First and Second Order Systems (a) (b) (c) (a) (b) (c) Consider the system x + ax = u. Let u = 0 for all time, and consider x(t). If x(0) and x(2) = e−6, what is the value of a? = 3 Now let a be the value found in Part (a). If u(t) = 1(t) is the unit step function and x(0) = 0, derive the response of x(t). = = 6, what is the value of u, so that x(t) approaches 3 as t tends to infinity for any initial value x(0)? Consider the following second-order system x+4x+3x= u. What are the poles of the system? What is the meaning that the system be stable in terms of system response x(t)? Is the system stable or not? Let r(t) be a constant reference. Design a PD controller - - u(t) = Kp(r − x) – Kax so that the system response to a step input has a settling time around 2 sec and an overshoot of about 5%. Show all working.

First and Second Order Systems (a) (b) (c) (a) (b) (c) Consider the system x + ax = u. Let u = 0 for all time, and consider x(t). If x(0) and x(2) = e−6, what is the value of a? = 3 Now let a be the value found in Part (a). If u(t) = 1(t) is the unit step function and x(0) = 0, derive the response of x(t). = = 6, what is the value of u, so that x(t) approaches 3 as t tends to infinity for any initial value x(0)? Consider the following second-order system x+4x+3x= u. What are the poles of the system? What is the meaning that the system be stable in terms of system response x(t)? Is the system stable or not? Let r(t) be a constant reference. Design a PD controller - - u(t) = Kp(r − x) – Kax so that the system response to a step input has a settling time around 2 sec and an overshoot of about 5%. Show all working.

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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