19-03-2014, 11:33 AM
STATE SPACE MODELS
STATE SPACE.ppt (Size: 110.5 KB / Downloads: 47)
Why State Space Models
The state space model represents a physical system as n first order differential equations. This form is better suited for computer simulation than an nth order input-output differential equation.
PARTS OF A STATE SPACE REPRESENTATION
State Variables: a subset of system variables which if known at an initial time t0 along with subsequent inputs are determined for all time t>t0+
State Equations: n linearly independent first order differential equations relating the first derivatives of the state variables to functions of the state variables and the inputs.
Output equations: algebraic equations relating the state variables to the system outputs.
Explanation
The first row of A and the first row of B are the coefficients of the first state equation for x'. Likewise the second row of A and the second row of B are the coefficients of the second state equation for v'. C and D are the coefficients of the output equation for y.
EXTRACTING A, B, C, D MATRICES FROM A STATE SPACE MODEL
In order to extract the A, B, C, and D matrices from a previously defined state space model, use MATLAB's ssdata command.
[A, B, C, D] = ssdata(statespace)
where statespace is the name of the state space system.
STEP RESPONSE USING THE STATE SPACE MODEL
Once the state space model is entered into MATLAB it is easy to calculate the response to a step input. To calculate the response to a unit step input, use:
step(statespace)
where statespace is the name of the state space system.
For steps with magnitude other than one, calculate the step response using:
step(u * statespace)
where u is the magnitude of the step and statespace is the name of the state space system.