Model and Controller Simplification

Order reduction of plant models and synthesized controllers

Complex models are not always required for good control. Optimization methods, including methods based on H_∞, H₂, and µ-synthesis optimal control theory, generally produce controllers with at least as many states as the plant model. Model-order reduction commands help you to find less complex low-order approximations to plant and controller models.

Functions

`ncfmr`	Model reduction from normalized coprime factorization
`reduce`	Simplified access to Hankel singular value based model reduction functions
`balancmr`	Balanced model truncation via square root method
`bstmr`	Balanced stochastic model truncation (BST) via Schur method
`hankelmr`	Hankel minimum degree approximation (MDA) without balancing
`hankelsv`	Compute Hankel singular values for stable/unstable or continuous/discrete system
`modreal`	Modal form realization and projection
`schurmr`	Balanced model truncation via Schur method
`dcgainmr`	Reduced order model
`slowfast`	Slow and fast modes decomposition

Topics

Why Reduce Model Order?
In the design of robust controllers for complicated systems, model reduction fits several goals.
Hankel Singular Values
Hankel singular values define the energy of each state in the system. Model reduction techniques based on Hankel singular values can achieve a reduced-order model that preserves important system characteristics.
Model Reduction Techniques
Model reduction routines are categorized into two groups, additive error and multiplicative error types.
Approximate Plant Model by Additive Error Methods
Reduce a model with balancmr and examine the resulting model error.
Approximate Plant Model by Multiplicative Error Method
Reduce a model with bstmr and examine the resulting model error.
Using Modal Algorithms
modreal lets you reduce a model while preserving jω-axis poles.
Reducing Large-Scale Models
modreal can be the best way to start when reducing large models.
Normalized Coprime Factor Reduction
Compute a reduced-order model by truncating a balanced coprime set of a model.
Simplifying Representation of Uncertain Objects
Simplify uncertain models built up from uncertain elements to ensure that the internal representation of the model is minimal.

Featured Examples

Simplifying Higher-Order Plant Models

Approximate high-order plant models by simpler, low-order models.

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