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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.


hinfstruct H∞ tuning of fixed-structure controllers
hinfstructOptions Set options for hinfstruct
hinfsyn Compute H∞ optimal controller for LTI plant
h2syn H2 control synthesis for LTI plant
sdhinfsyn Compute H∞ controller for sampled-data system
h2hinfsyn Mixed H2/H∞ synthesis with pole placement constraints
hinfnorm H∞ norm of dynamic system
augw State-space or transfer function plant augmentation for use in weighted mixed-sensitivity H∞ and H2 loopshaping design
mkfilter Generate Bessel, Butterworth, Chebyshev, or RC filter
makeweight First-order weighting function with specified DC gain, crossover frequency, and high-frequency gain

Examples and How To

H Tuning of Fixed-Structure Controllers

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.

Fixed-Structure H-infinity Synthesis with HINFSTRUCT

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

Speed Up Tuning with Parallel Computing Toolbox Software

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

Active Suspension Control Design

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.


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.

About H-Infinity Synthesis

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.

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