H-Infinity Synthesis

Frequency-domain design of MIMO controllers

Robust Control Toolbox™ commands let you apply the powerful methods of H synthesis to control design problems. You can use hinfstruct to tune fixed-structure control systems, which are control systems that have predefined architectures and controller structures. Commands such as hinfsyn perform traditional synthesis of full-order, centralized controllers. For more information about the difference, see Difference Between Fixed-Structure Tuning and Traditional H-Infinity Synthesis.

Functions

hinfstructH∞ tuning of fixed-structure controllers
hinfstructOptionsSet options for hinfstruct
hinfsynCompute H-infinity optimal controller
hinfsynOptionsOption set for hinfsyn and mixsyn
hinffcFull-control H-infinity synthesis
hinffiFull-information H-infinity synthesis
h2synCompute H2 optimal controller
h2synOptionsOption set for h2syn
sdhinfsynCompute H∞ controller for sampled-data system
h2hinfsynMixed H2/H∞ synthesis with regional pole placement constraints
hinfnormH∞ norm of dynamic system
makeweightWeighting function with monotonic gain profile
mkfilterGenerate Bessel, Butterworth, Chebyshev, or RC filter
augwPlant augmentation for weighted mixed-sensitivity H∞ and H2 loop-shaping design

Topics

About Fixed-Structure Controller Tuning

What Is a Fixed-Structure Control System?

Fixed-structure control systems are have predefined architectures and controller structures.

Difference Between Fixed-Structure Tuning and Traditional H-Infinity Synthesis

Traditional H synthesis designs a full-order, centralized controller. Fixed-structure tuning lets you specify your control architecture and the structure and parameterization of the tunable elements of your system.

What Is hinfstruct?

hinfstruct lets you use H synthesis to tune control systems that have predefined architectures and controller structures.

Formulating Design Requirements as H-Infinity Constraints

To use hinfstruct, you express your design requirements as constraints on the closed-loop gain.

Structured H-Infinity Synthesis Workflow

Get an overview of the steps required to perform structured H synthesis.

H Tuning of Fixed-Structure Controllers

Fixed-Structure H-infinity Synthesis with HINFSTRUCT

This example shows the complete workflow for tuning a control system with hinfstruct.

Build Tunable Closed-Loop Model for Tuning with hinfstruct

To tune a control system with hinstruct, create a generalized LTI model of the system that includes the fixed and tunable elements and weighting functions that represent your design requirements.

Tune the Controller Parameters

Use hinfstruct to tune the tunable parameters in the genss model of your control system.

Interpret the Outputs of hinfstruct

hinfstruct returns a tuned version of the control system model a parameter that indicates how well the requirements are met.

Validate the Controller Design

To validate the hinfstruct control design, examine the performance of the tuned system.

Speed Up Tuning with Parallel Computing Toolbox Software (Control System Toolbox)

If you have the Parallel Computing Toolbox™ software installed, you can speed up the tuning of fixed-structure control systems.

H Synthesis of Centralized Controllers

Robust Control of an Active Suspension

In this example, use H synthesis to design a controller for a nominal plant model. Then, use μ synthesis to design a robust controller that accounts for uncertainty in the model.

Control of a Two-Tank System

This example shows how to use Robust Control Toolbox™ to design a robust controller (using D-K iteration) and to do robustness analysis on a process control problem.

Norms and Singular Values

For MIMO systems the transfer functions are matrices, and relevant measures of gain are determined by singular values, H, and H2 norms.

Interpretation of H-Infinity Norm

There are several ways of defining norms of a scalar signal, which have different physical interpretations and provide different measures of performance.

H-Infinity Performance

Many types of control objectives can be posed as a minimization of norms of closed-loop transfer functions.