0010(b.2) causal(b.3) stable(b.4) FIRFULLHD144HZF4F5F7(o)Pause-果#34.7.399I Consider an LTI system described by the impulse responseh[n] = 4°u[2-n](a) Sketch h[n](b) For this LTI system, determine and explain whether the following properties are true:(b.1) memoryless(b.2) causal

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Answered: Consider an LTI system described by the…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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3. Consider the system a) Use state feedback ? = ?? to assign the eigenvalues of ? + ?? at −0.5 ± ?0.5. Plot TT x(t) = [x1(t), x2(t)] for the open- and closed-loop system with x(0) = [−0.6, 0.4] . b) Design an identity observer with eigenvalues at −? ± ?, where ? > 0. What is the observer gain ? in this case? c) Use the state estimate ?̂ from (b) in the linear feedback control law ? = ? ?̂, where ? was found in (a). Derive the state-space description of the closed-loop system. If ? = ? ?̂ + ?, what is the transfer function between ? and ?? TT d) For ?(0) = [−0.6, 0.4] and ?̂(0)= [0, 0] , plot ?(?), ?̂ (?), ?(?), and ?(?) of the closed- loop system obtained in (c) and comment on your results. Use ? = 1, 2, 5, and 10, and comment on the effects on the system response. Remark: This exercise illustrates the deterioration of system response when state observers are used to generate the state estimate that is used in the feedback control law.
Please solve this problem
A PID controller has the following transfer function and gains: It is decided that this controller will have an open-loop pole at s = 0 and two zeros, both at s = -1. Calculate the values of KI’ and KD’.
1 G(s) = s(s? + s +1)(s + 2)*
For a signal x[n] = [1,–1,0, 2] where n = 0~ 3. a) Express x[n] as the sum of shifted and scaled 8[n] b) find its 4-point DFT X[k] for k = 0~3. c) find its DTFT X(e/") d) find X(e/") for w = 0,", = 0,5, 1, and make a drawing to show the four sample points on the unit 2 circle. e) compare your results from b) and d) and explain your findings. What is the relationship between X(el") and X[k]? f) What is the DC value of this signal?

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Consider an LTI system described by the impulse response h[n] = 4°u[2-n] (a) Sketch h[n] (b) For this LTI system, determine and explain whether the following properties are true: (b.1) memoryless (b.2) causal