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Design of Low-Order Controllers With H-Infinity Specifications in Parameter Space

Наименование конференции: 

  • Russian-Swedish Control Conferences


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Год издания: 



This paper is aimed to describe the regions in the controller parameter space such that the given single-input single-output plant is stable and the H1 norm of a related transfer function is less than a prescribed level. The approach isfocused on structurally simple controllers (PI, PID, first-order) as the most widely used in industrial applications.This structural simplicity makes their principle easy to understand and sufficient ability of solving many practicalcontrol problems have greatly contributed to a wide acceptance. The problem of robust performance design is to synthesize a controller for which the closed-loop system is internally stable and the desired performance specifications are satisfied despite plant uncertainty. H1 norm originally appeared in the problem of sensitivity reduction by feedback. Nowadays, H1 optimization is a beautiful theory for robust performance design and other issues. However, its application results in the order of a proposed controller tends to be greater than the plant order and it is hardly applicable for the case of fixed order controller. Recent attempts to carry out H1 design problems for certain kind of low-order controllers are based on the stabilization to the case of complex polynomials. Although the set of controller parameters satisfying given criteria is obtained via linear programming, the technique obliges to introduce an additional parameter. For each parameter value the stabilization problem is solved, thus gridding in this parameter sufficiently increases the number of linear programs. The contribution of this paper is two approaches for H1 design, both of them allow to describe the regions, where robustness and/or performance criterion holds. The first approach represents the domain of interest as an intersection of admissible sets, that are either exteriors or interiors of a family of particular second order curves. In the second approach the boundary of the desired domain is computed explicitly via D-decomposition-like idea. Both approaches allow user-friendly graphical representation and are computationally tractable for a wide class of controllers, e.g. PI, PID and first-order controllers. The main limitation is the treatment of single-input single-output systems only. Nevertheless, it can be easily extended to various H1 criteria involving sensitivity function, complementary sensitivity function or input sensitivity function as well as plant stabilization with frequency uncertainty. Due to the predominance of low-order controllers in practice the obtained result represents a step in enabling the use of H1 controllers in industrial control.

Библиографическая ссылка: 

Грязина Е.Н. Design of Low-Order Controllers With H-Infinity Specifications in Parameter Space / . -: -, 2006. С. -.