PS State-Space

Implement linear state-space system

Since R2025a

• 

Libraries:
Simscape / Foundation Library / Physical Signals / Linear Operators

Description

The PS State-Space block implements a state-space representation of the linear time-invariant system, defined by equations:

$$\begin{array}{l}E\dot{x}=Ax+Bu,\\ y=Cx+Du,\end{array}$$

where:

• x is the dimensionless state vector.

• u is the input vector.

• y is the output vector.

• E is the descriptor matrix.

• A is the state matrix.

• B is the input matrix.

• C is the output matrix.

• D is the feedthrough, or direct transmission matrix.

The state-space model provides a compact and efficient way to represent and analyze systems with multiple inputs and outputs. This model is particularly useful for control design and simulation of dynamic systems.

You can define matrices in your workspace and then use these workspace variables as block parameters.

Examples

Heat Sink Using PS State-Space Block

How the PS State-Space block can be used to model a heat sink in air. The heat sink is modeled as rods with distributed masses along the length of the rods fixed to a base. The rods extend from the surface that undergoes conduction along its length and convection with air in the direction perpendicular to its length.

• Open Model

Ports

Input

U — Input physical signal vector, u, untyped

physical signal

Input physical signal.

Output

Y — Output physical signal vector, y, untyped

physical signal

Output physical signal.

Parameters

A — State matrix

[0, 1; -1, -2] (default) | scalar | matrix

State matrix, specified as an n-by-n matrix, where n is the number of states.

B — Input matrix

[0, 1] (default) | scalar | vector | matrix

Input matrix, specified as an n-by-m matrix, where n is the number of states and m is the number of elements in the input vector.

C — Output matrix

[1, 0] (default) | scalar | vector | matrix

Output matrix, specified as an r-by-n matrix, where r is the number of elements in the output vector and n is the number of states.

D — Feedthrough, or direct transmission matrix

0 (default) | scalar | vector | matrix

Feedthrough, or direct transmission matrix, specified as an r-by-m matrix, where r is the number of elements in the output vector and m is the number of elements in the input vector.

E — Descriptor matrix

[1, 0; 0, 1] (default) | scalar | matrix

Mass matrix of the system. The mass matrix can be singular or nonsingular and must have the same dimensions as the state matrix A.

Initial state vector — Initial condition of state vector

[0; 0] (default) | scalar | vector | matrix

Dimensionless vector that represents the initial conditions of the state vector at time t=0.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2025a