*Article* **Single-Neuron Adaptive Hysteresis Compensation of Piezoelectric Actuator Based on Hebb Learning Rules**

#### **Yanding Qin \* and Heng Duan**

College of Artificial Intelligence; Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin 300350, China; 2120180411@mail.nankai.edu.cn

**\*** Correspondence: qinyd@nankai.edu.cn

Received: 4 December 2019; Accepted: 11 January 2020; Published: 12 January 2020

**Abstract:** This paper presents an adaptive hysteresis compensation approach for a piezoelectric actuator (PEA) using single-neuron adaptive control. For a given desired trajectory, the control input to the PEA is dynamically adjusted by the error between the actual and desired trajectories using Hebb learning rules. A single neuron with self-learning and self-adaptive capabilities is a non-linear processing unit, which is ideal for time-variant systems. Based on the single-neuron control, the compensation of the PEA's hysteresis can be regarded as a process of transmitting biological neuron information. Through the error information between the actual and desired trajectories, the control input is adjusted via the weight adjustment method of neuron learning. In addition, this paper also integrates the combination of Hebb learning rules and supervised learning as teacher signals, which can quickly respond to control signals. The weights of the single-neuron controller can be constantly adjusted online to improve the control performance of the system. Experimental results show that the proposed single-neuron adaptive hysteresis compensation method can track continuous and discontinuous trajectories well. The single-neuron adaptive controller has better adaptive and self-learning performance against the rate-dependence of the PEA's hysteresis.

**Keywords:** piezoelectric actuator; hysteresis compensation; single-neuron adaptive control; Hebb learning rules; supervised learning
