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 http://www.staff.ncl.ac.uk/damian.giaouris/ EEE8044

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

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

Gereral State Space Model

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

Complete Model

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.

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. EEE8044

Relation of state space and TF EEE8044

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 EEE8044

Observability It is not possible to see how the state x2 behaves… EEE8044

Controllability It is not possible to influence x2… EEE8044

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). EEE8044 13