.18 The steady-state solution of stable systems is due to simple poles in the j2 axis of the s-planecoming from the input. Suppose the transfer function of the system isY (s)H (s) =X (s)1(s + 1)² +4(a) Find the poles and zeros of H (s) and plot them in the s-plane. Find then the correspond-ing impulse response h(t). Determine if the impulse response of this system is absolutelyintegrable so that the system is BIBO stable.243236CHAPTER 3 THE LAPLACE TRANSFORM(b) Let the input x (t) = u(t) and the initial conditions be zero, find y(t) and from it determinethe steady-state solution.(c)Let the input x (t) = tu(t) and the initial conditions be zero, find y(t) and from it determinethe steady-state response. What is the difference between this case and the previous one?(d) To explain the behavior in the case above consider the following: Is the input x (t) =tu(t)bounded? That is, is there some finite value M such that |x(t)| < M for all times? So whatwould you expect the output to be, given that the system is stable?Answers: System is BIBO stable; yss (t) = 0.2.

*Keeping a note ?as per our company guidelines we are supposed to answer ?️only first 3️⃣ sub-parts.…

18 The steady-state solution of stable systems is due to simple poles in the j2 axis of the s-plane coming from the input. Suppose the transfer function of the system is Y (s) H (s) = X (s) 1 (s + 1)² +4° (a) Find the poles and zeros of H (s) and plot them in the s-plane. Find then the correspond- ing impulse response h(t). Determine if the impulse response of this system is absolutely integrable so that the system is BIBO stable. 243

18 The steady-state solution of stable systems is due to simple poles in the j2 axis of the s-plane coming from the input. Suppose the transfer function of the system is Y (s) H (s) = X (s) 1 (s + 1)² +4° (a) Find the poles and zeros of H (s) and plot them in the s-plane. Find then the correspond- ing impulse response h(t). Determine if the impulse response of this system is absolutely integrable so that the system is BIBO stable. 243

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

O Exercise. In this exercise, you will examine the changes to the analytic step response of a transfer function with a single zero. Consider the transfer function used in the previous activity: 12+2 (a) Compute the symbolic form of the step response of the transfer function, x(1). You can perform the analytic computations by hand or using the Symbolic Math Toolbox. X Use these synbolic variables syns s z_e t positive X Write your solution here x = NaN (b) Plot the analytic step response with zo =-1 on the interval E (0, 10]. If you computed the step response function with the Symbolic Math Toolbox, you can use the matlabFunction command to convert it to a function handle that you can evaluate. X Create your plot here (c) Using the analytic form of the transfer function, compute the limit of the function as t+ 0o. X Write your solution here tlim = NaN
There are cases when there is a zero in the first column while forming the Routh-Hurwitz table for a particular system. Describe how to modify the Routh-Hurwitz table that has one of the cases above using the transfer function of an open-loop system shown below as an example. G(s) =1000/ s5+ 2s4+ 3s3+ 6s2+ 5s + 3
k(s – 2) s' +4s +13 10. Form sketching the root-locus of the system has transfer function G(s) = 2 find the break-in point on the negative real axis.
3. For the block diagram below, a. Find the closed loop transfer function b. Find the poles and tell the natures of damping of the closed loop system c. Based on the transfer function, please write down the time domain differential equations between inputs and outputs d. For step input, calculate %OS and R(s) + 10 s(s+2) C(s) - wn, S. Tp. T:
b- Below is the transfer function for a 1st order IIR (Infinite Impulse Response) system. Convert this system to differential equation form and implement it as 1st Direct form and 2nd Direct form. 1+ 2z-1 Н(2) 1- 0.5z-1
The input and output voltages of a filter operating under sinusoidal steady-state conditions are observed on an oscilloscope. The peak amplitude of the input is 7 V and the output is 28 V. The period of both signals is 4 ms. The input reaches a positive peak at t = 1.0 ms, and the output reaches its positive peak at t = 1.8 ms. Determine the corresponding value of the transfer function. Enter your answer using polar notation. Express argument in degrees. H(f) = ?
D Using - transformation. find the impulse response af System desoribed by Sn+ 3, where Sn is a unit impulse function.
L Exercise. You can write the DC motor angular velocity transfer function as s + bs +c (a) Suppose that a DC motor has constants g = 60, b = 2.3, and e = 11. Define the transfer function in MATLAB using the tf function. % write your code here (b) Is the system stable? You can plot the poles in the s-plane using the pzmap function. For example, to plot the poles of a transfer function G, use: pznap(G) % write your code here (c) What are the poles of the transfer function? You can use the pole function to compute the poles of a dynamic system in MATLAB. For example, to identify the poles of a transfer function R, use: pole(R) % write your code here
Question 1 Determine the transfer functions in the figure below. You can assume that the transfer functions are either 1-order or 2nd order and underdamped, and that a unit step input has been applied at t =0 seconds. 1.2 25 0.8 0.6 1.5 0.4 0.2 10 15 1.2 1. 0.8 0.6 0.4 2 0.2 10 15 0.5 1.5 Figure 1: Step responses of four different systems. Unit step input applied at t =0 seconds.
A system is Causal. The transfer function of system is as below Find the impulse response of system 522 22 – z – 6
For the circuit shown in figure: R= 40 L=1H V„(t) ( our (t) C= 0.2 F a) Calculate the transfer function (out) of the circuit. Vin Vc(s) H(s) = 1 Vin (s) LCs² + RCs +1 Write your answer here b) Using MATLAB use the transfer function you got in part (a) to plot the impulse response. Insert screen shot of MATLAB code and Result here c) Using MATLAB, use the transfer function you got in part (a) to plot the step response. Insert screen shot of MATLAB code and Result here d) Explain in details, what is the difference between Impulse and step response? Write your answer here
Consider the following block diagram. a. Find the poles and zeros of the open-loop transfer function (that is, K=K,=0) b. Find the closed-loop transfer function. + 1 1 s-1 (s +3)(s – 1) R2 K,