Course introduction state space analysis.pdf

NPTEL

2. State Space Approach to Control
System Analysis and Design
A P Tiwari
Visiting Professor
School of Computing and Electrical Engineering
Indian Institute of Technology Mandi
Kamand (HP), India
Course Introduction

3. Introduction
•System: A combination of components that act together to perform
a function not possible with any of individual components.
•Control System: the means by which any quantity of interest in a
system can be maintained or manipulated as desired.
•Open Loop System: A system in which the output has no effect on
the input.
•Closed Loop System: A system in which the output does have effect
on the input.
State Space Approach to Control System Analysis and
Design: Course Introduction
Reference
Selector
Forward ElementsCommand
Input
Output
Reference
Selector
Forward ElementsCommand
Input
Output
Feedback
Elements
Reference
Input
Feedback
Signal

4. Introduction (Contd.)
•Command Input: The motivating input signal to the system;
which is independent of the output and exercises control
over it.
•Reference Selector/Input transducer: A unit that establishes
the value of the reference input. The reference selector is
calibrated in terms of the desired value of the system
output.
•Reference Input: The command expressed in a form directly
usable by the system.
State Space Approach to Control System Analysis and
Design: Course Introduction
Reference
Selector
Forward
Elements
Command
Input
Output
Feedback
Elements
Reference
Input
Feedback
Signal

5. Introduction (Contd.)
•Forward Element: the unit that reacts to an actuating signal
to produce a desired output.
•Output: The quantity that must be maintained at a
prescribed value.
•Feedback Element: The unit that provides the means for
feeding back the output quantity.
•Actuating Signal: The signal that is the difference between
the reference input and the feedback signal.
State Space Approach to Control System Analysis and
Design: Course Introduction
Reference
Selector
Forward
Elements
Command
Input
Output
Feedback
Elements
Reference
Input
Feedback
Signal

6. Dynamical System: A system in which the present output is
dependent on the present as well as the past values of the
input. A dynamical system can be described in terms of
•Input and Output Variables
•Input, State and Output Variables
Dynamical System Representation
State Space Approach to Control System Analysis and
Design: Course Introduction
G(s) Output, y(s)Input, u(s)
A
⌠
⌡
BInput, u(t) Output, y(t)C
x(t)dx(t)/dt

7. Course Coverage
•Mathematical Modeling of Dynamical Systems from
first principles and representation into standard state-
space form
•Solution of State Equations, STM, methods of
determining STM
•Controllability, Observability
•Stability
•Control System Design: Pole placement, LQR, POF &
FOS Feedback
•Design of Observer/State Estimator
•Case Studies
State Space Approach to Control System Analysis and
Design: Course Introduction

8. Prerequisites
•First Course in Control Systems Engineering
•Engineering Mathematics
–Differential Equations
–Elementary Matrix Theory
–Laplace Transform
State Space Approach to Control System Analysis and
Design: Course Introduction

9. Outcome
Impart knowledge/expertise
–to analyze the system behaviour
–to work out improved design of Control
–to implement State feedback controllers based on
observed/estimated states
–to implement multirate output feedback controllers
capable of achieving response comparable to that
based on state feedback
State Space Approach to Control System Analysis and
Design: Course Introduction

10. Self-study topic
•You can refer to text books by
(1)John D’ Azzo and C H Houpis
(2)Jean F Franklin, David Powell and A Emami Naeni
(3)Norman S. Nise
and prepare a short note on Evolution of Control Systems.
State Space Approach to Control System Analysis and
Design: Course Introduction