Short Notes: State Space Analysis | Control Systems - Electrical Engineering (EE) PDF Download

 Page 1


STATE SPACE ANALYSIS
Page 2


STATE SPACE ANALYSIS
Introduction
• State space analysis is an powerful and modern approach for the design 
and analysis of control systems.
• The conventional or old methods for the design and analysis of control
systems is based on transfer function method.
• The transfer function method for design and analysis had many drawbacks 
such as..
– Transfer function is defined under zero initial conditions
– Applicable to LTI systems
– SISO systems
– Does not provide the information regarding internal state of 
the system
• Initial conditions can be incorporated in the system design
• State equations are highly compatible for simulation on analog or digital 
computers
Page 3


STATE SPACE ANALYSIS
Introduction
• State space analysis is an powerful and modern approach for the design 
and analysis of control systems.
• The conventional or old methods for the design and analysis of control
systems is based on transfer function method.
• The transfer function method for design and analysis had many drawbacks 
such as..
– Transfer function is defined under zero initial conditions
– Applicable to LTI systems
– SISO systems
– Does not provide the information regarding internal state of 
the system
• Initial conditions can be incorporated in the system design
• State equations are highly compatible for simulation on analog or digital 
computers
Advantagesofstatevariable
analysis.
This can be applicable to
• Linear systems
• Non-linear system
• Time variant systems
• Time invariant systems
• Multiple input multiple output systems
• This gives idea about the internal state of the 
system
Page 4


STATE SPACE ANALYSIS
Introduction
• State space analysis is an powerful and modern approach for the design 
and analysis of control systems.
• The conventional or old methods for the design and analysis of control
systems is based on transfer function method.
• The transfer function method for design and analysis had many drawbacks 
such as..
– Transfer function is defined under zero initial conditions
– Applicable to LTI systems
– SISO systems
– Does not provide the information regarding internal state of 
the system
• Initial conditions can be incorporated in the system design
• State equations are highly compatible for simulation on analog or digital 
computers
Advantagesofstatevariable
analysis.
This can be applicable to
• Linear systems
• Non-linear system
• Time variant systems
• Time invariant systems
• Multiple input multiple output systems
• This gives idea about the internal state of the 
system
Concept
The output not only depends on the input applied to the 
system for t > t
0
, but also on the initial conditions at time t = t
0
y(t) = y(t)¦ 
t=t0
+ y(t)¦
t=t0
`
-8 t
0
t
0
t
= ? y t + ? y(t)
t
= y(t
0
) + ?
0
y(t)
The term y(t
0
) is called the state of the system.
The variable that represents this state of the system is called 
the state variable
SYSTEM
Output
y(t)
Input
r(t)
Page 5


STATE SPACE ANALYSIS
Introduction
• State space analysis is an powerful and modern approach for the design 
and analysis of control systems.
• The conventional or old methods for the design and analysis of control
systems is based on transfer function method.
• The transfer function method for design and analysis had many drawbacks 
such as..
– Transfer function is defined under zero initial conditions
– Applicable to LTI systems
– SISO systems
– Does not provide the information regarding internal state of 
the system
• Initial conditions can be incorporated in the system design
• State equations are highly compatible for simulation on analog or digital 
computers
Advantagesofstatevariable
analysis.
This can be applicable to
• Linear systems
• Non-linear system
• Time variant systems
• Time invariant systems
• Multiple input multiple output systems
• This gives idea about the internal state of the 
system
Concept
The output not only depends on the input applied to the 
system for t > t
0
, but also on the initial conditions at time t = t
0
y(t) = y(t)¦ 
t=t0
+ y(t)¦
t=t0
`
-8 t
0
t
0
t
= ? y t + ? y(t)
t
= y(t
0
) + ?
0
y(t)
The term y(t
0
) is called the state of the system.
The variable that represents this state of the system is called 
the state variable
SYSTEM
Output
y(t)
Input
r(t)
Definitions
State: The state of a dynamic system is the smallest set of 
variables called state variables such that the knowledge of 
these variables at time t = t
o
(Initial condition), together 
with the knowledge of input for t = ?? 0
, completely 
determines the behavior of the system for any time ?? = ?? 0
.
StateVariables: A set of variables which describes the 
system at any time instant are called state variables
Statevector: A vector whose elements are the state 
variables
Statespace: The n-dimensional space whose co-ordinate 
axes consists of the x
1
axis, x
2
axis,.... x
n
axis, (where x
1
, x
2
,..... x
n
are state variables:) is called a state space.