CTN.

Table of Contents

1. Lec 4 Frequency response of a linear system
   1. I. What a linear system does to a sine wave
   2. II. How to calculated frequency response
      1. a. Introduction
      2. b. Example
         1. 1.
         2. 2.
   3. III. Calculating steady-state motion
   4. IV. Bode plot
   5. V. Nyquist plot
   6. VI. Nyquist stability criterion

Lec 4 Frequency response of a linear system

I. What a linear system does to a sine wave

• note that one is mutliplication and the other is sum.

It’s necessary to know the frequency, amplititude and inital phase.

As examples are simple, so they’re left behind.

II. How to calculated frequency response

a. Introduction

b. Example

1.

2.

III. Calculating steady-state motion

IV. Bode plot

It’s two graph of frequency and amplitude with different scales.

V. Nyquist plot

VI. Nyquist stability criterion

If we know Nyquist plot of an open-loop system. We wanna determine stability of the corresponding closed-loop system.

How?

IF W(s) is unstable, then the closed-loop system will be stable if the Nyquist plot of W(jω) encircles at the point (-1,0) as many times, as there are poles of w(s) in the right half plane.