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Adaptive control of systems with nonsmooth nonlinearities

Posted on:1998-04-09Degree:Ph.DType:Dissertation
University:University of VirginiaCandidate:Tian, MingFull Text:PDF
Adaptive control schemes are designed for systems containing dead-zone, piecewise linearity, backlash and hysteresis which are ubiquitously found in control systems, and particularly in actuators or sensors. These nonlinearities are usually unknown and possibly time-varying, which often lead to undesired oscillations and sometimes even instability. Therefore, adaptive control schemes are needed to compensate these nonsmooth nonlinearities. However, most existing adaptive control methods deal with linear systems and smooth nonlinear systems. Recently, adaptive control of systems with such nonsmooth nonlinearities, using an adaptive inverse approach, emerged as a new area of control research, with both theoretical and practical interest.; This dissertation aims to continue the research in this area. The adaptive inverse approach is further developed. The main idea of this approach is to use adaptive nonlinearity inverses as part of adaptive controllers to cancel the harmful effects of the nonsmooth nonlinearities. First, these nonlinear characteristics are expressed in a linear parametrization in terms of their parameters such as slopes and break points. Then their inverse models are designed with the desired properties: when implemented with the true nonlinearity parameters, the inverses cancel the nonlinearity effects; when implemented with parameter estimates, the inverses result in a linear parametrized error term with a crucial disturbance, which is crucial to the development of adaptive laws for updating the inverse parameters.; In this dissertation, two classes of control problems are considered: the first one is input nonlinearity problem when the nonlinearities are in the actuators of control systems and the second one is output nonlinearity problems when the nonlinearities are in the sensors of control systems. Unified adaptive inverse control designs are proposed for linear plants with input nonsmooth nonlinearities where full state feedback is available. The adaptive inverse control approach is extended to linear plants with input or output multi-segment piecewise-linear nonlinearities. New adaptive control schemes, based on pole placement control and adaptive inverse, are proposed for known nonminimum phase plants with unknown input or output dead-zones. Adaptive inverse control schemes are further developed for smooth nonlinear systems with input nonsmooth nonlinearities. The smooth nonlinear systems considered in the dissertation are parametric-strict-feedback systems with full state feedback and output-feedback canonical systems. The sensor imperfection problem in control systems is addressed and adaptive control schemes are developed for linear plants with a class of sensor uncertainties.; Issues such as control problem formulation, plant modeling, adaptive controller structure, error model, adaptive law, stability and robustness analysis, and system performance evaluation are extensively investigated. Stability analysis and simulation results show that the adaptive controllers with adaptive nonlinearity inverses schemes can significantly improve system performance despite the presence of actuator and sensor nonlinearities.
Keywords/Search Tags:Adaptive, Systems, Linear, Schemes, Inverse
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