ee 380 linear control systems lecture 3
TRANSCRIPT
![Page 1: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/1.jpg)
EE 380 Fall 2014Lecture 3.
EE 380
Linear Control Systems
Lecture 3
Professor Jeffrey SchianoDepartment of Electrical Engineering
1
![Page 2: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/2.jpg)
EE 380 Fall 2014Lecture 3.
Lecture 3 Topics
• Methods for Representing Continuous-Time Linear Systems– Examples
• State-Space Representation– Transfer function from state-space matrices
2
![Page 3: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/3.jpg)
EE 380 Fall 2014Lecture 3.
Example 1: Mechanical System
• Represent the mechanical system
using an ODE, transfer function, block diagram, all-integrator block diagram, and state-space model
3
MK
1B
( )u t
( )y t
2BInput: Force ( ) [ ]Output: Displacement ( ) [ ]
u t Ny t m
![Page 4: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/4.jpg)
EE 380 Fall 2014Lecture 3.
Solution
4
![Page 5: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/5.jpg)
EE 380 Fall 2014Lecture 3.
Solution
5
![Page 6: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/6.jpg)
EE 380 Fall 2014Lecture 3.
Example 2: Systems with m > 0• Consider a system with input u(t), output y(t),
and ODE model where n = 2 and m = 1
• Represent this system using – transfer function– block diagram– all-integrator block diagram– state-space model
6
5 6y y y u u
![Page 7: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/7.jpg)
EE 380 Fall 2014Lecture 3.
Solution
7
![Page 8: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/8.jpg)
EE 380 Fall 2014Lecture 3.
Solution
8
![Page 9: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/9.jpg)
EE 380 Fall 2014Lecture 3.
Transfer Function Representation• For a system represented by the state-space model
show that the transfer function representation is
9
,x Fx Guy Hx Ju
1
transfer function
Y s H sI F G J U s
![Page 10: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/10.jpg)
EE 380 Fall 2014Lecture 3.
Transfer Function Derivation
10
![Page 11: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/11.jpg)
EE 380 Fall 2014Lecture 3.
Transfer Function Derivation
11
![Page 12: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/12.jpg)
EE 380 Fall 2014Lecture 3.
Example 3• Determine the transfer function representation of the
single-input single-output (SISO) system with state-space representation
12
0 1 06 5 1
1 1
x x u
y x
![Page 13: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/13.jpg)
EE 380 Fall 2014Lecture 3.
Solution
13
![Page 14: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/14.jpg)
EE 380 Fall 2014Lecture 3.
Solution
14
![Page 15: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/15.jpg)
EE 380 Fall 2014Lecture 3.
EE 380
Linear Control Systems
Lecture 3
Professor Jeffrey SchianoDepartment of Electrical Engineering
1
![Page 16: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/16.jpg)
EE 380 Fall 2014Lecture 3.
Lecture 3 Topics
• Methods for Representing Continuous-Time Linear Systems– Examples
• State-Space Representation– Transfer function from state-space matrices
2
![Page 17: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/17.jpg)
EE 380 Fall 2014Lecture 3.
Example 1: Mechanical System
• Represent the mechanical system
using an ODE, transfer function, block diagram, all-integrator block diagram, and state-space model
3
![Page 18: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/18.jpg)
EE 380 Fall 2014Lecture 3.
Solution
4
![Page 19: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/19.jpg)
EE 380 Fall 2014Lecture 3.
Solution
5
![Page 20: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/20.jpg)
EE 380 Fall 2014Lecture 3.
Example 2: Systems with m > 0• Consider a system with input u(t), output y(t),
and ODE model where n = 2 and m = 1
• Represent this system using – transfer function– block diagram– all-integrator block diagram– state-space model
6
![Page 21: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/21.jpg)
EE 380 Fall 2014Lecture 3.
Solution
7
![Page 22: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/22.jpg)
EE 380 Fall 2014Lecture 3.
Solution
8
![Page 23: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/23.jpg)
EE 380 Fall 2014Lecture 3.
Transfer Function Representation• For a system represented by the state-space model
show that the transfer function representation is
9
![Page 24: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/24.jpg)
EE 380 Fall 2014Lecture 3.
Transfer Function Derivation
10
![Page 25: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/25.jpg)
EE 380 Fall 2014Lecture 3.
Transfer Function Derivation
11
![Page 26: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/26.jpg)
EE 380 Fall 2014Lecture 3.
Example 3• Determine the transfer function representation of the
single-input single-output (SISO) system with state-space representation
12
![Page 27: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/27.jpg)
EE 380 Fall 2014Lecture 3.
Solution
13
![Page 28: EE 380 Linear Control Systems Lecture 3](https://reader034.vdocuments.site/reader034/viewer/2022043013/626ba16520f1e55f694e83cd/html5/thumbnails/28.jpg)
EE 380 Fall 2014Lecture 3.
Solution
14