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

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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.