Non-smooth structured control design with application to PID loop-shaping of a process.

*(English)*Zbl 1127.93326Summary: Feedback controllers with specific structure arise frequently in applications because they are easily apprehended by design engineers and facilitate on-board implementations and re-tuning. This work is dedicated to \(H_{\infty}\) synthesis with structured controllers. In this context, straightforward application of traditional synthesis techniques fails, which explains why only a few ad hoc methods have been developed over the years. In response, we propose a more systematic way to design \(H_\infty\) optimal controllers with fixed structure using local optimization techniques. Our approach addresses in principle all those controller structures which can be built into mathematical programming constraints. We apply non-smooth optimization techniques to compute locally optimal solutions, and provide practical tests for descent and optimality. In the experimental part we apply our technique to \(H_\infty\) loop-shaping proportional integral derivative (PID) controllers for MIMO systems and demonstrate its use for PID control of a chemical process.

##### MSC:

93B51 | Design techniques (robust design, computer-aided design, etc.) |

93B36 | \(H^\infty\)-control |

93B50 | Synthesis problems |

93C99 | Model systems in control theory |

##### Keywords:

non-smooth optimization; \(H_{\infty}\) synthesis; structured controllers; PID NP-hard problems
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\textit{P. Apkarian} et al., Int. J. Robust Nonlinear Control 17, No. 14, 1320--1342 (2007; Zbl 1127.93326)

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