Control theory
2. Does the transfer function \(P(s)=s^{6}+s^{5}+5 s^{4}+s^{3}+2 s^{2}-2 s-8\) represents a stable or an unstable system? Suggest the number/s of poles lying on different region of s-plane.
Homework Answers
A Calculator is allowed. Question 7: The following transfer function is unstable. H(s) = ! Explain...
A Calculator is allowed. Question 7: The following transfer function is unstable. H(s) = ! Explain why the function is unstable. Plot any existing poles and zeros on the complex (s-domain) plane. Find a feedback method (P,D, or Ior any summative combination of P, D, or I) to make the system stable. Prove it is stable mathematically.
You are given an unstable plant with a transfer function P(s) = Tote -1 R(S) Y(8)...
You are given an unstable plant with a transfer function P(s) = Tote -1 R(S) Y(8) 11+ C(8) P(s) You are to design a proportional controller, C(s) = K, such that the closed-loop system is BIBO stable and meets the following performance specifications: (i) Rise time T, < 0.5 seconds (where T, = 28) (ii) Percent overshoot %OS < 50%. Do the following: (a) Sketch the region in the complex plane where you would like the poles of the closed-loop...
210y= 3r + 6r (1) What is the characteristic equation of this system? (2) What are the system's poles and zeros...
210y= 3r + 6r (1) What is the characteristic equation of this system? (2) What are the system's poles and zeros (3) Plot the poles and the zeros on the s-plane (4) Is this system stable or unstable? Why or why not? (5) Estimate the system's response (not knowing the type of the input)
210y= 3r + 6r (1) What is the characteristic equation of this system? (2) What are the system's poles and zeros (3) Plot the poles and...
please do all step clean and neat Apply Routh-Hurwitz criterion to determine whether the given control...
please do all step clean and neat
Apply Routh-Hurwitz criterion to determine whether the given control system is stable or unstable? b) Tell how many poles of the closed loop transfer function lie in the right half-plane. left half-plane, and on the jo-axis? Justify your answer. a Cis) R(s) +4s-3 .4p832+ 20 15
a continuous time causal LTI system has a transfer function: H(s)=(s+3)/(s^2 +3s +2) a) find the...
a continuous time causal LTI system has a transfer function: H(s)=(s+3)/(s^2 +3s +2) a) find the poles and zeros b) indicate the poles and the zeros on the s-plane indicate the region of convergence (ROC) c) write the differential equation of the system. d) determine the gain of the system at dc (ie the transfer function at w=0) e) is the system described by H(s) stable? explain f) for the system described by H(s), does the Fourier transform H(jw) exist?...
1. Use the Routh-Hurwitz test to determine if the system described by the following transfer function...
1. Use the Routh-Hurwitz test to determine if the system described by the following transfer function is stable. If the system is unstable, how many poles are outside the LHP? Use Matlab to check your answers. C() 10-8) R(s) s2 +7s +28 2. Repeat problem 1) above for the system with transfer function C (s) R(5s +Bs+ 40 s2 +2s+4 3. Use the Routh-Hurwitz test to determine if the system described by the following characteristic equation is stable. If the...
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....
Problem 2 and 3 A simplified model of a magnetic levitation system has the dynamic model...
Problem 2 and 3
A simplified model of a magnetic levitation system has the dynamic model 1 2 (a) Find the transfer function G(s) of the system. (b) Find the poles and zeros of the system. (c) The plant is unstable. Explain why Problem 2 The plant in Problem 1 is to be stabilized by use of "proportional plus derivative" control: U(s)-(Kis + K2)Y(s) Find and sketch the region in the Ki, K2 plane for which the closed loop system,...
. (15 points) An unstable system can be stabilized by using negative feedback with a gain...
. (15 points) An unstable system can be stabilized by using negative feedback with a gain K in the feedback loop. For instance, consider an unstable system with transfer function which has a pole in the right-hand s-plane, making the impulse response of the system h) grow as increases. Use negative feedback with a gain K> 0 in the feedback loop, and put H) in the forward loop. Draw a block diagram of the system. Obtain the transfer function Gus)...
Show all your work leading up to tne laT JUlu (1) Plot the poles and zeros of the following transfer functions. Also, identify if the transfer function represents a stable system. (20) (s+2)(s-5...
Show all your work leading up to tne laT JUlu (1) Plot the poles and zeros of the following transfer functions. Also, identify if the transfer function represents a stable system. (20) (s+2)(s-5) (s+4) (s2+6s)(s2 +16) s(s+4)(s+7) (s+2) (s+3) (s2+9) (s2+4s2+13s) (s-1)(s2+10s+34) C. (22
Show all your work leading up to tne laT JUlu (1) Plot the poles and zeros of the following transfer functions. Also, identify if the transfer function represents a stable system. (20) (s+2)(s-5) (s+4) (s2+6s)(s2 +16)...
A Calculator is allowed. Question 7: The following transfer function is unstable. H(s) = ! Explain why the function is unstable. Plot any existing poles and zeros on the complex (s-domain) plane. Find a feedback method (P,D, or Ior any summative combination of P, D, or I) to make the system stable. Prove it is stable mathematically.
You are given an unstable plant with a transfer function P(s) = Tote -1 R(S) Y(8) 11+ C(8) P(s) You are to design a proportional controller, C(s) = K, such that the closed-loop system is BIBO stable and meets the following performance specifications: (i) Rise time T, < 0.5 seconds (where T, = 28) (ii) Percent overshoot %OS < 50%. Do the following: (a) Sketch the region in the complex plane where you would like the poles of the closed-loop...
210y= 3r + 6r (1) What is the characteristic equation of this system? (2) What are the system's poles and zeros (3) Plot the poles and the zeros on the s-plane (4) Is this system stable or unstable? Why or why not? (5) Estimate the system's response (not knowing the type of the input)
210y= 3r + 6r (1) What is the characteristic equation of this system? (2) What are the system's poles and zeros (3) Plot the poles and...
please do all step clean and neat
Apply Routh-Hurwitz criterion to determine whether the given control system is stable or unstable? b) Tell how many poles of the closed loop transfer function lie in the right half-plane. left half-plane, and on the jo-axis? Justify your answer. a Cis) R(s) +4s-3 .4p832+ 20 15
1. Use the Routh-Hurwitz test to determine if the system described by the following transfer function is stable. If the system is unstable, how many poles are outside the LHP? Use Matlab to check your answers. C() 10-8) R(s) s2 +7s +28 2. Repeat problem 1) above for the system with transfer function C (s) R(5s +Bs+ 40 s2 +2s+4 3. Use the Routh-Hurwitz test to determine if the system described by the following characteristic equation is stable. If the...
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....
Problem 2 and 3
A simplified model of a magnetic levitation system has the dynamic model 1 2 (a) Find the transfer function G(s) of the system. (b) Find the poles and zeros of the system. (c) The plant is unstable. Explain why Problem 2 The plant in Problem 1 is to be stabilized by use of "proportional plus derivative" control: U(s)-(Kis + K2)Y(s) Find and sketch the region in the Ki, K2 plane for which the closed loop system,...
. (15 points) An unstable system can be stabilized by using negative feedback with a gain K in the feedback loop. For instance, consider an unstable system with transfer function which has a pole in the right-hand s-plane, making the impulse response of the system h) grow as increases. Use negative feedback with a gain K> 0 in the feedback loop, and put H) in the forward loop. Draw a block diagram of the system. Obtain the transfer function Gus)...
Show all your work leading up to tne laT JUlu (1) Plot the poles and zeros of the following transfer functions. Also, identify if the transfer function represents a stable system. (20) (s+2)(s-5) (s+4) (s2+6s)(s2 +16) s(s+4)(s+7) (s+2) (s+3) (s2+9) (s2+4s2+13s) (s-1)(s2+10s+34) C. (22
Show all your work leading up to tne laT JUlu (1) Plot the poles and zeros of the following transfer functions. Also, identify if the transfer function represents a stable system. (20) (s+2)(s-5) (s+4) (s2+6s)(s2 +16)...
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