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An unstable LTI system has the impulse response h(t)=sin (4t)u(t). Show that proportional feedback (G(s) =...
The unit impulse response and the input to an LTI system are given by: h(t) u(t)...
The unit impulse response and the input to an LTI system are given by: h(t) u(t) - u(t - 4) x(t) e2[u(t)-u(t - 4)] x(t) 1 y(t) h(t) 1. Determine the output signal, i.e.y(t), you may use any method. 2. Is this system memoryless? Why? 3. Is this system causal? Why? 4. Is this system BIBO stable? Why?
IV. (5 pts). Given the feedback system shown below, with H)--1 and Gs) 5+α where a...
IV. (5 pts). Given the feedback system shown below, with H)--1 and Gs) 5+α where a and K constants. Note that H(s) represents an unstable open-loop system. We are going to determine the value of the constants that make the overall closed-loop system stable. H(s) vu) x(t) wt) G(s) 0(s) a) Find the system function, Q(s), of the closed-loop system in terms ofa and K. A quick test that you probably got the right answer: ( ONMwm.→ b) Find 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.
Consider the feedback sy PID COntroller Plant R(S) Y(s) the closed-loop transfer function T(s) = Y...
Consider the feedback sy PID COntroller Plant R(S) Y(s) the closed-loop transfer function T(s) = Y controller (Kp Find er p 1, Ks K ) and show that the system is marginally stable with two imaginary roots. (s)/R(s) with no sabl thosed-loop transfer function T(s) Y (S/R(s) with the (three- term) PID controller added to stabilize the system. suming that Kd 4 and K, -100, find the values (range) of Kp that will stabilize the system.
Consider an LTI system with the impulse response h(t) = e- . Is the system casual?...
Consider an LTI system with the impulse response h(t) = e- . Is the system casual? Explain. Find and plot the output s(t) given that the system input is x(t) = u(t). Note that s(t) in this case is commonly known as the step response of the system. If the input is x(t) = u(t)-u(t-T). Express the output y(t) as a function of s(t). Also, explicitly write the output y(t) as a function of t. a) b) c)
2) Sketch te respose of te LTI system with impulse response h(t) to the input r(t)...
2) Sketch te respose of te LTI system with impulse response h(t) to the input r(t) Problem1 Cosider the cicuil shown below The switch SW closes at = 0. Before the switch SW closes at t = 0, the capacitor C gets charged due to the voltage source V through the resistive network . As the switch closes at t= 0, there is redistribution of charge across (t) he capacior as the capacitor is now coced lo both RN, and...
Exercise 2.5 response of the LTI system with impulse response h(t)-e cos(2t)u(t)
Exercise 2.5 response of the LTI system with impulse response h(t)-e cos(2t)u(t)
Consider a continuous-time LTI system S with impulse response h(t) = 2(u(t + 1)-u(t 1)). Determine...
Consider a continuous-time LTI system S with impulse response h(t) = 2(u(t + 1)-u(t 1)). Determine the values of the amplitude scaling and the tme shifting that takes place when each of the following input signals is provided to the system S. Don't use the convolution integral, instead use the result about how LTI systems respond to complex exponential signals. (a) x(t) 2 (b) x(t) ej0.5Tt (c) x(t) = e-j0.5πt (d) x(t) = e-jmt (e) x(t) = cos (0.5t) (f)...
Given a zero-state LTI system whose impulse response h(t) = u(t) u(t-2), if the input of...
Given a zero-state LTI system whose impulse response h(t) = u(t) u(t-2), if the input of the system is r(t), find the system equation which relates the input to the output y(t) 4. (20 points) If a causal signal's s-domain representation is given as X (s) = (s+ 2)(s2 +2s + 5) (a) find all the poles and zero of the function. 2 1 52243 orr
Question# 1 (25 points) For a unity feedback system with open loop transfer function K(s+10)(s+20) (s+30)(s2-20s+2...
Question# 1 (25 points) For a unity feedback system with open loop transfer function K(s+10)(s+20) (s+30)(s2-20s+200) G(s) = Do the following using Matlab: a) Sketch the root locus. b) Find the range of gain, K that makes the system stable c) Find the value of K that yields a damping ratio of 0.707 for the system's closed-loop dominant poles. d) Obtain Ts, Tp, %OS for the closed loop system in part c). e) Find the value of K that yields...
The unit impulse response and the input to an LTI system are given by: h(t) u(t) - u(t - 4) x(t) e2[u(t)-u(t - 4)] x(t) 1 y(t) h(t) 1. Determine the output signal, i.e.y(t), you may use any method. 2. Is this system memoryless? Why? 3. Is this system causal? Why? 4. Is this system BIBO stable? Why?
IV. (5 pts). Given the feedback system shown below, with H)--1 and Gs) 5+α where a and K constants. Note that H(s) represents an unstable open-loop system. We are going to determine the value of the constants that make the overall closed-loop system stable. H(s) vu) x(t) wt) G(s) 0(s) a) Find the system function, Q(s), of the closed-loop system in terms ofa and K. A quick test that you probably got the right answer: ( ONMwm.→ b) Find 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.
Consider the feedback sy PID COntroller Plant R(S) Y(s) the closed-loop transfer function T(s) = Y controller (Kp Find er p 1, Ks K ) and show that the system is marginally stable with two imaginary roots. (s)/R(s) with no sabl thosed-loop transfer function T(s) Y (S/R(s) with the (three- term) PID controller added to stabilize the system. suming that Kd 4 and K, -100, find the values (range) of Kp that will stabilize the system.
Consider an LTI system with the impulse response h(t) = e- . Is the system casual? Explain. Find and plot the output s(t) given that the system input is x(t) = u(t). Note that s(t) in this case is commonly known as the step response of the system. If the input is x(t) = u(t)-u(t-T). Express the output y(t) as a function of s(t). Also, explicitly write the output y(t) as a function of t. a) b) c)
2) Sketch te respose of te LTI system with impulse response h(t) to the input r(t) Problem1 Cosider the cicuil shown below The switch SW closes at = 0. Before the switch SW closes at t = 0, the capacitor C gets charged due to the voltage source V through the resistive network . As the switch closes at t= 0, there is redistribution of charge across (t) he capacior as the capacitor is now coced lo both RN, and...
Exercise 2.5 response of the LTI system with impulse response h(t)-e cos(2t)u(t)
Consider a continuous-time LTI system S with impulse response h(t) = 2(u(t + 1)-u(t 1)). Determine the values of the amplitude scaling and the tme shifting that takes place when each of the following input signals is provided to the system S. Don't use the convolution integral, instead use the result about how LTI systems respond to complex exponential signals. (a) x(t) 2 (b) x(t) ej0.5Tt (c) x(t) = e-j0.5πt (d) x(t) = e-jmt (e) x(t) = cos (0.5t) (f)...
Given a zero-state LTI system whose impulse response h(t) = u(t) u(t-2), if the input of the system is r(t), find the system equation which relates the input to the output y(t) 4. (20 points) If a causal signal's s-domain representation is given as X (s) = (s+ 2)(s2 +2s + 5) (a) find all the poles and zero of the function. 2 1 52243 orr
Question# 1 (25 points) For a unity feedback system with open loop transfer function K(s+10)(s+20) (s+30)(s2-20s+200) G(s) = Do the following using Matlab: a) Sketch the root locus. b) Find the range of gain, K that makes the system stable c) Find the value of K that yields a damping ratio of 0.707 for the system's closed-loop dominant poles. d) Obtain Ts, Tp, %OS for the closed loop system in part c). e) Find the value of K that yields...
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