Dynamic control of nonlinear systems involving nonsmooth nonlinearity with application to industrial systems

非光滑非线性，通常被称为“硬非线性”，本质上是不连续的，或者不能在整个域上连续微分。重要的例子包括机械反弹、死区、摩擦和迟滞。这些非线性在工业控制系统中非常常见，从高科技应用（半导体制造中的微操纵、高性能机器人、涡轮轴的超精密车削、细胞生物学中的微流体系统）到传统应用（电液定位系统、机床控制、机器人操纵器、主动悬架控制、汽车传动系统、注塑机）。非光滑非线性常常严重限制系统性能。一个重要的例子是压电致动器，它在需要高精度的领域找到了许多新的应用。然而，压电致动器的主要限制是由于迟滞非线性导致的精度限制。如果执行器以开环方式操作，则由迟滞引起的最大误差可达全运动范围的15-20%。如果没有反馈控制技术的帮助来克服滞后效应，只能达到有限的定位精度。

Nonsmooth nonlinearities, often referred to as "hard nonlinearities", are either discontinuous in nature or cannot be continuously differentiated over the entire domain. Important examples include mechanical backlash, dead-zone, friction, and hysteresis. These nonlinearities are very common in industrial control systems, ranging from high technology applications (micromanipulation in semiconductor manufacturing, high performance robotics, ultra precision turning of turbine shafts, micro-fluidic systems in cellular biology) to traditional applications (electro-hydraulic positioning systems, machine tool control, robot manipulators, active suspension control, automotive drivetrain systems, injection moulding machines). Nonsmooth nonlinearities often severely limit system performance. An important example is piezoelectric actuators, which are finding many new applications in areas demanding high precision. The major limitation of piezoelectric actuators, however, is limited accuracy due to hysteresis nonlinearity. The maximum error due to hysteresis can be as large as 15-20% of the full range of motion if the actuator is operated in an open loop manner. Without the aid of feedback control techniques to overcome the hysteresis effect, it is only possible to achieve limited positioning accuracy.