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1- Consider a state space representation defined by LTI system, show why the system can be...
Please only solve part C Assume the following state space representation of a discrete-time servomotor system. (As a review for the Final Exam, you might check this state space representation with th...
Please only solve part C
Assume the following state space representation of a discrete-time servomotor system. (As a review for the Final Exam, you might check this state space representation with the difference equation in Problem 1 on Homework 2. This parenthetical comment is not a required part for Homework 8.) 2. 0.048371 u(n) 1.9048x(n) lo.04679 [1,0]x(n) y(n) Compute the open-loop eigenvalues of the system. That is, find the eigenvalues of Ф. Check controllability of the system. Or, answer the...
Consider the LTI system. Design a state-feedback control law of the form u(t)= -kx(t) such that...
Consider the LTI system. Design a state-feedback control law of
the form u(t)= -kx(t) such that x(t) goes to zero faster than
e^-t;
Problem 1: (15 points) Consider the LTI system 3 -1 (t)1 3 0 (t)2ut 0 0-1 Desig lim sate-feedback control law of the form u(t)ka(t) such that (t goes to zero faster than e i.e. Hint: fhink of where you want to place the eigenvalues of the closed-loop system.
Test 1 2: A state space representation of a system is given by: -2 011 y=[0...
Test 1 2: A state space representation of a system is given by: -2 011 y=[0 1]x 1. Design a state variable feedback control to place the closed-loop poles s =-3 ±j2. Assume that the complete state vector is available for feedback.。 Find the resulted close loop transfer function.
Problem 5. Given the system in state equation form, x=Ax + Bu where (a) A=10-3 01, B=10 0 0-2 (b)...
Problem 5. Given the system in state equation form, x=Ax + Bu where (a) A=10-3 01, B=10 0 0-2 (b) A=10-2 01,B=11 Can the system be stabilized by state feedback u-Kx, where K [k, k2 k3l?
Problem 5. Given the system in state equation form, x=Ax + Bu where (a) A=10-3 01, B=10 0 0-2 (b) A=10-2 01,B=11 Can the system be stabilized by state feedback u-Kx, where K [k, k2 k3l?
Please show all work, really need to double check this one. 3. Consider a system with...
Please show all work, really
need to double check this one.
3. Consider a system with a following transfer function: G(s) %3D s2 + 2s + 1 a. What are the state equations of the system in control canonical form? Assume the y(t) b. Assume you are using feedback of the form u(t) = -Kx(t) where K = [k, k2]. Calculate values of K so that the response of the system is critically damped. = x, (t).
An unstable LTI system has the impulse response h(t)=sin (4t)u(t). Show that proportional feedback (G(s) =...
An unstable LTI system has the impulse response h(t)=sin (4t)u(t). Show that proportional feedback (G(s) = K) cannot BIBO-stabilize the system. Show that derivative control feedback (G(s) = Ks) can stabilize the system. Using derivative control, choose K so that the closed loop system is critically damped. 7. (a) (b) (c) %3D E(s) System но) X(s) (E +Y(s) Feedback G(s) Y(s) Y(s) system G(s) Feedback loop Figure 4. o of
in the figure, obtain the state-space representation of the syster thè 1. Consider the mechanical system...
in the figure, obtain the state-space representation of the syster thè 1. Consider the mechanical system shown ssume y() is the output. (25 marks) ce representation of systel. ki lu k2
Problem 3 3. Consider the input-output representation of the system given below. Find a state-space representation...
Problem 3
3. Consider the input-output representation of the system given below. Find a state-space representation that is equivalent to this input-output representation.
6. Consider a state-space system x = Ax+ Bu, y = Cx for which the control...
6. Consider a state-space system x = Ax+ Bu, y = Cx for which the control input is defined as u- -Kx + r, with r(t) a reference input. This results in a closed-loop system x (A-BK)x(t)+ Br(t) = with matrices 2 -2 K=[k1 K2 For this type of controller, ki, k2 ER do not need to be restricted to positive numbers - any real number is fine (a) What is the characteristic equation of the closed-loop system, in terms...
Q3. The state-space representation of a dynamical system is given as follows: (2) (y = 2...
Q3. The state-space representation of a dynamical system is given as follows: (2) (y = 2 x 1. By finding the eigenvalues, eigenvectors of the A matrix, compute el via the diagonal transformation. 2. Assume that the control input is u(t) = 0, compute x(1) and y(t). 3. Assume that the input is u(t) = 1 + 2e-21, compute x(t) and y(t). 4. Given your answers to the previous question, compute x(t) when 1 00
Please only solve part C
Assume the following state space representation of a discrete-time servomotor system. (As a review for the Final Exam, you might check this state space representation with the difference equation in Problem 1 on Homework 2. This parenthetical comment is not a required part for Homework 8.) 2. 0.048371 u(n) 1.9048x(n) lo.04679 [1,0]x(n) y(n) Compute the open-loop eigenvalues of the system. That is, find the eigenvalues of Ф. Check controllability of the system. Or, answer the...
Consider the LTI system. Design a state-feedback control law of
the form u(t)= -kx(t) such that x(t) goes to zero faster than
e^-t;
Problem 1: (15 points) Consider the LTI system 3 -1 (t)1 3 0 (t)2ut 0 0-1 Desig lim sate-feedback control law of the form u(t)ka(t) such that (t goes to zero faster than e i.e. Hint: fhink of where you want to place the eigenvalues of the closed-loop system.
Test 1 2: A state space representation of a system is given by: -2 011 y=[0 1]x 1. Design a state variable feedback control to place the closed-loop poles s =-3 ±j2. Assume that the complete state vector is available for feedback.。 Find the resulted close loop transfer function.
Problem 5. Given the system in state equation form, x=Ax + Bu where (a) A=10-3 01, B=10 0 0-2 (b) A=10-2 01,B=11 Can the system be stabilized by state feedback u-Kx, where K [k, k2 k3l?
Problem 5. Given the system in state equation form, x=Ax + Bu where (a) A=10-3 01, B=10 0 0-2 (b) A=10-2 01,B=11 Can the system be stabilized by state feedback u-Kx, where K [k, k2 k3l?
Please show all work, really
need to double check this one.
3. Consider a system with a following transfer function: G(s) %3D s2 + 2s + 1 a. What are the state equations of the system in control canonical form? Assume the y(t) b. Assume you are using feedback of the form u(t) = -Kx(t) where K = [k, k2]. Calculate values of K so that the response of the system is critically damped. = x, (t).
An unstable LTI system has the impulse response h(t)=sin (4t)u(t). Show that proportional feedback (G(s) = K) cannot BIBO-stabilize the system. Show that derivative control feedback (G(s) = Ks) can stabilize the system. Using derivative control, choose K so that the closed loop system is critically damped. 7. (a) (b) (c) %3D E(s) System но) X(s) (E +Y(s) Feedback G(s) Y(s) Y(s) system G(s) Feedback loop Figure 4. o of
in the figure, obtain the state-space representation of the syster thè 1. Consider the mechanical system shown ssume y() is the output. (25 marks) ce representation of systel. ki lu k2
Problem 3
3. Consider the input-output representation of the system given below. Find a state-space representation that is equivalent to this input-output representation.
6. Consider a state-space system x = Ax+ Bu, y = Cx for which the control input is defined as u- -Kx + r, with r(t) a reference input. This results in a closed-loop system x (A-BK)x(t)+ Br(t) = with matrices 2 -2 K=[k1 K2 For this type of controller, ki, k2 ER do not need to be restricted to positive numbers - any real number is fine (a) What is the characteristic equation of the closed-loop system, in terms...
Q3. The state-space representation of a dynamical system is given as follows: (2) (y = 2 x 1. By finding the eigenvalues, eigenvectors of the A matrix, compute el via the diagonal transformation. 2. Assume that the control input is u(t) = 0, compute x(1) and y(t). 3. Assume that the input is u(t) = 1 + 2e-21, compute x(t) and y(t). 4. Given your answers to the previous question, compute x(t) when 1 00
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