EE 350 Continuous-Time Linear Systems Recitation...

Rec 15.School of Electrical Engineering and Computer Science

Jeffrey Schiano 2015-2017 All rights reserved.

EE 350

Continuous-Time Linear Systems

Recitation 15

1



Recitation 15 Topics

2

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

• MATLAB Exercises– SIMULINK graphical programming language



Problem 1

• Derive the Final Value Theorem

3

0lim ( ) lim ( )

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

t sf t sF s

sF s



Problem 1 Solution

4



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

5

12F(s)=

2 ( 3)s

s s s



Problem 2 Solution

6



Problem 2 Solution

7



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

8

2

10G (s) = 7 10p s s

R

YPK pG sE



Problem 3 Solution

9



Problem 3 Solution

10



Problem 3 Solution

11



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?

12

R

Y6

11s

E

14s



Problem 4 Solution

13



Problem 4 Solution

14



Problem 4 Solution

15



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

following frequency response functions

Verify your answers using the MATLAB command bode

16

2

1000H( ) = 10

100H( ) = 10

jj

jjj



Problem 5 Solution

17



Problem 5 Solution

18



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

19



EE 350

Continuous-Time Linear Systems

Recitation 15

1



Recitation 15 Topics

2

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

• MATLAB Exercises– SIMULINK graphical programming language



Problem 1

• Derive the Final Value Theorem

3



Problem 1 Solution

4



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

5



Problem 2 Solution

6



Problem 2 Solution

7



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

8



Problem 3 Solution

9



Problem 3 Solution

10



Problem 3 Solution

11



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?

12



Problem 4 Solution

13



Problem 4 Solution

14



Problem 4 Solution

15



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

following frequency response functions

Verify your answers using the MATLAB command bode

16



Problem 5 Solution

17



Problem 5 Solution

18



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

19

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EE 350 Continuous-Time Linear Systems Recitation...

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