H∞ tuning of fixed-structure controllers
CL = hinfstruct(CL0)
[CL,gamma,info] = hinfstruct(CL0)
[CL,gamma,info] = hinfstruct(CL0,options)
[C,gamma,info] = hinfstruct(P,C0,options)
the free parameters of the tunable
CL = hinfstruct(
This tuning minimizes the H∞ norm
of the closed-loop transfer function modeled by
CL0 represents a closed-loop control
system that includes tunable components such as controllers or filters.
CL0 can also include weighting functions that
capture design requirements.
the parametric controller blocks
C0. This tuning
minimizes the H∞ norm
of the closed-loop system
CL0 = lft(P,C0).
To use this syntax, express your control system and design requirements
as a Standard Form model, as in the following illustration:
P is a numeric LTI model that includes
the fixed elements of the control architecture.
also include weighting functions that capture design requirements.
be a single tunable component (for example, a Control
Design Block (Control System Toolbox) or a
or a cell array of multiple tunable components.
a parametric model or array of parametric models of the same types
Generalized state-space (
Numeric LTI model representing the fixed elements of the control
architecture to be tuned.
Single tunable component or cell array of tunable components of the control structure.
Each entry in
For more information and examples of creating tunable models, see Models with Tunable Coefficients (Control System Toolbox) in the Control System Toolbox™ User's Guide.
Set of options for
Tuned version of the generalized state-space (
To access the tuned parameter values, use
Tuned versions of the parametric models
Best achieved value for the closed-loop H∞ norm.
In some cases,
Data structure array containing results from each optimization
run. The fields of
hinfstruct is related to
hinfsyn, which also uses H∞ techniques
to design a controller for a MIMO plant. However, unlike
no restriction on the structure and order of the controller. For that
hinfsyn always returns a smaller
You can therefore use
hinfsyn to obtain a lower
bound on the best achievable performance.
hinfstruct requires some
familiarity with H∞ techniques.
It requires expressing your design requirements as frequency-weighting
functions on plant inputs and outputs, as described in Formulating Design Requirements as H-Infinity Constraints.
For a simpler approach to fixed-structure tuning, use
hinfstruct uses specialized nonsmooth optimization
techniques to enforce closed-loop stability and minimize the H∞ norm
as a function of the tunable parameters. These techniques are based
on the work in .
 P. Apkarian and D. Noll, "Nonsmooth H-infinity Synthesis," IEEE Transactions on Automatic Control, Vol. 51, Number 1, 2006, pp. 71-86.
 Bruisma, N.A. and M. Steinbuch, "A Fast Algorithm to Compute the H∞-Norm of a Transfer Function Matrix," System Control Letters, 14 (1990), pp. 287-293.