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;
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Consider the LTI system. Design a state-feedback control law of
the form u(t)= -kx(t) such that...
Problem 3. Consider the system -2 01 Design feedback control u =-Kx such that the closed-loop pol...
Problem 3. Consider the system -2 01 Design feedback control u =-Kx such that the closed-loop poles are at s=-2+)2 and s=-2-j2. Assume K= [k1
Problem 3. Consider the system -2 01 Design feedback control u =-Kx such that the closed-loop poles are at s=-2+)2 and s=-2-j2. Assume K= [k1
3. Consider a system with the following state equation h(t)] [0 0 21 [X1(t) [x1(t) y(t)...
3. Consider a system with the following state equation h(t)] [0 0 21 [X1(t) [x1(t) y(t) [0.1 0 0.1x2(t) X3(t) The unit step response is required to have a settling time of less than 2 seconds and a percent overshoot of less than 5%. In addition a zero steady-state error is needed. The goal is to design the state feedback control law in the form of u(t) Kx(t) + Gr(t) (a) Find the desired regon of the S-plane for two...
Design a state feedback control u=-Kx, Find K, that could place the closed loop poles at-21 -3,-4...
the place poles are -2 ; -3 ; -4
Design a state feedback control u=-Kx, Find K, that could place the closed loop poles at-21 -3,-4 Given that: Consider the systemi Ar Bu with A-10-201. B-10 1 2) Exploiting the structure of A and B, find a different feedback gain that place the poles in the same location. This steps shows that there are several ways to design K; by inspection for instance.
Design a state feedback control u=-Kx, Find...
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
a-represent system in state space form? b-find output response y(t? c-design a state feedback gain controller? 3- A dyn...
a-represent system in state space form?
b-find output response y(t?
c-design a state feedback gain controller?
3- A dynamic system is described by the following set of coupled linear ordinary differential equations: x1 + 2x1-4x2-5u x1-x2 + 4x1 + x2 = 5u EDQMS 2/3 Page 1 of 2 a. Represent the system in state-space form. b. For u(t) =1 and initial condition state vector x(0) = LII find the outp (10 marks) response y(t). c. Design a state feedback gain...
1- Consider a state space representation defined by LTI system, show why the system can be...
1- Consider a state space representation defined by LTI system, show why the system can be stabilized whether or not by using the state feedback control u=-Kx, whatever K is chosen? 35p [*]-[:][:] [:)
Problem 6. Consider the system *1 = x1 + u iz = -x1 + x2 (a)...
Problem 6. Consider the system *1 = x1 + u iz = -x1 + x2 (a) Determine the stability of the open-loop system by checking the eigenvalues of the above system. (b) Define the output to be y = X1. Use the MATLAB command “Iqr” to find the constant optimal feedback control law gains by solving the infinite-horizon output regulator problem with Q=1 and R=0.1. (c) Determine the closed-loop stability by calculating the eigenvalues of the closed- loop system when...
Problem 4 A full-state feedback control law is to be designed which . Forces the state...
Problem 4 A full-state feedback control law is to be designed which . Forces the state r to zero from a nonzero starting state, and . Makes toe poles of the the closed loop system lie at Problem 5 The Full state feedback control law of Problem 4 is to be moditied to where ru is a desired (nonzero) value of the output. Determine Gu
Problem 4 (25%) Consider the attitude control system of a rigid satellite shown in Figure 1.1....
Problem 4 (25%) Consider the attitude control system of a rigid satellite shown in Figure 1.1. Fig. 1.1 Satellite tracking control system In this problem we will only consider the control of the angle e (angle of elevation). The dynamic model of the rigid satellite, rotating about an axis perpendicular to the page, can be approximately written as: JÖ = tm - ty - bė where ) is the satellite's moment of inertia, b is the damping coefficient, tm is...
3. Consider the system It is desired to design an output feedback controller such that all closed-loop eigenvalues sati...
3. Consider the system It is desired to design an output feedback controller such that all closed-loop eigenvalues satisfy R, [A S-3 and the output y is to track a constant reference r. (a) Design the controller using the feedback compensator method. (b) Design the controller using the integral-control method.
3. Consider the system It is desired to design an output feedback controller such that all closed-loop eigenvalues satisfy R, [A S-3 and the output y is to track a...
Problem 3. Consider the system -2 01 Design feedback control u =-Kx such that the closed-loop poles are at s=-2+)2 and s=-2-j2. Assume K= [k1
Problem 3. Consider the system -2 01 Design feedback control u =-Kx such that the closed-loop poles are at s=-2+)2 and s=-2-j2. Assume K= [k1
3. Consider a system with the following state equation h(t)] [0 0 21 [X1(t) [x1(t) y(t) [0.1 0 0.1x2(t) X3(t) The unit step response is required to have a settling time of less than 2 seconds and a percent overshoot of less than 5%. In addition a zero steady-state error is needed. The goal is to design the state feedback control law in the form of u(t) Kx(t) + Gr(t) (a) Find the desired regon of the S-plane for two...
the place poles are -2 ; -3 ; -4
Design a state feedback control u=-Kx, Find K, that could place the closed loop poles at-21 -3,-4 Given that: Consider the systemi Ar Bu with A-10-201. B-10 1 2) Exploiting the structure of A and B, find a different feedback gain that place the poles in the same location. This steps shows that there are several ways to design K; by inspection for instance.
Design a state feedback control u=-Kx, Find...
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
a-represent system in state space form?
b-find output response y(t?
c-design a state feedback gain controller?
3- A dynamic system is described by the following set of coupled linear ordinary differential equations: x1 + 2x1-4x2-5u x1-x2 + 4x1 + x2 = 5u EDQMS 2/3 Page 1 of 2 a. Represent the system in state-space form. b. For u(t) =1 and initial condition state vector x(0) = LII find the outp (10 marks) response y(t). c. Design a state feedback gain...
1- Consider a state space representation defined by LTI system, show why the system can be stabilized whether or not by using the state feedback control u=-Kx, whatever K is chosen? 35p [*]-[:][:] [:)
Problem 6. Consider the system *1 = x1 + u iz = -x1 + x2 (a) Determine the stability of the open-loop system by checking the eigenvalues of the above system. (b) Define the output to be y = X1. Use the MATLAB command “Iqr” to find the constant optimal feedback control law gains by solving the infinite-horizon output regulator problem with Q=1 and R=0.1. (c) Determine the closed-loop stability by calculating the eigenvalues of the closed- loop system when...
Problem 4 A full-state feedback control law is to be designed which . Forces the state r to zero from a nonzero starting state, and . Makes toe poles of the the closed loop system lie at Problem 5 The Full state feedback control law of Problem 4 is to be moditied to where ru is a desired (nonzero) value of the output. Determine Gu
Problem 4 (25%) Consider the attitude control system of a rigid satellite shown in Figure 1.1. Fig. 1.1 Satellite tracking control system In this problem we will only consider the control of the angle e (angle of elevation). The dynamic model of the rigid satellite, rotating about an axis perpendicular to the page, can be approximately written as: JÖ = tm - ty - bė where ) is the satellite's moment of inertia, b is the damping coefficient, tm is...
3. Consider the system It is desired to design an output feedback controller such that all closed-loop eigenvalues satisfy R, [A S-3 and the output y is to track a constant reference r. (a) Design the controller using the feedback compensator method. (b) Design the controller using the integral-control method.
3. Consider the system It is desired to design an output feedback controller such that all closed-loop eigenvalues satisfy R, [A S-3 and the output y is to track a...
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