(b) The input and output of a certain discrete time system are related by the linear constant coefficient difference equation defined by the expression below: y[n] - 5y[n-1] + 6y[n - 2] = x[n] + 3x[n-1] + 5x[n-2] (i) Sketch the system implementation structure using direct form 1. (ii) Find the transfer function of the system and plot the zero-pole map. Will you expect this system to be stable? Explain your answer. (iii) Find the impulse response h[n] of the system.

(b) The input and output of a certain discrete time system are related by the linear constant coefficient difference equation defined by the expression below: y[n] - 5y[n-1] + 6y[n - 2] = x[n] + 3x[n-1] + 5x[n-2] (i) Sketch the system implementation structure using direct form 1. (ii) Find the transfer function of the system and plot the zero-pole map. Will you expect this system to be stable? Explain your answer. (iii) Find the impulse response h[n] of the 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

A car was ignited & a signal from the engine i.e a(z) was passed through a cascade of 2 passive RC lowpass filters to generate an output signal, b(z).a.Show a differential equation derivation to describe the systemb.Make a sketch utilizing circuit diagramc.Mention if the RC system in question above isi.Time in-variant / Time variant ii.Non linear / lineariii.Non-invertible / Invertibleiv. Non-causal / Causal v. Have no memory / Have memory sytems.d. d2b(z)/dz2 + 3(db(z)/dz) +2b(z) = 3(da(z)/dz) +2a(z)Let's assume that the d.e(differential equation) above is that which is characterised by the RC system in the main question above.Where a(z) & b(z) is the input & output of the RC system respectively.Considering an impulse of a(z)=δ(z) is applied to the system, determine the output b(z) of the system
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
Open loop transfer function G( s ) = K/ s(s+3)(s+4) for a systema) using the Routh Hurwitz criterion, the poles of the closed loop system are purely imaginary calculate the value that K will get so that it has roots on the axis.b) calculate the maximum value that K will receive so that the system can be stablec) calculate the values that K will get so that the system can have roots at -1 on the real axis
Given a plant P(s)=−3s+1s+a and a model for measureable output disturbance d with transfer function Q(s)=1s+b. Compute the DC feedforward solution uP=u+Fd, where u is the feedback control, F is the feedforward gain, abd uP is the plant input, when a = 4.3 and b = 3 (use 2 decimals).
loop transfer function of the system given in the photo below;( K(s+A)/s(s2+s+B) Find the asymptotes and plot them in the s-plane. Calculate the gain when the two roots are on the imaginary axis. Calculate the angle of separation from the complex poles. draw root locus. A=5 B=4
Obtain the equation of motion by drawing the free body diagram of the given systems. a) Obtain the transfer function of the system and find the unit step response. Show all intermediate operations in detail. m=1 kg b=20 Ns/m k=125 N/m b) Obtain the transfer function of the system. X(s)/Pg(s) =? Show all intermediate operations in detail. Obtain the equation of motion by drawing the free body diagram of the given systems.
In a linear time-invariant discrete-time system, x[n] is the input and y[n] is the output. Unit at the entrance of the systemWhen initial conditions are zero when step (u[n]) is applied y[n] = 3(1/2)^n It is known that u[n] is output.Accordingly, create the transfer function of the system and find the unit sample answer for this system. (h[n]=?) Reminder: This question also covers z-transformation and inverse z-transformation.
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.
The input output relation for a discrete time system is expressed by the following difference equation: y(n)=ax(n)+bx(n-1)+cx(n-2)+dy(n-1)+ey(n-2) where a,b,c,d,e are non zero coefficients. Find out the two intermediate transfer functions if the system is to be realised by direct form 1.
A hard disk drive (HDD) is an electro-mechanical data storage device that stores and retrieves digital data using magnetic storage and one or more rigid rapidly rotating platters coated with magnetic material. Figure 1 shows a simplified block diagram of a HDD. For analysis purposes, given gain K=30 and G(s)=1 / s(s+4) determine the open-loop and closed loop poles of the HDD and plot these separately in the S-Plane. Also discuss the stability using two different approaches.
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
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.