ee 380 linear control systems lecture 3
TRANSCRIPT
EE 380 Fall 2014Lecture 3.
EE 380
Linear Control Systems
Lecture 3
Professor Jeffrey SchianoDepartment of Electrical Engineering
1
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
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
EE 380 Fall 2014Lecture 3.
Solution
4
EE 380 Fall 2014Lecture 3.
Solution
5
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
EE 380 Fall 2014Lecture 3.
Solution
7
EE 380 Fall 2014Lecture 3.
Solution
8
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
EE 380 Fall 2014Lecture 3.
Transfer Function Derivation
10
EE 380 Fall 2014Lecture 3.
Transfer Function Derivation
11
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
EE 380 Fall 2014Lecture 3.
Solution
13
EE 380 Fall 2014Lecture 3.
Solution
14
EE 380 Fall 2014Lecture 3.
EE 380
Linear Control Systems
Lecture 3
Professor Jeffrey SchianoDepartment of Electrical Engineering
1
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
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
EE 380 Fall 2014Lecture 3.
Solution
4
EE 380 Fall 2014Lecture 3.
Solution
5
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
EE 380 Fall 2014Lecture 3.
Solution
7
EE 380 Fall 2014Lecture 3.
Solution
8
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
EE 380 Fall 2014Lecture 3.
Transfer Function Derivation
10
EE 380 Fall 2014Lecture 3.
Transfer Function Derivation
11
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
EE 380 Fall 2014Lecture 3.
Solution
13
EE 380 Fall 2014Lecture 3.
Solution
14