Consider the following state-space representationA =; B = []; C = [10].1- The transfer function G(s) isa) G(s)=s²+45+31) G(s)=52-45+32- The state equation in observer canonical form isa) * = [¯¹³ à] + [9] u3- The system in the above state-space isb) x = [3] + [] ua) observable and controllable b) neither observable nor controllable4- The system isa) Stableb) Unstable5- The state transition matrix in time domain is[0.5 (e-3+e) 0.5 (e-t-e-t)]a) 0(t) = 0.5(e-t-e-t) 0.5 (e-³ + e-')]6- The state response if a unit step applied isa) x(t) =3tb) Ø(t)=[0.5(e³ + e²) 0.5(e³t — e²)]L0.5(e³-e) 0.5(e³t + e²)]b) x(t)=A A

Part 2:Explanation:1. Transfer Function \( G(s) \):Step 1: Identify the state-space representation…

Answered: Consider the following state-space…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Given the following second-order difference equation: y/n] + 1.4y[n – 1] + 0.45y[n – 2] = x[n] – x[n – 1] %3D with an input of x[n] = 0.1"u[n] and initial conditions y[-1] = 0 and y[-2] = 1. Determine the particular solution, yp[n].
a) Find the numerical expression for the transfer function Io/I, as a function of u for the circuit in the figure. b) Find the largest µ that will produce a bounded output signal for a bounded input signal. c) Find io for u = -3, 0, 4, 5, and 6 if i, = 5u(t) A. 8 kN va3 2 kN i 32 H Answers: 1000(1- 4) + 1000(5 – H) a) H(s) b) u < 5 H H(s) -3 4000/(s+8000) I, 20,000/s(s +8000) 0 1000/(s +5000) 5000/s(s + 5000) 4 -3000/(s + 1000)-15,000/s(s + 1000) 5 -4000/s -20,000/s2 6 -5000/(s - 1000) -25,000/s(s - 1000) c)
Өз (s) of a mechanical system in Figure Q1(c). T1(s) (c) Determine the transfer function
Consider the following second-order difference equation: y[n] + 1.4y[n – 1] +0.45y[n – 2] = x[n] – x[n – 1] with an input of x[n] = 0.1"u[n] and initial conditions y[-1] = 0 and y[-2] = 1.
3. given the system coefficients below. The initial conditions are given as y(-1) = 1 and y(-2) = 1, and x(n) = 3u(n). Solve for the zero-input, zero-state responses, and the total response of the system b, =[1 -2 1] a = [1 -0.77178 0.7225]
Draw the waveform of the following signal (draw from n=0 to n=5 only): X(n)=3u(n)-2r(n-2)+4r(n-3) Also draw y(n)=x(-n) Where, u(n) and r(n) are unit step, unit ramp DT functions, respectively
PROBLEM 3 Consider the electrical circuit shown in the diagram below, where: R1 = R2 = 0.5 Ohms L = 1 Henry C = 1 Farad (These values are UNREALISTIC, but they are used here for ease of calculation). No It) Nit) R2 OUTPUT INPUT For this problem assume that the analysis implies NULL initial conditions. (All the initial conditions are 0). a) What is the Transfer Function, H(s) = Vo(s) /Vi(s), for this system? b) What is the impulse response function, h(t) , for this circuit?
For an electrical circuit system shown in Figure Q1, analyze the circuit and then describe the transfer function, G (s) = Eo (s) / Ei (s). R1 R2 V(s) Vo(s) I(s) V(s) R3 V2(8) C
1) Given Figure 1, find the transfer function VC(s)/V(s). R₁ = 10 k v(t) fv₁ = 4 N-s/m f(1). fv₂² 80404040 = 4 N-s/m R, = 10 ΚΩ Figure 1 2) Find the transfer function X₁ (s)/V(s) of the system shown in Figure 2. 18 N-m-s/rad -X₁ (1) M₁-4 kg 0₁(1) L = 200 H 5 kg-m² K= 5 N/m 0000 -X₂(1) Figure 2 3) Find the transfer function, 0₂ (s)/T(s), for the rotational mechanical system shown in Figure 3. elle X3 (1) fv₂=4N-s/m 9 N-m/rad 1 N-m-s/rad T(t) 0₂(1) Figure 3 C = 10 µF 3 kg-m² M₂=4 kg fv4=4 N-s/m 0000 3 N-m/rad AAA!
Consider the difference equation below u(k)-3u(k-1)+4u(k-2)=e(k)-2e(k-1) where e(k) is the input and u(k) is the output (i) Calculate the transfer function (ii)If the input is a unit step, find U(z)
Given the two signals below, find a) the autocorrelation of x[n] b.) the autocorrelation of z[n] c.) the convolution of x[n] & z[n] using any method and lastly d) the cross correlation of these two signals. Show your solution.
Question 1: A) Derive the transfer function of the electrical circuits shown in Figure below and then show the output signal when the input is a unit step. V₁(s) Vc (s) V(s) elle Ls -18

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