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# Model and Controller Simplification

Order reduction of plant models and synthesized controllers

Complex models are not always required for good control. Unfortunately, optimization methods, including methods based on HH2, and µ-synthesis optimal control theory, generally tend to 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

 `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 `ncfmr` Balanced model truncation for normalized coprime factors `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 -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.

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