Abstract
This work focuses on the problem of automatic loop shaping in the context of robust control. More specifically in the framework given by Quantitative Feedback Theory (QFT), traditionally the search of an optimum design, a non convex and nonlinear optimization problem, is simplified by linearizing and/or convexifying the problem. In this work, the authors propose a suboptimal solution using a fixed structure in the compensator and evolutionary optimization. The main idea in relation to previous work consists of the study of the use of fractional compensators, which give singular properties to automatically shape the open loop gain function with a minimum set of parameters, which is crucial for the success of evolutionary algorithms. Additional heuristics are proposed in order to guide evolutionary process towards close to optimum solutions, focusing on local optima avoidance.
Highlights
This work focuses on the problem of automatic loop shaping in the context of robust control
In the framework given by Quantitative Feedback Theory QFT, traditionally the search of an optimum design, a non convex and nonlinear optimization problem, is simplified by linearizing and/or convexifying the problem
It is a well-known fact that there is no general procedure to exactly solve nonlinear nonconvex optimization problems when the solutions belong to continuous solution sets 1
Summary
It is a well-known fact that there is no general procedure to exactly solve nonlinear nonconvex optimization problems when the solutions belong to continuous solution sets 1. In this paper the authors study the use of evolutionary algorithms-based optimization, proposing the addition, with respect to previous work, of some heuristics, very much specific to the particular problem under consideration, which help to improve obtained solutions accuracy and computation time needed to obtain these solutions. In this sense, a good structure for the compensator, in terms of using a reduced set of parameters, but with a rich frequency domain behavior, is of crucial importance.
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