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

All of the tuning commands systune, looptune, and hinfstruct tune the controller parameters by optimizing the H_∞ norm across a closed-loop system (see [1]). However, these functions differ in important ways from traditional H_∞ methods.

Traditional H_∞ synthesis designs a full-order, centralized controller. Traditional H_∞ synthesis provides no way to impose structure on the controller and often results in a controller that has high-order dynamics. Thus, the results can be difficult to map to your specific real-world control architecture. Additionally, traditional H_∞ synthesis requires you to express all design requirements in terms of a single weighted MIMO transfer function.

Fixed-structure control systems are control systems that have predefined architectures and controller structures. For example:

• A single-loop SISO control architecture where the controller is a fixed-order transfer function, a PID controller, or a PID controller plus a filter.

• A MIMO control architecture where the controller has fixed order and structure. For example, a 2-by-2 decoupling matrix plus two PI controllers is a MIMO controller of fixed order and structure.

• A multiple-loop SISO or MIMO control architecture, including nested or cascaded loops, with multiple gains and dynamic components to tune.

Unlike traditional H_∞ synthesis, structured H_∞ synthesis allows you to describe and tune the specific control system with which you are working. You can specify your control architecture, including the number and configuration of feedback loops. You can also specify the complexity, structure, and parameterization of each tunable component in your control system, such as PID controllers, gains, and fixed-order transfer functions. Additionally, you can easily combine requirements on separate closed-loop transfer functions.

You can use systune, looptune, or hinfstruct for frequency-domain tuning of virtually any SISO or MIMO feedback architecture to meet your design requirements. You can use both approaches to tune fixed structure control systems in either MATLAB^® or Simulink^® (requires Simulink Control Design™). systune and looptune can tune fixed-structure control systems to meet many types of tuning goals that you specify directly.

With hinfstruct, you express your tuning goals in terms of weighting functions applied to your closed-loop system. To use hinfstruct, you describe your weighted control system as a Generalized LTI model that keeps track of the tunable components of your system. hinfstruct tunes those parameters by minimizing the closed-loop gain from the system inputs to the system outputs (the H_∞ norm).

hinfstruct is the counterpart of hinfsyn for fixed-structure controllers. The methodology and algorithm behind hinfstruct are described in [1].

Bibliography

[1] P. Apkarian and D. Noll, "Nonsmooth H-infinity Synthesis," IEEE Transactions on Automatic Control, Vol. 51, Number 1, 2006, pp. 71-86.