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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 (performed using the hinfsyn or loopsyn commands) 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.

In contrast, 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.


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

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