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Parameter Tuning of Multi-Proportional-Integral-Derivative Controllers Based on Optimal Switching Algorithms

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Abstract

Under the framework of switched systems, this paper considers a multi-proportional-integral-derivative controller parameter tuning problem with terminal equality constraints and continuous-time inequality constraints. The switching time and controller parameters are decision variables to be chosen optimally. Firstly, we transform the optimal control problem into an equivalent problem with fixed switching instants by introducing an auxiliary function and a time-scaling transformation. Because of the complexity of constraints, it is difficult to solve the problem by conventional optimization techniques. To overcome this difficulty, a novel exact penalty function is introduced for these constraints. Furthermore, the penalty function is appended to the cost functional to form an augmented cost functional, giving rise to an approximate nonlinear parameter optimization problem that can be solved using any gradient-based method. Convergence results indicate that any local optimal solution of the approximate problem is also a local optimal solution of the original problem as long as the penalty parameter is sufficiently large. Finally, an example is provided to illustrate the effectiveness of the developed algorithm.

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Acknowledgements

The authors express their sincere gratitude to Professor Franco Giannessi, Professor David G. Hull, the editor, and the anonymous reviewers for their constructive comments in improving the presentation and quality of this manuscript. This work was supposed by the Chinese National Outstanding Youth Foundation under Grant No. 61125306, the Major Program of Chinese National Natural Science Foundation under Grants Nos. 91016004 and 11190015.

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Authors and Affiliations

  1. School of Automation, Southeast University, Nanjing, 210096, China

    Xiang Wu, Kanjian Zhang & Changyin Sun

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  1. Xiang Wu
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  2. Kanjian Zhang
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Correspondence to Xiang Wu.

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Wu, X., Zhang, K. & Sun, C. Parameter Tuning of Multi-Proportional-Integral-Derivative Controllers Based on Optimal Switching Algorithms. J Optim Theory Appl 159, 454–472 (2013). https://doi.org/10.1007/s10957-013-0306-8

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  • DOI: https://doi.org/10.1007/s10957-013-0306-8

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