Consider the following transfer function: [mark 25%] 4. Y(s) U(s) 5s1 2 G(s) (3) a. If...
4. Consider the transfer function, Y(s)_ 3 F(s) + s(s2 + 2s + 4) (a) Qualitatively, what is the time response y(t) if f(t) represents a unit-step input? What is the value of y(t) when time is sufficiently large? What is the time constant that we may use to evaluate the "speed" of response? (b) Repeat step (a) if f(t) represents an impulse input. What is y(t) when time is sufficiently large?
4. Consider the transfer function, Y($) F(S) 3 S(52 +2s + 4) (a) Qualitatively, what is the time response y(t) if f(t) represents a unit-step input? What is the value of y(t) when time is sufficiently large? What is the time constant that we may use to evaluate the "speed" of response? (b) Repeat step (a) if f(t) represents an impulse input. What is y(t) when time is sufficiently large?
Problem 3 (25) Consider the unity-feedback system with the open-loop transfer function: 10 G(s) = 1 Obtain the steady-state output of the system when it is subjected to each of the following inputs: a)r(t) sin(t30*) b) r(t) 2cos(2t - 45) c) r(t) sin(t+30") + 2cos(2t -45)
Problem 3 (25) Consider the unity-feedback system with the open-loop transfer function: 10 G(s) = 1 Obtain the steady-state output of the system when it is subjected to each of the following inputs: a)r(t)...
The transfer function of a linear system is G(s) = Y(s) S-1 U(s) 5? + 4s +3 a. Express this system in the modal form. b. Express this system in the standard controllable form (SCF). (Parts d, e, f, and g use this system) c. In the standard controllable form, suppose the output is replaced by y=[-1 a] | [x2] Give a value for a which makes the system unobservable. d. What is y(t) if y(0-)=-3, ay = 6 and...
(40) 3. Make an approximation of the transfer function (s+10) G(s)-Y(s)/U(s) =__ (s+25) using Euler's approximation. Find the actual solution and the approximate solution for a sampling interval T-0.1 sec for t=0, 0.1, 0.2. u(t) = 10tfort O and u(t) =0 fort 30
a system is given by the following transfer function Y(s)/u(s) = 1/(s^2-16) a)find the output in time domain Y(t) if the input u(t) is a unit step. (Hint the transfer function of the unit step function is 1/s) b)what is Y(t) as t goes to infinity
Problem 1: Given the transfer function from input u(t) to output y(t), Y (s) U(s) = s 2 − 4s + 3 (s 2 + 6s + 8)(s 2 + 25) (a) Develop a state space model for this transfer function, in the standard form x˙ = Ax + Bu y = Cx + Du (b) Suppose that zero input is applied, such that u = 0. Perform a modal analysis of the state response for this open-loop system. Your...
1. (4 pts) Consider the system whose transfer function is YS) – H(S) = Tos +1 Tis +1 U(s) Obtain the steady-state output, y(t), of the system when it is subjected to the input u(t) = A sin wt.
y(s) 2 u(s) s1 -. Consider the open-loop unstable system G(s) integral controller to regulate the output y to a constant reference r. The desired closed-loop transfer function is G) +16s +100 Design the simplest output feedback (20 pts)
y(s) 2 u(s) s1 -. Consider the open-loop unstable system G(s) integral controller to regulate the output y to a constant reference r. The desired closed-loop transfer function is G) +16s +100 Design the simplest output feedback (20 pts)
3. Work the following problems: a. The transfer function of a system is: Y(s)/R(s) = 15(s+1)/(s2+9s+14). Determine y(t) when r(t) is a unit step input. b. Consider the following system: R(s)_ 0 G(s) i. Find the closed-loop transfer function Y(s)R(S) when G(s) = 10/(S2+2s+10) ii. Determine Y(s) when the input R(s) is a unit step. iii. Compute y(t).