Robust Control Toolbox

Reducing Plant and Controller Order

Detailed first-principles or finite-element plant models often have a large number of states. Similarly, H-infinity and mu-synthesis algorithms tend to produce high-order controllers with superfluous states. Robust Control Toolbox provides algorithms that let you reduce the order (number of states) of a plant or controller model while preserving its essential dynamics. As you extract lower-order models, which are more cost-effective to implement, you can control the approximation error.

Bode plots comparing magnitude and phase of original and reduced-order models.
Bode plots comparing the magnitude and phase of the original and reduced-order models for the rigid body motion dynamics of a multistory building.

The model reduction algorithms are based on Hankel singular values of the system, which measure the energy of the states. By retaining high-energy states and ignoring low-energy states, the reduced model preserves the essential features of the original model. You can use the absolute or relative approximation error to select the order, and use frequency-dependent weights to focus the model reduction algorithms on specific frequency ranges.

Simplifying Higher-Order Plant Models
Approximate higher-order plant models with simpler, lower-order models.

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Contrôle Commande avec Matlab et Simulink : du PID au gain scheduling

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