Glossary · Control theory and process control
State-space model
Also known as: State-space representation
German: Zustandsraummodell
In control engineering, a state-space model describes a dynamic system by a set of first-order differential or difference equations that relate inputs, internal state variables and outputs, usually written in matrix form.
- Control theory
In one sentence
A state-space model describes a dynamic system with first-order equations linking inputs, internal states and outputs, often in matrix form.
Example
The engineer models a two-mass drive train as a state-space model with motor speed, load speed and shaft torsion as states to design a vibration-damping controller.
How it applies
- Engineering: State-space models handle multiple inputs and outputs naturally and are the basis of state feedback, observers, Kalman filter design and Model predictive control (MPC). They can come from physics or from system identification with measured data.
- Simulation: Virtual commissioning and digital twin simulations often use state-space models of drives and processes.
- Documentation: Treat the model as an engineering artifact: record its states, units, parameter sources, validity range and version. In MBSE environments, link it to the System model elements it represents so changes can be traced.
State-space model vs. transfer function
A transfer function describes the input-output behavior of a linear system in the frequency domain. A state-space model also describes internal states and extends more easily to nonlinear and multivariable systems.