*Article* **Robust Model-Free Adaptive Iterative Learning Control for Vibration Suppression Based on Evidential Reasoning**

#### **Liang Bai 1,\*, Yun-Wen Feng 1, Ning Li 2 and Xiao-Feng Xue 1**


Received: 11 February 2019; Accepted: 13 March 2019; Published: 19 March 2019

**Abstract:** 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 to improve the convergence speed of feedback gain. In order to enhance the robustness of the system and achieve fast response for error tracking, the SM control is integrated with the MFA control to design the appropriate learning gain. Real-time feedback gains which are extracted from controllers construct the basic probability functions (BPFs). The evidence theory is adopted to the design and experimental investigations on a piezoelectric smart cantilever plate are performed to validate the proposed control algorithm. The results demonstrate that the robust MFA-IL control presents a faster learning speed, higher robustness and better control performance in vibration suppression when compared with the P-type IL control.

**Keywords:** P-type IL; MFA control; SM control; evidence theory; active vibration control; piezoelectric smart structure
