y(t) =-=-= is the unit step output for the system ....... 0 ſo 2 31 [0]...
y(t) =ş - e-st is the unit step output for the system ....... -2 1 0 1 0 0 1 x + 0u(t) 0 -6 -1 0 0 y = [1 0 0]x; x(0) = 0 0 X 0 1 0 -12 -8 1 X+0 u(t) 0 0 -2 y(t) = [1 1 0]x; x(0) = 0 »- 0 -3 1 07 [01 ? ܠ 0 -6 17x+11111(1) . . 0_0 -5 0 = ܐ [0 1 1]K; x(0) =...
Problem 2: (40 pts) Part A: (20pts) A third-order system has an of Y(s)-L[y(t) corresponding to a unit step input u(t) is known to be input of u(t) and an output of y(t). The forced response portion 1 Ys) (3 +3s2+ 4s +5) = a) Determine the input-output differential equation for the system b) From your result in a), determine the transformed free response Yee (s) corresponding to initial conditions of: y(0)= y(0) = 0 and ý(0)-6 Part B (20pts)...
5- For the following system: x( Input: x(t)s u(t) Output: y() With the initial condition y(0) 1, y(O)-0, RI-1, R2-12, CI-2F, C2-1F. Identify the natural and forced response of the system a) Find the zero input response. b) Unit impulse response. c) zero state response. d) The total response. e Identify the natural and forced response of the system. 5- For the following system: x( Input: x(t)s u(t) Output: y() With the initial condition y(0) 1, y(O)-0, RI-1, R2-12, CI-2F,...
1. (20 p) Compute and sketch the output y(t) of the continuous-time LTI system with impulse response h(t) = el-tuſt - 1)for an input signal x(t) = u(t) - ut - 3). 2. (20p) Consider an input x[n] and an unit impulse response h[n] given by n-2 x[n] = (4)”- u[n – 2] h[n] = u(n + 2] Determine and plot the output y[n] = x[n] *h[n].
1. Evaluate and sketch the convolution integral (the output y(t)) for a system with input x(t) and impulse response h(t), where x(t) = u(1-2) and h(t)= "u(t) u(t) is the unit step function. Please show clearly all the necessary steps of convolution. Determine the values of the output y(t) at 1 = 0,1 = 3,1 = 00. (3 pts)
Problem 1 Let's consider an LTI system with intput and output relatex through the equation y(t) - --- (T 2) dr a) Find the impulse response h(t) for the given system (1). b) Is this system cansal or not? c) Determine the output of the system when the input x(t) is as shown below. Problem 2 Evaluate the following convolution where (t) and y(t) are plotted helow z(t) = z(t) * y(t) Hint. Expr the signals as a linear combination...
2. When a unit step is applied to a system at 0 its response is y(1) = | 4 +-e-3,-e-2,(2 cos 41 + 3 sin 41) | u(t) (a) What is the transfer function of the system? (b) What is the governing differential equation for this system?
Q3 (LSM2). An LTI system has a unit-step response of s(t) = (1 – e-t-1))u(t – 1). What is the output y(t) of the system in response to input r(t) = 8(t+1)? (a) y(t) = e-lu(t). (b) y(t) = e-(e+1)u(t+ 1). (c) y(t) = (1 – e-")u(t). (d) y(t) = (1 – e-(+1) )u(t + 1).
2- Solve for y(t) for the following system 1 01 -3 represented in state space, where u(t) is the unit step. Use the Laplace transform approach to solve the state eqiation. 1 u(t) 0 -6 1|x + 0 -5 [0 1 1 ]x; x(0) = 0 %3D
An LTI system, with an input g(t) and an output y(t), is represented with the following state and output matrices. Assuming a zero-state condition, identify the steady state error if the system is subject to a unit step function. [x1 [x2. ) = [] : [22] + [3] AND y = [2 -1) [x3] + [2]g 4. 0 2 1 3 5