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An LTI system, with an input g(t) and an output y(t), is represented with the following...
The output of an LTI system is yı(t) when xy(t) is the input. System yı(t) -1...
The output of an LTI system is yı(t) when xy(t) is the input. System yı(t) -1 1 The output of the system is yz(t) when x2(t) is the input. x (t) 3 N yz(t) System Express yz(t) in terms of yı(t) using the following format yz(t) = a, y(t-by) + a2 yı(t-b2)
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,...
UestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Fin...
uestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Find a state equation and state transition matrices (A,B, C and D) of the system for a step input 6u(t). ii) Find the state transition matrix eAt) ii) Find the output response of system y(t) to a step input 6u(t) using state transition matrix, iv) Obtain the output response y(t) of the system with two other methods for step input óu(t). Question IV. A system is described...
Q5. The measured input-output pair of for an LTI system is observed as follows: LTI system...
Q5. The measured input-output pair of for an LTI system is observed as follows: LTI system imput: x(t)-1+2cos(t)+5cos (2t)+4cos(t) LTI system output: y(t)-3+cos(t) +6cos(3t) For a new input x(t) = 1+2*cos(t)+5.5*cos(2t)+4*cos(3t), the conrespondding output is observed in the form of y (t)-A+Bcos(t)+Ccos (2t)+Dcos(3t). Determine the values of coefficients of A, B, C, and D A- D- Submit Answer Tries 0/3
3. Consider a system with the following state equation h(t)] [0 0 21 [X1(t) [x1(t) y(t)...
3. Consider a system with the following state equation h(t)] [0 0 21 [X1(t) [x1(t) y(t) [0.1 0 0.1x2(t) X3(t) The unit step response is required to have a settling time of less than 2 seconds and a percent overshoot of less than 5%. In addition a zero steady-state error is needed. The goal is to design the state feedback control law in the form of u(t) Kx(t) + Gr(t) (a) Find the desired regon of the S-plane for two...
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
The input-output relationship for a system is ¨y(t) + ˙y(t) = x(t). (a) Find the impulse...
The input-output relationship for a system is ¨y(t) + ˙y(t) = x(t). (a) Find the impulse response of the system. (b) Find the zero-state response when the input is a unit step. (c) Find the zero-state response when the input is x(t) = 1.6u(t) − 0.6u(t − 1).
3) Consider the system depicted below xz Input: F. Output: x Assume that all initial conditions a...
3) Consider the system depicted below xz Input: F. Output: x Assume that all initial conditions are zero. a) Derive mathematical model of the system b Find unit step response c) Find the transfer function T(s) X2(s)/Fs) d) What is the final value of the output be. limx)-7) for F)- 4) Find the transfer function state space R(s) for each of the following sytems represented in a) 10 y-[1 0 0 b) 2 -3-8 3 -5 y-1 3 6 c)...
3. a) Find a state space representation for a linear system represented by the following differen...
3. a) Find a state space representation for a linear system represented by the following differential equation, where v(t) denotes the input and y(1) is the output: b) Consider a linear system represented by the following differential equation, where x() denotes the input and y(t) is the output: )+4()+4y()x(t) i) Write down its transfer function and frequency response function i) What is the form of the steady state response of the above system due to a periodic input that has...
14. An LTI system has the following transfer function, determine the output system response y(t) due...
14. An LTI system has the following transfer function, determine the output system response y(t) due to the input x(t) e u(t) H(s) s+2 S+7s+12 Answer: y(t)
The output of an LTI system is yı(t) when xy(t) is the input. System yı(t) -1 1 The output of the system is yz(t) when x2(t) is the input. x (t) 3 N yz(t) System Express yz(t) in terms of yı(t) using the following format yz(t) = a, y(t-by) + a2 yı(t-b2)
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,...
uestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Find a state equation and state transition matrices (A,B, C and D) of the system for a step input 6u(t). ii) Find the state transition matrix eAt) ii) Find the output response of system y(t) to a step input 6u(t) using state transition matrix, iv) Obtain the output response y(t) of the system with two other methods for step input óu(t). Question IV. A system is described...
Q5. The measured input-output pair of for an LTI system is observed as follows: LTI system imput: x(t)-1+2cos(t)+5cos (2t)+4cos(t) LTI system output: y(t)-3+cos(t) +6cos(3t) For a new input x(t) = 1+2*cos(t)+5.5*cos(2t)+4*cos(3t), the conrespondding output is observed in the form of y (t)-A+Bcos(t)+Ccos (2t)+Dcos(3t). Determine the values of coefficients of A, B, C, and D A- D- Submit Answer Tries 0/3
3. Consider a system with the following state equation h(t)] [0 0 21 [X1(t) [x1(t) y(t) [0.1 0 0.1x2(t) X3(t) The unit step response is required to have a settling time of less than 2 seconds and a percent overshoot of less than 5%. In addition a zero steady-state error is needed. The goal is to design the state feedback control law in the form of u(t) Kx(t) + Gr(t) (a) Find the desired regon of the S-plane for two...
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
3) Consider the system depicted below xz Input: F. Output: x Assume that all initial conditions are zero. a) Derive mathematical model of the system b Find unit step response c) Find the transfer function T(s) X2(s)/Fs) d) What is the final value of the output be. limx)-7) for F)- 4) Find the transfer function state space R(s) for each of the following sytems represented in a) 10 y-[1 0 0 b) 2 -3-8 3 -5 y-1 3 6 c)...
3. a) Find a state space representation for a linear system represented by the following differential equation, where v(t) denotes the input and y(1) is the output: b) Consider a linear system represented by the following differential equation, where x() denotes the input and y(t) is the output: )+4()+4y()x(t) i) Write down its transfer function and frequency response function i) What is the form of the steady state response of the above system due to a periodic input that has...
14. An LTI system has the following transfer function, determine the output system response y(t) due to the input x(t) e u(t) H(s) s+2 S+7s+12 Answer: y(t)
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