QUESTION THREE a) a. Find the equivalent sampled impulse response and the equivalent z- transfer function for the cascade of the two analog systems with sampled input H₁ (s) = 1 H₂ (s) = 2 S +4 S+ 2 (i) If the system are directly connected (ii)If the systems are separated by a sampler b) The z-transform X (z) of a function X (k), is given by; z (0.1065z+0.09021) X (z) = (2-1)(z²-1.5z+0.6967) Determine an expression for X (k), by finding the inverse z-transform function of X(z) AP (8) c) Briefly explained the function of the hold device in a digital control system.

QUESTION THREE a) a. Find the equivalent sampled impulse response and the equivalent z- transfer function for the cascade of the two analog systems with sampled input H₁ (s) = 1 H₂ (s) = 2 S +4 S+ 2 (i) If the system are directly connected (ii)If the systems are separated by a sampler b) The z-transform X (z) of a function X (k), is given by; z (0.1065z+0.09021) X (z) = (2-1)(z²-1.5z+0.6967) Determine an expression for X (k), by finding the inverse z-transform function of X(z) AP (8) c) Briefly explained the function of the hold device in a digital control system.

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...

See similar textbooks

Similar questions

The impulse response of an LTI system is h(n) = 3δ(n) + (1/4)n u(n). Find the frequency response, H(e jω), and the difference equation of this system. An input signal x(n) = (1/3)n u(n), is applied to this system and an output signal y(n) is observed. Find the output signal, y(n), using DTFT methods. Give the system function H(z) using the frequency response H(ejω). Find the zeros, poles and ROC of this system and show them on the complex plane. Discuss the stability, causality, FIR/IIR and memory properties of this system.
The transfer function is H(s) = (1.2s+0.18)/(s3 + 0.74s2 + 0.92s) and C(s) = (K(s+1))/ s A) A disturbance input W(s) =W/sk , where W is a constant, into the feedbackcontroller as shown below. We set R(s) = 0. What type of disturbance input W(s)(step, ramp, or parabola) can thesystem reject (i.e., the steady-state error ess is a nonzero constant)? (B) Suppose you want to design the controller C(s) to produce a closed-loop response to areference step input that has no more than 30% maximum overshoot (Mp ≤ 0.30) and a peak timeof no more than 8 sec (tp ≤ 8). Given the specifications on Mp and tp , compute the constraintson the damping ratio ζ and the damped natural frequency ω, assuming that the closed-loop systemis approximated as a 2nd-order underdamped system. Sketch the allowable regions in thecomplex plane (the s-plane) that these constraints define, and shade in the regions where the polesshould not be placed.
You are given an unknown digital system with just the information that it is stable and causal. You are supposed to determine the frequency response and impulse response of it, so you apply a known input x(n) = u(n) to the system and observe y(n) = (30/13) [ 0.8n – (-0.5)n ] u(n) output. Give the system function H(z), its ROC, and the frequency response H(ejω). Calculate the impulse response h(n). Give the difference equation of the system. Is this system FIR/IIR ?
Examine the closed loop stability of a system whose open-loop transfer function is given by.G(s) H(s) =1+4s/s^2(1+s )(1+2s) use nyquist plot
y[n]+1.2y[n-1]+0.2y[n-2]=x[n]-0.5x[n-1] x[n] is system's input, y[n] is system's output. a) Find the transfer function of the system, H(z). Show the region of convergence by drawing the zero-pole diagram. b) Draw the block diagram representation of the system. c) Find h[n], which is the impulse response of the system. d) Is the frequency response H(e^jw) defined for this system? H(e^jw) if defined?
A system is described as: w (n + 1) = 0.5 w(n) — x(n) y(n) = w (n) - x(n) Where x(n) and y(n) are input and output signals, respectively. 1. Draw a block diagram or signal flow graph representation for this system by using Direct form II 2. Find the system function H(z) and the impulse response h(n) of this system. 3. Is this system causal or not? Why? 4. Is this system stable or not? why? 5. If the input impulse Dirac 8 find the difference equation.
A stable x(n) input signal is applied to an LTI system with a unit impulse response h(n), and y(n)=2 (1/4)'' u(n) output is obtained. a) Find the frequency response,H(ejω), of the system. b) Find the x(n) sign and spectrum applied to the input by DTFT. c) Give the input/output differential equation of the system.
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 here for ease of calculation) For this problem assume that implies NULL initial conditions (all the initial conditions are 0) a) what is the transfer function H(s) =Vo(s)/Vi(s) for the system ? b) what is the impulse response function h(t), for this circuit?
Apply the Circular convolution property of DFT to produce the result of an input signalx(n) =B{,B/2,B/3} with the impulse response H(n)= C{ C/2,C/3} Where B=32 C= 1.6
1. Since this is a first order system, provide expression for the time constant. 2. Provide a state space representation of the system. 3. Obtain the transfer function of the system using the state space model. 4. Determine the control gain Kp that results in steady-state error of 0.1
PleaseThe input-output relationship of a discrete-time LTI system is given as follows?[n] = 2x[n − 4] − 3x[n − 6].a) Determine the impulse response of the system, h[n].b) Using h[n], show that the system is causal.c) Using h[n], show that whether the system is BIBO stable or not.d) Determine the transfer function H(z). Plot pole-zero diagram. Indicate ROC.e) Using H(z), show that whether the system is stable or not.f) Determine the frequency response of the system, if exists. Why?g) Determine the impulse response of the inverse system calculated in f).
1.Draw the s-domain equivalent circuit for the circuit shown in Figure Q1.2 and then find the norton equivalent of the respective circuit you have drawn (with respect to terminal A-B)2.With the help of the Norton equivalent circuit in previous answer, calculate the transfer function for the circuit shown in Figure Q1.2.