Mathematical Modelling: State Space Representation of Transfer Function Systems 1. Based on the following ordinary differential equations: x₁ (t) = = x₂(t) R *₂ (t) = x₁(t)-x₂(1) + m(t) y(t) = x₁(t) Obtain the transfer function of the system.

Q: H.W G(s) RS) CCS) S+5 HCS) = 1

A: Control systems are represented by transfer function. This can be written in both time domain and…

Q: 2: For r(t) shown below, sketch the signal y(t) = r(1– t)[u(t + 1) – u(2 – 31)](note that u(t) is…

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Q: Jetermine the output signal y(t) for the given system such that the input signal x(t) and the…

A: So first we will use convolution to find the output of the system.

Q: Find the Transfer Function of the system modeled by the following differential equation: dy(t) dx(t)…

A: The solution is given below

Q: a) If the input is vi (t) and the output is vo (t), determine the Transfer Function of the circuit.…

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Q: C(s) Find the transfer function of a system having differential equation R(S)

A: The transfer function of a control system is defined as the ratio of the Laplace transform of the…

Q: Determine i(t) if the transfer function s2 + 2s + 6 I(s) = 5. s2 + 3s + 2 H(s) = V(s) and v(1)=10e…

A: Given  I(s)V(s)=5s2+2s+6s2+3s+2v(t)=10 e-3t u(t)  Convert v(t) into s-domain, V(s)=10s+3

Q: Can you answer the following question? The answer is posted below: 10. Consider a system with the…

A: The diffrential equations,(a) b)

Q: 2. A system is described by the following ordinary differential equation: y + 3y + 5y + y = x + 4x +…

A: The transfer function is the Laplace transform of output to the input. so the transfer function can…

Q: Q1) A) Draw the root locus of the system represented by the following transfer function; G(S)= k…

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Q: A LTI CT system has transfer function H(s) = s² +1 (s + 1)(s² + 2s +17) Compute the steady-state and…

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Q: For given signals: x(t) = 2[u(t) -u(t − 2)], g(t) = (2-t)[u(t) -u(t - 2)] 1) plot x(t) 2) plot g(t)…

A: In this question we need to  a) Plot x(t),  b) Plot g(t),  c) Find convolution of x(t) and g(t),…

Q: Q5. Obtain the graphical convolution of the following two signals: for – 3 <t< 3 x(t) = {6 %D…

A: Explanation:

Q: Find the Transfer Function of the system modeled by the follo d²y(t) dt² dy(t) dt d³ y(t) dt3 +3-…

A: Given data, Differential equation is given as, d3ytdt3+3d2ytdt2+2dytdt=d2xtdt2+3xt

Q: a) Convert the circuit to the s domain. b) Determine the s domain voltage, Vc(s). c) Determine the…

A: The circuit diagram,The initial voltage across the capacitor,

Q: The block diagram of a time-invariant, linear, continuous-time system is given below. X 1 (s) and X…

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Q: Given u(t)=step(t) and h(t)=exp(-alpha t). a) perform convolution using different methods b) use…

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Q: A system is described by the following differential equation: d^y _d³y d²y dy 5- +4 + 2y = 2u dt³…

A: it us asked to represent the given differential equation in controllable canonical form and to find…

Q: A system produce the following mathematical expression: () 3t²-9t + 10. Is y(t) u(t) u(t) is a…

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Q: transfer function G(s) = X(s)/ F(s) Select one a. 5s2 b. 1/ 5s c. 1 / (5s2 ) d. 5s   Which of the…

A: In this question we will write about transfer function of given system....

Q: Q2: For the s-domain circuit in figure below. Find: (a) the transfer function [V,(s)/V(s)], (b) the…

A: The circuit in s-domain is shown below,

Q: FAST PLEASE Find the convolution of the signals using graphical procedure. - 2 x(1) = [I(,*): TE);…

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Q: Problem 6. Find the system functions and the block diagram representation (using integrators) for…

A: In this question,  We need to determine the transfer function.  We are solving this problem using…

Q: Consider the transfer function 6s² + 6s +12 3s² +9s +6 Which one of the following state-space…

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Q: Sketch the following signals, label the graphs properly: x() = u(t+1)- 21(t-1) +u(t- 3) - x() = 3e"…

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Q: 5 F(s) = => f(t) =? > f(t) (s+A)²(s+B)³

A: First we will write the given function in factor form then we will take inverse Laplace transform

Q: Homework 4 It is known that the differential equation of the system is d'y(t) +4 di dy(t) +3y(t) =…

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Q: Find the Transfer Function of the system modeled by the following differential ec d³y(t) d²y(t) dt²…

A: In this question we will find laplace transform of given equation....

Q: 7. A certain system is described by a differential equation d? y(t) di? + 3y(t) + 11y(t) = 5x(t) dt…

A: In this question,  Find the transfer function of the given system.  Transfer function is define the…

Q: A system with a transfer function Y(s)\R(s). Determine the steady state error to a unit step input.…

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Q: A discrete time signal is given by: x(n) = [2, 2, 2, 2, 3] Sketch the following signals : x(n)…

A: Given: A discrete time signal is x[n] = {2, 2, 2, 2, 3} To sketch : x[n] u[n-1]

Q: Solve the given initial-value problem. Give the largest interval I over which the solution is…

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Q: Q2. Derive the transfer function of the (R-L-R) circuit, and then find the state space…

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Q: g(t) 20sin (400rt) Find the fundamental period of g(t). The fundamental period of g(f) is ms.

A: Given g(t)=20sin(400πt)

Q: Find the transfer function G(S)= Y(s)/R(s) for the following system represented in the state space:

A: The state space matrix is  A=010001-3-2-5,B=0010 and C=100 Need to find the transfer function from…

Q: Détérmine the transfer function from the given differential equation. y""(t) + 3y'(t) + 6y(t) =…

A: When finding transfer function  We have to take zero initial conditions Use Laplace of differential

Q: y(5) + 8y(4) + 9y"" + 12y" + 13y' – 10y = x" – 3x' + 2x y(5) + 4y(4) + 8y" + 10y" + 7y' + 5y = x" –…

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Q: Provide equation of, c(t). if there is a numerical answer that is nonterminating, is should be…

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