Modern Control Systems (MCS) : Lecture-41-42 Design of Control Systems in Sate Space
Modern Control Systems (MCS) : Lecture-41-42 Design of Control Systems in Sate Space
Modern Control Systems (MCS) : Lecture-41-42 Design of Control Systems in Sate Space
(MCS)
Lecture-41-42
Design of Control Systems in Sate Space
Quadratic Optimal Control
Dr. Imtiaz Hussain
email:
imtiaz.hussain@faculty.muet.edu.pk
URL
:http://imtiazhussainkalwar.weebly.co
m/
Outline
Introduction
Quadratic Cost Function
Optimal Control System based on
Quadratic Performance Index
Optimization by Second Method of
Liapunov
Quadratic Optimal Control
Examples
Introduction
Optimization is the selection of a best element(s)
from some set of available alternatives.
In control Engineering, optimization means
minimizing a cost function by systematically
choosing parameter values from within an allowed
set of tunable parameters.
A cost function or loss function or
performance indexis a function that maps
aneventor values of one or more variables onto
areal numberintuitively representing some "cost"
associated with the event (e.g. error function).
Example-1
Consider the system given below
Where
Example-1
We find that
Example-1
Example-1
Step-2: Calculate K using following equation