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y(t) =ş - e-st is the unit step output for the system ....... -2 1 0...
y(t) =-=-= is the unit step output for the system ....... 0 ſo 2 31 [0]...
y(t) =-=-= is the unit step output for the system ....... 0 ſo 2 31 [0] X = 0 6 5 x + u(t) 1 4 2 y = [1 2 0x :-2 0 0 0 +XI u(1) 0 -6 -1 y = [1 0 0]x; x(0) = 0 26 --- -0 O -3 0 0 -6 1 x+ (1) 0 0-5 y = [ 011]x; x(0) = 0 ed o LO 0 1 * = -12 -8 1 x...
Laplace transform of the unit step function y"+y= St/2, if 0 St<6, 13, if t >...
Laplace transform of the unit step function
y"+y= St/2, if 0 St<6, 13, if t > 6 y(0) = 6, y'(0) = 8
2- Solve for y(t) for the following system 1 01 -3 represented in state space, where...
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
1. Evaluate and sketch the convolution integral (the output y(t)) for a system with input x(t)...
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)
Q3 (LSM2). An LTI system has a unit-step response of s(t) = (1 – e-t-1))u(t –...
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. When a unit step is applied to a system at 0 its response is y(1)...
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?
5- For the following system: x( Input: x(t)s u(t) Output: y() With the initial condition y(0) 1...
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. Consider the system described by: *(t) - 6 m (0) + veu(t): y(t) = 01...
1. Consider the system described by: *(t) - 6 m (0) + veu(t): y(t) = 01 (1) 60 = {1, 1421 a) Find the state transition matrix and the impulse response matrix of the system. b) Determine whether the system is (i) completely state controllable, (ii) differentially control- lable, (iii) instantaneously controllable, (iv) stabilizable at time to = 0. c) Repeat part (b) for to = 1. d) Determine whether the system is (i) observable, (ii) differentially observable, (iii) instanta-...
Problem 2: (40 pts) Part A: (20pts) A third-order system has an of Y(s)-L[y(t) corresponding to...
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)...
Laplace transform of the unit step function y" + 4y = ſi, if 0 <t<, y(0)...
Laplace transform of the unit step function
y" + 4y = ſi, if 0 <t<, y(0) = 0, y'(0) = 0. 10, if a St<oo.'
y(t) =-=-= is the unit step output for the system ....... 0 ſo 2 31 [0] X = 0 6 5 x + u(t) 1 4 2 y = [1 2 0x :-2 0 0 0 +XI u(1) 0 -6 -1 y = [1 0 0]x; x(0) = 0 26 --- -0 O -3 0 0 -6 1 x+ (1) 0 0-5 y = [ 011]x; x(0) = 0 ed o LO 0 1 * = -12 -8 1 x...
Laplace transform of the unit step function
y"+y= St/2, if 0 St<6, 13, if t > 6 y(0) = 6, y'(0) = 8
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
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)
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. 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?
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. Consider the system described by: *(t) - 6 m (0) + veu(t): y(t) = 01 (1) 60 = {1, 1421 a) Find the state transition matrix and the impulse response matrix of the system. b) Determine whether the system is (i) completely state controllable, (ii) differentially control- lable, (iii) instantaneously controllable, (iv) stabilizable at time to = 0. c) Repeat part (b) for to = 1. d) Determine whether the system is (i) observable, (ii) differentially observable, (iii) instanta-...
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)...
Laplace transform of the unit step function
y" + 4y = ſi, if 0 <t<, y(0) = 0, y'(0) = 0. 10, if a St<oo.'
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