system using s-domain analysis by finding: a)...
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...
(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)
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...
(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...
solve completely Routh Stability Criterion, Steady State Tracking Performance, Feedforward Control, Simulation of DC Motors Problem...
solve completely
Routh Stability Criterion, Steady State Tracking Performance, Feedforward Control, Simulation of DC Motors Problem 1: Consider the following control system: RIS) Y G() cs) Con traller Process The process transfer function is G(s) = Y(s) _ s* +3s' +30s2 + 30s + 200 s+6s s6s +200 U(s) 1.1. Are there any zeros of G(s) in RHP? How many? Use Routh table 1.2. Are there any poles of G(s) in RHP? How many? Use Routh table. Is G(s) stable?...
Question 1 Sketch the polar plot and use the Nyquist criterion to investigate the stability of...
Question 1 Sketch the polar plot and use the Nyquist criterion to investigate the stability of the system whose open loop transfer functions are 10 0 0. 100(1+3D) (3+D)(1+2D) 1602 (1+4D) (D+1)(D+100)
4. (10 points) For the feedback system with open loop transfer function 16/3 a. (6 pts) Draw the Root Locus and Nyquist plot of the system with no 16/3 S41 Using Nyquist stability criterion, find...
4. (10 points) For the feedback system with open loop transfer function 16/3 a. (6 pts) Draw the Root Locus and Nyquist plot of the system with no 16/3 S41 Using Nyquist stability criterion, find the critical value of the delay. b. (4 pts)
4. (10 points) For the feedback system with open loop transfer function 16/3 a. (6 pts) Draw the Root Locus and Nyquist plot of the system with no 16/3 S41 Using Nyquist stability criterion, find the...
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....
The Nyquist plot of a plant P in a unity feedback system is shown below. It is know that P has on...
The Nyquist plot of a plant P in a unity feedback system is
shown below. It is know that P has one pole with a non-negative
real part.
6.13 The Nyquist plot of a plant P in a unity feedback system is shown below. It is known that P has one pole with non-negative real part 1. What is the number of poles of P with zero real part? 2. What is the number of unstable poles of P? 3....
Question 2 System Stability in the s-Domain and in the Frequency Domain: Bode Plots, Root Locus Plots and Routh- Hurwitz Criterion ofStability A unit feedback control system is to be stabilized using a Proportional Controller, as shown in Figure Q2.1. Proportional Controller Process The process transfer function is described as follows: Y(s) G(s) s2 +4s 100 s3 +4s2 5s 2 Figure Q2.1 Your task is to investigate the stability of the closed loop system using s-domain analysis by finding: a)...
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...
(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)
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...
(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...
solve completely
Routh Stability Criterion, Steady State Tracking Performance, Feedforward Control, Simulation of DC Motors Problem 1: Consider the following control system: RIS) Y G() cs) Con traller Process The process transfer function is G(s) = Y(s) _ s* +3s' +30s2 + 30s + 200 s+6s s6s +200 U(s) 1.1. Are there any zeros of G(s) in RHP? How many? Use Routh table 1.2. Are there any poles of G(s) in RHP? How many? Use Routh table. Is G(s) stable?...
Question 1 Sketch the polar plot and use the Nyquist criterion to investigate the stability of the system whose open loop transfer functions are 10 0 0. 100(1+3D) (3+D)(1+2D) 1602 (1+4D) (D+1)(D+100)
4. (10 points) For the feedback system with open loop transfer function 16/3 a. (6 pts) Draw the Root Locus and Nyquist plot of the system with no 16/3 S41 Using Nyquist stability criterion, find the critical value of the delay. b. (4 pts)
4. (10 points) For the feedback system with open loop transfer function 16/3 a. (6 pts) Draw the Root Locus and Nyquist plot of the system with no 16/3 S41 Using Nyquist stability criterion, find the...
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....
The Nyquist plot of a plant P in a unity feedback system is
shown below. It is know that P has one pole with a non-negative
real part.
6.13 The Nyquist plot of a plant P in a unity feedback system is shown below. It is known that P has one pole with non-negative real part 1. What is the number of poles of P with zero real part? 2. What is the number of unstable poles of P? 3....
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