Xi (1)--0.3134 (1) +56.7% (1) +0.23211(1) h(,)--0013%, (r)-0 4264(,)-0.020%(,) jl)-56.7%(,) Calcu...
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1, (20 points) Suppose we have a İTİ system with impulse response(h(t) described as following h(t) 6u(t) where u(t) is unit step function. The output(Y (s)) is expressed as the product of input (R(s)) and transfer function Y(s) = R(s)H(s) The Laplace transform is defined as LTI system R(H) Y (s) Figure 1: LTI system in s-plane (a) (5 points) Find the tranisfer function(H(s)) of the LITI system. (b) (5 points) Find the Laplace transform of the input(r(t)....
A system with input r(t) and output y(t) has transfer function G(s) = 10 (s + 1)(s + 2). Find y(t) for t ≥ 0 if the following inputs are applied (with zero initial conditions): (a) r(t) = u(t) (b) r(t) = e^ −t*u(t)
S+5 e. L1 = 10nH, R = 1009, and R2 = 0!! 6) Given a system with a transfer function of H(S) = 7002 a. Write the steady state output of the system if the input is y(t) = sin(2000) b. Sketch the Bode plot no 30 1
For a control system, its transfer function from the input to the output is H(s) = 4/ (s2 + 2s + 2 ) if the input is r(t) = u(t), the steady-state tracking error is . a. 0 b. 1. c. 2 d. −1 e. None
Find the transfer function H(jω) for the
circuit above as a function of jω. (Leave R and L as variables).
Assume V R to be the output and V S to be the input.
С L RVR(t) vs (t) A. Find the transfer function H(jo) for the circuit above as a function of jaw. (Leave R and L as variables). Assume V to be the output and V to be the input. S R B. Find the Magnitude and Phase...
1. Consider a feedback system given below: T(s) Disturbance Controller Dynamics R(S) + Gc(s) G.(s) U(s) Sensor H(s) IMs) Sensor noise where the input and transfer functions are given as follows: R(s) = –,7,(s) = 0, N(s) = 0, G, - 15,6, -_- , and H(s) = 1. s's + 3) a. Derive the system transfer function Y(s)/R(s) = G,, poles, $, On, and, from the response function y(t), the performance measures: rise time Tr, peak time Tp, percent overshoot...
Problem 1: Let y()- r(t+2)-r(t+1)+r(t)-r(t-1)-u(t-1)-r(t-2)+r(t-3), where r(t) is the ramp function. a) plot y(t) b) plot y'() c) Plot y(2t-3) d) calculate the energy of y(t) note: r(t) = t for t 0 and 0 for t < 0 Problem 2: Let x(t)s u(t)-u(t-2) and y(t) = t[u(t)-u(t-1)] a) b) plot x(t) and y(t) evaluate graphically and plot z(t) = x(t) * y(t) Problem 3: An LTI system has the impulse response h(t) = 5e-tu(t)-16e-2tu(t) + 13e-3t u(t) The input...
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.
2. An effective control design concerns itself with more than the transfer function between the reference input, r(t), and the system output, y(t). For well-posedness and eventually internal stability (see (DFT) Sections 3.1 and 3.2), all nine transfer functions between the input signals R[S], D[s], and N[s] and the outputs of the summing junctions e1[s], e2[S], and e3 [S], must exist and be stable, respectively. For this problem, find the following four transfer functions in terms of G1 [s], G2...
1 4.4-1 The circuit shown in Fig. P4.4-1 has system function given by H(S) = Let R= 2 and 1+RCS C = 3 and use Laplace transform techniques to solve the following. (a) Find the output y(t) given an initial capaci- tor voltage of y(0%) =3 and an input x(t) u(t). (b) Given an input x(t) = u(t – 3), determine the initial capacitor voltage y(0%) so that the output y(t) is 1 volt at t = 6 seconds. =...