Hybrid Reliability-Based Control Optimization for Piezoelectric Structures via Adaptive Sequential Decoupling

Piezoelectric structures are widely used in active vibration control, but various uncertainties in practical engineering may lead to system failure. In this paper, a hybrid reliability-based proportional–integral–derivative (PID) controller design optimization framework is proposed for piezoelectric active control systems considering both interval and fuzzy uncertainties, taking the most widely used PID controller as an example. First, the fuzzy uncertainty is transformed into interval uncertainty by the cut-set strategy, and the adaptive dichotomy is used to select membership sample points intelligently to calculate the response boundary of the system. Then, the reliability index is defined in a nonprobabilistic way (the area ratio of the safety region of the limit state function to the total region) to quantify system safety. Next, a sequential decoupling strategy is adopted to optimize the PID parameters efficiently. This strategy updates the displacement constraints iteratively to meet the reliability requirements. Finally, the advantages of the proposed framework in terms of calculation accuracy and efficiency are verified by a piezoelectric plate example, and the influence of various uncertainties on the optimization results is analyzed by a piezoelectric shell example.