Two-stage vibration-suppression framework for optimal robust placements design and reliable PID gains design via set-crossing theory and artificial neural network

Structure vibration control is a significant problem in practical engineering, and Proportional-Integral-Differential (abbreviated as “PID†) control is widely used. The design of a PID controller contains the robust design of placements of actuators and sensors (abbreviated as “ASPD†), and the reliable design of PID gains. Because of the uncertain parameters in practical engineering, the controller designed from the deterministic system has the possibility of failure when applied to a practical system. To solve this problem, this paper proposed a two-stage framework for uncertain vibration active control systems via non-probabilistic time-dependent reliability (abbreviated as “NTDR†) and artificial neutral network (abbreviated as “ANN†). This framework decouples the ASPD and PID gains design as two stages. Considering the insufficient sample data, uncertain parameters are quantified with non-probabilistic interval forms. The optimization objective of ASPD combines the deterministic eigenvalues of controllability gramian or observability gramian, the robust theory and placements constraints to carry out the optimization. In this way the optimization objective can be less affected by uncertain parameters and has practical significance. For the reliable design of PID gains, the NTDR is adapted to evaluate the safety of an uncertain system. Then ANNs from uncertain parameters and PID gains to the optimization objective considering NTDR are established. By carrying out the optimization to the last ANN, the efficiency of optimization is improved while the accuracy is guaranteed. Two numerical examples and one experimental example show the practicability and effectiveness of the proposed method.