Through combining P-type iterative learning (IL) control, model-free adaptive (MFA)control and sliding mode (SM) control, a robust model-free adaptive iterative learning (MFA-IL)control approach is presented for the active vibration control of piezoelectric smart structures.Considering the uncertainty of the interaction among actuators in the learning control process,MFA control is adopted to adaptively adjust the learning gain of the P-type IL control in order toimprove the convergence speed of feedback gain. In order to enhance the robustness of the systemand achieve fast response for error tracking, the SM control is integrated with the MFA control todesign the appropriate learning gain. Real-time feedback gains which are extracted fromcontrollers construct the basic probability functions (BPFs). The evidence theory is adopted to thedesign and experimental investigations on a piezoelectric smart cantilever plate are performed tovalidate the proposed control algorithm. The results demonstrate that the robust MFA-IL controlpresents a faster learning speed, higher robustness and better control performance in vibrationsuppression when compared with the P-type IL control.
Keywords: MFA control; P-type IL; SM control; active vibration control; evidence theory; piezoelectric smart structure.