1. State Space Analysis and Controller Design
EEE3001 – EEE8013
State Space Analysis and Controller Design
This lecture will be recorded and
you will be able to download it
Dr Damian Giaouris
EEE8044

2. State Space Very difficult to be studied => so we use computers
Computers are better with 1st order ODE
1 nth => n 1st
Powerful tools from the linear algebra
This is the “state space” approach
a) Multi Input Multi Output systems
b) Non-linear and time variant systems
c) Alternative controller design approaches

3. State Space Models x1 and x2 define the state vector x
defines the state (a complete summary/description) of the system
Knowing the current state and the future inputs we can predict the future states

4. Gereral State Space Model

5. Output
Sensors for both variables (the speed and the displacement)

6. Complete Model

7. State space rules
The state vector describes the system => Gives its state =>
The state of a system is a complete summary of the system at a particular point in time.
If the current state of the system and the future input signals are known then it is possible to define the future states and outputs of the system.
The choice of the state space variables is free as long as some rules are followed:
They must be linearly independent.
They must specify completely the dynamic behaviour of the system.
Finally they must not be input of the system.

8. State space The system’s states can be written in a vector form as:
A standard orthogonal basis (since they are linear independent)
for an n-dimensional vector space called state space.
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9. Relation of state space and TF
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10. Relation of state space and TF
where Bi is the ith column of the matrix B and Cj is the jth row of C.
Characteristic Equation
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11. Observability It is not possible to see how the state x2 behaves…
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12. Controllability
It is not possible to influence x2…
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13. Basic state space model ODEs => SS model Relation with TF
Summary:
Basic state space model
ODEs => SS model
Relation with TF
Observability (basic concept).
Controllability (basic concept).
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