Антон Петрович Коротинський, Михайло Володимирович Коржик


In this article consider the problem of guaranteed quality controlled processes with uncertain parameters of the functional components of management, set interval or fuzzy way.

The basic techniques of robust control, namely: Robust quadratic stabilization, robust linear quadratic regulator Robust Stabilization using H∞ optimization, μ synthesis.

The theoretical framework for the work of regulators. The analysis and conclusions regarding the feasibility of using these methods. An advantages and disadvantages of each method.

A convenient apparatus robust stabilization technique is based on building a common quadratic Lyapunov function. The solution to this problem is reduced to solving linear matrix inequalities that meet all possible values of uncertainty. The advantage of this method is its simplicity, but the drawback is the large number of iterations.

Similarly, by reduction to linear matrix inequalities solve the problem of guaranteed value quadratic Quality Score for systems with parametric uncertainty. Advantages and disadvantages of similar listed above stabilizer.

Benefits H∞ synthesis: working with both stability and sensitivity of the system, a closed loop always steady, straight single pass algorithm synthesis.

Based on μ-analysis procedures can be built μ-synthesis. They are reduced to minimize sequential upper limit on the regulator for μ C and minimization of the border found in the controller C. It is not guaranteed that the maximum robust regulator will be found.

The analysis of the advantages and disadvantages offered synthesize and quadratic H∞ controller.

Powered synthesis algorithms described above regulators. The results of quadratic and H∞ controller. For comparison of regulators was built transient response with PID controller for nominal value models and robust synthesized regulators.

Conclusions regarding the robust regulators. With robust controllers work schedules shows that both provide a solution to the problem, namely providing guaranteed quality controlled processes with uncertain parameters of functional components. The result of this work is designed and quadratic H∞ controller, providing stability closed system not only for the nominal object, but for any object that belongs to the set of “perturbed” objects definable class of uncertainty.

Ключові слова

Robust control, quadratic stabilization; robust stabilization using H∞ optimization; μ synthesis.

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ISSN: 2617-9741 (Print); ISSN: 2664-1763 (Online)