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8.5 Consider a system with transfer function ĝ(s) = (s – 1)(s+2) (s + 1)(s –...
CONTROLS 2 Consider the transfer function V (s) Put the system in state space form. Compute the eigenvalues of the resulting A matrix. Is the system stable? 2 Consider the transfer function V (s...
CONTROLS
2 Consider the transfer function V (s) Put the system in state space form. Compute the eigenvalues of the resulting A matrix. Is the system stable?
2 Consider the transfer function V (s) Put the system in state space form. Compute the eigenvalues of the resulting A matrix. Is the system stable?
Consider a plant with transfer function 5- Gp(s) = s2 Design a proper compensator Gc(s) and a gain p for the feedback system shown below so that the resulting system has all poles at s=-2, and the ou...
Consider a plant with transfer function 5- Gp(s) = s2 Design a proper compensator Gc(s) and a gain p for the feedback system shown below so that the resulting system has all poles at s=-2, and the output C(s) will track asymptotically any step reference input R(s). Find the resulting overall transfer function T(s) R(s) Consider a plant with transfer function 5- Gp(s) = s2 Design a proper compensator Gc(s) and a gain p for the feedback system shown below...
Problem # 3 [15 Points] Consider the following single-input, single-output system: (a) Characterize the controllable subspace and the unobservable subspace of the system (b) Determine the transfe...
Problem # 3 [15 Points] Consider the following single-input, single-output system: (a) Characterize the controllable subspace and the unobservable subspace of the system (b) Determine the transfer function and the impulse response of the sys- tem. (c) Is the system asymptotically stable? Is it BIBO stable? Justify your
Problem # 3 [15 Points] Consider the following single-input, single-output system: (a) Characterize the controllable subspace and the unobservable subspace of the system (b) Determine the transfer function and the impulse response...
1. Consider a unity feedback control system with the transfer function G(s) = 1/[s(s+ 2)] in...
1. Consider a unity feedback control system with the transfer function G(s) = 1/[s(s+ 2)] in the forward path. (a) Design a proportional controller that yields a stable system with percent overshoot less that 5% for the step input (b) Find settling time and peak time of the closed-loop system designed in part (a); (c) Design a PD compensator that reduces the settling time computed in (b) by a factor of 4 while keeping the percent overshoot less that 5%...
Problem #4 [15 Points] Given -1001 00-1」 11 0 1 00 (a) Find the impulse response...
Problem #4 [15 Points] Given -1001 00-1」 11 0 1 00 (a) Find the impulse response h(t) and the transfer function matrix H(s). Which modes are present in h(t)? What are the poles of H(s)? b) Is the system asymptotically stable? Is it BIBO stable? Explain. (c) ls it possible to determine a linear state feedback control law u = Fr+r so that all closed loop eigenvalues are at -1? If yes, find such F
1. Consider the standard unity feedback system with the feedforward transfer function K(a+3) 82-2 KG(s) Using...
1. Consider the standard unity feedback system with the feedforward transfer function K(a+3) 82-2 KG(s) Using the root locus plot, determine the range(s) of K such that the closed-loop system is stable. Determin all the points of interest for the root locus plot.
9. Consider the diagram below F(s) Y(s) s 1 s +1 Σ s +1 k S...
9. Consider the diagram below F(s) Y(s) s 1 s +1 Σ s +1 k S (a) Determine the transfer function H(s) of the system. (b) When k = 2, determine whether the system is BIBO stable or not. (c) Which values of k can you have so that the system is BIBO stable?
Consider the unity feedback system is given below R(S) C(s) G(s) with transfer function: G() =...
Consider the unity feedback system is given below R(S) C(s) G(s) with transfer function: G() = K(+2) s(s+ 1/s + 3)(+5) a) Sketch the root locus. Clearly indicate any asymptotes. b) Find the value of the gain K, that will make the system marginally stable. c) Find the value of the gain K, for which the closed-loop transfer function will have a pole on the real axis at (-0.5).
Consider the unity feedback system is given below R(S) C(s) G() with transfer function: G(s) =...
Consider the unity feedback system is given below R(S) C(s) G() with transfer function: G(s) = K s(s + 1)(s + 2)(8 + 6) a) Find the value of the gain K, that will make the system stable. b) Find the value of the gain K, that will make the system marginally stable. c) Find the actual location of the closed-loop poles when the system is marginally stable.
Consider a system modelled by means of the following transfer function 10 G(s) s(s +1)(s +10)...
Consider a system modelled by means of the following transfer function 10 G(s) s(s +1)(s +10) Given the standar negative feedback control structure, and the Bode plot of G(s): 1. Obtain (if possible) a lead compensator controller (C(s) Kc1+ts) that satisfies that the corresponding steady state error with respect to the ramp input is and that the overshoot is not greater than 15 per cent 2. Obtain (if possible) a lead compensator that satisfies that the correspond- ing steady state...
CONTROLS
2 Consider the transfer function V (s) Put the system in state space form. Compute the eigenvalues of the resulting A matrix. Is the system stable?
2 Consider the transfer function V (s) Put the system in state space form. Compute the eigenvalues of the resulting A matrix. Is the system stable?
Problem # 3 [15 Points] Consider the following single-input, single-output system: (a) Characterize the controllable subspace and the unobservable subspace of the system (b) Determine the transfer function and the impulse response of the sys- tem. (c) Is the system asymptotically stable? Is it BIBO stable? Justify your
Problem # 3 [15 Points] Consider the following single-input, single-output system: (a) Characterize the controllable subspace and the unobservable subspace of the system (b) Determine the transfer function and the impulse response...
Problem #4 [15 Points] Given -1001 00-1」 11 0 1 00 (a) Find the impulse response h(t) and the transfer function matrix H(s). Which modes are present in h(t)? What are the poles of H(s)? b) Is the system asymptotically stable? Is it BIBO stable? Explain. (c) ls it possible to determine a linear state feedback control law u = Fr+r so that all closed loop eigenvalues are at -1? If yes, find such F
1. Consider the standard unity feedback system with the feedforward transfer function K(a+3) 82-2 KG(s) Using the root locus plot, determine the range(s) of K such that the closed-loop system is stable. Determin all the points of interest for the root locus plot.
9. Consider the diagram below F(s) Y(s) s 1 s +1 Σ s +1 k S (a) Determine the transfer function H(s) of the system. (b) When k = 2, determine whether the system is BIBO stable or not. (c) Which values of k can you have so that the system is BIBO stable?
Consider the unity feedback system is given below R(S) C(s) G(s) with transfer function: G() = K(+2) s(s+ 1/s + 3)(+5) a) Sketch the root locus. Clearly indicate any asymptotes. b) Find the value of the gain K, that will make the system marginally stable. c) Find the value of the gain K, for which the closed-loop transfer function will have a pole on the real axis at (-0.5).
Consider the unity feedback system is given below R(S) C(s) G() with transfer function: G(s) = K s(s + 1)(s + 2)(8 + 6) a) Find the value of the gain K, that will make the system stable. b) Find the value of the gain K, that will make the system marginally stable. c) Find the actual location of the closed-loop poles when the system is marginally stable.
Consider a system modelled by means of the following transfer function 10 G(s) s(s +1)(s +10) Given the standar negative feedback control structure, and the Bode plot of G(s): 1. Obtain (if possible) a lead compensator controller (C(s) Kc1+ts) that satisfies that the corresponding steady state error with respect to the ramp input is and that the overshoot is not greater than 15 per cent 2. Obtain (if possible) a lead compensator that satisfies that the correspond- ing steady state...
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