Discrete-time observer-form state-space model with varying matrix values
Control System Toolbox / Linear Parameter Varying
Use this block to implement a discrete-time varying state-space model in observer form. The system matrices A, B, C, and D describe the plant dynamics, and the matrices K and L specify the state-feedback and state-observer gains, respectively. Feed the instantaneous values of these matrices to the corresponding input ports. The observer form is given by:
where uk is the plant input, yk is the plant output, xk is the estimated state, and εk is the innovation, the difference between the predicted and measured plant output. The observer form works well for gain scheduling of state-space controllers. In particular, the state xk tracks the plant state, and all controllers are expressed with the same state coordinates.
Use this block and the other blocks in the Linear Parameter Varying library to implement common control elements with variable parameters or coefficients. For more information, see Model Gain-Scheduled Control Systems in Simulink.
yk— Measurement signal
Measured plant output signal.
A— Plant state matrix
Plant state matrix of dimensions Nx-by-Nx, where Nx is the number of plant states.
B— Plant input matrix
Plant input matrix of dimensions Nx-by-Nu, where Nu is the number of plant inputs.
C— Plant output matrix
Plant output matrix of dimensions Ny-by-Nx, where Ny is the number of plant outputs.
D— Plant feedforward matrix
Plant feedforward matrix of dimensions Ny-by-Nu.
K— State-feedback matrix
State-feedback matrix of dimensions Nu-by-Nx.
L— State-observer matrix
State-observer matrix of dimensions Nx-by-Ny.
uk— Control signal
Control signal (plant input).
xk— Estimated plant state vector
Vector of estimated plant states.
To enable this port, select the Output states parameter.
xk+1— Estimated next state vector
Estimated state values at next time step.
To enable this port, select the Output state updates parameter.
Initial conditions— System initial conditions
Initial state values, specified as a scalar or a vector whose length is the number of plant states.
Sample time (-1 for inherited)— Block sample time
Block sample time, specified as either –1 (inherited sample time) or a positive scalar value.
Output states— Provide state output
Select to enable the estimated states output port, xe.
Output state derivatives— Provide state updates
Select to enable the estimated state updates output port, xk+1.