Qi Xue, Shi Weijia, Wang Shaokai, Zhao Bo, Tan Jiubin
Center of Ultra-precision Optoelectronic Instrument engineering, Harbin Institute of Technology, Harbin 150080, China; Key Lab of Ultra-precision Intelligent Instrumentation (Harbin Institute of Technology), Ministry of Industry and Information Technology, Harbin 150080, China.
Center of Ultra-precision Optoelectronic Instrument engineering, Harbin Institute of Technology, Harbin 150080, China; Key Lab of Ultra-precision Intelligent Instrumentation (Harbin Institute of Technology), Ministry of Industry and Information Technology, Harbin 150080, China.
Ultrasonics. 2022 Aug;124:106727. doi: 10.1016/j.ultras.2022.106727. Epub 2022 Mar 12.
Piezoelectric actuators (PEAs) are widely applied in precision positioning. However, the nonlinear characteristics such as hysteresis and creep limit the ultra-precision applications. This paper proposes a linear model predictive control (MPC) scheme for compensating the nonlinearity of PEA. Firstly, a global linearization predictor is constructed based on Koopman theory to represent the hysteresis behavior of PEA. The high-precision predictor is implemented by a novel memory related neural network (NN), and the prediction error reaches only 0.002 μm. Then the tracking control problem is transformed into a linear MPC optimization problem, thereby avoids the sophisticated nonconvex optimization problem. In practice, the constrained MPC problem is rewritten into a dense form, and solved by quadratic programming technique. Finally, the validity of the proposed scheme is demonstrated by experiments. The short-term steady-state error of the proposed scheme is 0.002 μm, which is far less than that of the inversion method; the long-term steady-state performance also indicates its effectiveness in compensating creep. Further, the excellent frequency-dependent results show that the proposed scheme is superior to the existing control method. Especially, the computational efficiency can be improved by 20%. The proposed predictor and control method are of great significance for the tracking control of PEA.
压电驱动器（PEA）在精密定位中得到广泛应用。然而，诸如滞后和蠕变等非线性特性限制了其超精密应用。本文提出一种线性模型预测控制（MPC）方案来补偿PEA的非线性。首先，基于库普曼理论构建全局线性化预测器以表征PEA的滞后行为。高精度预测器由一种新型的与记忆相关的神经网络（NN）实现，预测误差仅达到0.002μm。然后将跟踪控制问题转化为线性MPC优化问题，从而避免了复杂的非凸优化问题。在实际中，将约束MPC问题重写为密集形式，并通过二次规划技术求解。最后，通过实验验证了所提方案的有效性。所提方案的短期稳态误差为0.002μm，远小于逆方法的稳态误差；长期稳态性能也表明其在补偿蠕变方面的有效性。此外，出色的频率相关结果表明所提方案优于现有控制方法。特别是，计算效率可提高20%。所提预测器和控制方法对PEA的跟踪控制具有重要意义。
