a-represent system in state space form?
b-find output response y(t?
c-design a state feedback gain controller?
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 controller K [ki k2 ] so that the desired closed-loop eigenvalues should be located at (-3-j 6). (6 marks)
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a-represent system in state space form? b-find output response y(t? c-design a state feedback gain controller? 3- A dyn...
find the following: a)state transition matrix? b)output as function of time? c)design a state feedback controller to...
find the following:
a)state transition matrix?
b)output as function of time?
c)design a state feedback controller to place closed loop at (-3)
and (-5)
Question (: (10 hO Considering the following system, 01x + 0 t<0 tt t20 Where x(0)-L1] , u(t)-(% ,u(t) a) Find the state transition matrix. (3 marks) b) Find the output as a function of time. (3 marks) c) Design a state feedback controller to place the closed loop poles at (-3) and (-5). (4 marks)...
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...
0.12S [10 marks] 1(e) Determine the input to the system when the output of the system is [10 marks] 1(f) It is required to adjust the gain and the feedback of the states in the companion form state-...
0.12S [10 marks] 1(e) Determine the input to the system when the output of the system is [10 marks] 1(f) It is required to adjust the gain and the feedback of the states in the companion form state-space representation so that the impulse response of the new system with the adjusted gain and feedback is (i) Determine the required transfer function of the new system (i) Form the companion form state-space representation for the new (ii) From the results in...
( 12 marks LO3) Consider an undan ed two-degree-of-freedom spring-mass system, shown in the f g re below. The motion of the system Es con pletely described by the coordinate 치(t) and x2(t). le H...
( 12 marks LO3) Consider an undan ed two-degree-of-freedom spring-mass system, shown in the f g re below. The motion of the system Es con pletely described by the coordinate 치(t) and x2(t). le Ho Assume: kI- k2 k3 2 Nm, m-m2-1 kg and F-F2- Use the provided white paper to work out your answers, then pick the proper choice from the drop down list The equation of motion of mass 1 is EQ 1-x+6x1-4x2 0 EO 2 x1+4x1-2x2 The...
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...
SKEE 313 SKEU 3133 Q.3 (a) A linear dynamic system is characterized by the following equations,...
SKEE 313 SKEU 3133 Q.3 (a) A linear dynamic system is characterized by the following equations, xi(t) + 2x2(t) = 3x1(t) + 4x2(t) – 5u(t) xi(t) – x2(t) = 2xı(t) + x2(t) + u(t) y(t) = xi(t) + 2x2(t) where: u(t): input y(t): output xi(t) dan xz(t): state variables Write the system's state space representation, (the state and output equations) in matrix format. (6 marks)
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.
Convert following the transfer function into state space representation (Marks 5) 3 +45² T($) = 54...
Convert following the transfer function into state space representation (Marks 5) 3 +45² T($) = 54 +52 +7 Convert the following state space into a transfer function. (Marks 5) x = 11 * = x + ( u 21 y = [02]x + [2]u Evaluate the steady-state error of state-space system. (Marks 5) i [ 10] [21. *= 15 2]* +11 y = [ 02]x + [2]u Evaluate the steady-state error of state-space system. (Marks 5) -1 0x+lu x =...
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...
3) Given x1 = x2 with kER, find the forced output response y(t) and steady state...
3) Given x1 = x2 with kER, find the forced output response y(t) and steady state output response yss(t) to an input u(t) = 1 + sint and find values of k E R such that ly(t) - a 0.05 for allt 10-2sec. yss
find the following:
a)state transition matrix?
b)output as function of time?
c)design a state feedback controller to place closed loop at (-3)
and (-5)
Question (: (10 hO Considering the following system, 01x + 0 t<0 tt t20 Where x(0)-L1] , u(t)-(% ,u(t) a) Find the state transition matrix. (3 marks) b) Find the output as a function of time. (3 marks) c) Design a state feedback controller to place the closed loop poles at (-3) and (-5). (4 marks)...
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...
0.12S [10 marks] 1(e) Determine the input to the system when the output of the system is [10 marks] 1(f) It is required to adjust the gain and the feedback of the states in the companion form state-space representation so that the impulse response of the new system with the adjusted gain and feedback is (i) Determine the required transfer function of the new system (i) Form the companion form state-space representation for the new (ii) From the results in...
( 12 marks LO3) Consider an undan ed two-degree-of-freedom spring-mass system, shown in the f g re below. The motion of the system Es con pletely described by the coordinate 치(t) and x2(t). le Ho Assume: kI- k2 k3 2 Nm, m-m2-1 kg and F-F2- Use the provided white paper to work out your answers, then pick the proper choice from the drop down list The equation of motion of mass 1 is EQ 1-x+6x1-4x2 0 EO 2 x1+4x1-2x2 The...
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...
SKEE 313 SKEU 3133 Q.3 (a) A linear dynamic system is characterized by the following equations, xi(t) + 2x2(t) = 3x1(t) + 4x2(t) – 5u(t) xi(t) – x2(t) = 2xı(t) + x2(t) + u(t) y(t) = xi(t) + 2x2(t) where: u(t): input y(t): output xi(t) dan xz(t): state variables Write the system's state space representation, (the state and output equations) in matrix format. (6 marks)
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.
Convert following the transfer function into state space representation (Marks 5) 3 +45² T($) = 54 +52 +7 Convert the following state space into a transfer function. (Marks 5) x = 11 * = x + ( u 21 y = [02]x + [2]u Evaluate the steady-state error of state-space system. (Marks 5) i [ 10] [21. *= 15 2]* +11 y = [ 02]x + [2]u Evaluate the steady-state error of state-space system. (Marks 5) -1 0x+lu x =...
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...
3) Given x1 = x2 with kER, find the forced output response y(t) and steady state output response yss(t) to an input u(t) = 1 + sint and find values of k E R such that ly(t) - a 0.05 for allt 10-2sec. yss
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