State Space
Purpose
Model linear time-invariant system as state-space model
Library
Control / Continuous
Description
The State Space block models a state-space system of the form
where \(\mathbf{x}\) is the state vector, \(\mathbf{u}\) is the input vector, and \(\mathbf{y}\) is the output vector. The widths of the input and output signals are determined by the number of columns of the \(\mathbf{B}\) matrix and the number of rows of the \(\mathbf{C}\) matrix, respectively.
For a single-input system (i.e. if the \(\mathbf{B}\) matrix has only one column), the State Space block performs scalar expansion: If the input signal is a vector, the state-space model is applied to each element of the input vector individually, and the output signal is a concatenated vector of all system outputs.
Parameters
- A, B, C, D
The coefficient matrices for the state-space system. The dimensions for the coefficient matrices must conform to the dimensions shown in Fig. 158:
Fig. 158 State space system matrix dimensions
where \(n\) is the number of states, \(m\) is the width of the input signal and \(p\) is the width of the output signal.
If the matrix \(D\) is empty, it is internally expanded to a zero matrix of the size \(p \times m\).
- Initial condition
A vector of initial values for the state vector, \(\mathbf{x} = [x_0, x_1 \ldots x_n]\).
Note
A scalar initial condition will be applied to all internal states.
Note
In case of scalar expansion (the system is a single-input system with multiple input signals), the initial condition can also be a matrix, where each row defines the initial condition for the individual inputs.
Probe Signals
- Input
The input vector, \(\mathbf{u}\).
- Output
The output vector, \(\mathbf{y}\).
- State
The state vector, \(\mathbf{x}\).