Model and Controller Simplification
Complex models are not always required for good control. Optimization methods, including methods based onH∞,H2, andµ-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 preservingjω-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.
- 简化代表resentation of Uncertain Objects
Simplify uncertain models built up from uncertain elements to ensure that the internal representation of the model is minimal.