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Some system has the transfer function shown. Choose the correct answer regarding the stability of the...
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...
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...
Question 6 The open-loop transfer function G(s) of a control system is given as G(8)- s(s+2)(s +5...
Question 6 The open-loop transfer function G(s) of a control system is given as G(8)- s(s+2)(s +5) A proportional controller is used to control the system as shown in Figure 6 below: Y(s) R(s) + G(s) Figure 6: A control system with a proportional controller a) Assume Hp(s) is a proportional controller with the transfer function H,(s) kp. Determine, using the Routh-Hurwitz Stability Criterion, the value of kp for which the closed-loop system in Figure 6 is marginally stable. (6...
(1) When a polynomial for the numerator of a transfer function is represented by the vector...
(1) When a polynomial for the numerator of a transfer function is represented by the vector [1 3 0j in Matlab, what is the polynomial (in )? Ss35 (2) What is the final value of a response which is given b1612 (o)- (0)-3(0)3 ()undefined (3) Determine the damping ratio of the system described by)235 )1(b) 2.5 (c)5 (d) 10 (e) 25 (f) something else (4) (True or alse) The system with the following characteristic equation is stable. (5) Marginally stable...
For each of the following discrete systems described by either its transfer function or its unit...
For each of the following discrete systems described by either its transfer function or its unit impulse response, determine if the system is asymptotically stable, marginally stable, or unstable 1. z +1 / I. 1.5% 1 0.5 (b) Mn]:e-n sin(m)11[n]
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)...
QUESTION ONE (a) Determine the stability of the system whose overall transfer function is given below;...
QUESTION ONE (a) Determine the stability of the system whose overall transfer function is given below; 2s +5 55 +1.554 +253 +4s+55 +10 If the system is found unstable, how many roots has it has with positive real parts? (b) Determine the stability of a closed-loop control system whose characteristics equation is; ss +54 +253 +252 +11S + 10 = 0 (20 marks)
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....
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.
Consider an LTI system for which the system (transfer) function H(s) has a zero at s=2...
Consider an LTI system for which the system (transfer) function H(s) has a zero at s=2 and poles at s=-12, -7, -6. If the system is known to be causal and stable, choose the ROC associated with the given system function. *
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...
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...
Question 6 The open-loop transfer function G(s) of a control system is given as G(8)- s(s+2)(s +5) A proportional controller is used to control the system as shown in Figure 6 below: Y(s) R(s) + G(s) Figure 6: A control system with a proportional controller a) Assume Hp(s) is a proportional controller with the transfer function H,(s) kp. Determine, using the Routh-Hurwitz Stability Criterion, the value of kp for which the closed-loop system in Figure 6 is marginally stable. (6...
(1) When a polynomial for the numerator of a transfer function is represented by the vector [1 3 0j in Matlab, what is the polynomial (in )? Ss35 (2) What is the final value of a response which is given b1612 (o)- (0)-3(0)3 ()undefined (3) Determine the damping ratio of the system described by)235 )1(b) 2.5 (c)5 (d) 10 (e) 25 (f) something else (4) (True or alse) The system with the following characteristic equation is stable. (5) Marginally stable...
For each of the following discrete systems described by either its transfer function or its unit impulse response, determine if the system is asymptotically stable, marginally stable, or unstable 1. z +1 / I. 1.5% 1 0.5 (b) Mn]:e-n sin(m)11[n]
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)...
QUESTION ONE (a) Determine the stability of the system whose overall transfer function is given below; 2s +5 55 +1.554 +253 +4s+55 +10 If the system is found unstable, how many roots has it has with positive real parts? (b) Determine the stability of a closed-loop control system whose characteristics equation is; ss +54 +253 +252 +11S + 10 = 0 (20 marks)
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....
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.
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