EE 350 Continuous-Time Linear Systems Recitation...

transcript

Rec 15.School of Electrical Engineering and Computer Science

EE 350

Continuous-Time Linear Systems

Recitation 15

Recitation 15 Topics

• Solved Problems – Analysis of Feedback Control Systems– Bode Plots

• MATLAB Exercises– SIMULINK graphical programming language

Problem 1

• Derive the Final Value Theorem

0lim ( ) lim ( )

Provided that ( ) has no poles on theimaginary axis or in th right-half lane

t sf t sF s

Problem 1 Solution

Problem 2

• Determine the final value of f(t) by– Solving for f(t) and taking the limit as t approaches infinity– Applying the final value theorem

12F(s)=

2 ( 3)s

Problem 2 Solution

Problem 3• A certain plant has the transfer function representation

• Is the zero-state unit-step response of the plant overdamped, critically damped, or underdamped?

• Choose the proportional gain KP so that the zero-state unit-step response of the closed-loop system is critically damped, and determine the resulting steady-state error

10G (s) = 7 10p s s

YPK pG sE

Problem 3 Solution

Problem 4• Determine the closed-loop transfer function Y(s)/R(s) for

the following feedback system

• Is the closed-loop system BIBO stable? If so, is the zero-state unit-step response underdamped, overdamped, or critically damped?

Problem 4 Solution

Problem 5• Sketch the Bode magnitude and phase plot of the

following frequency response functions

Verify your answers using the MATLAB command bode

1000H( ) = 10

100H( ) = 10

Problem 5 Solution

Problem 6

• Simulate the closed-loop system in Problem 3 using SIMULINK

• Write a MATLAB M-file that– Represents the system using a transfer function– Plots the zero-state unit-step response