Identification And Control Of The Nonsmooth Sandwich Steystems

Dead zone, backlash and hysteresis often exist in practical engineering systems. Actually, those non-smmoth nonlinearities exist in plane elevator droved by hydraulic actuators, electronic scanner microscope with piezoceramic actuators, ultraprecise moving stage and positioning servo control system with gear and so on. Therefore, those non-smooth nonlineairies do not exist isolatively but with the other sub-systems. In fact, they are more likely sandwiched between two linear subsystems in engineering applications. For the convenience of dealing with the problem of such systems, we define this kind of the systems as the sandwich systems. In the nonsmooth sandwich systems, the input and output of the nonlinear sub-system often cannot be measurable directly. Thus, the identification of this sort of systems becomes even more difficult especially when the nonlinear sub-system is backlash or hysteresis which is a nonsmooth nonlinearity with multi-valued mapping. So it is not easy to use the traditional identification and control methods to effectively handle the problems of modeling and control of such systems. In this dissertation, the identification and control on those nonsmooth systems, i.e., the sandwich system with dead zone, backlash or hysteresis are investigated. The main contributions are briefly described as follows:Firstly, based on the key term separation principle, a novel form of the model to describe the sandwich system with dead zone is proposed. Then, a modified recursive general identification algorithm (MRGIA) is developed to estimate the model parameters. Also, the convergence of the algorithm is proved. Thus, the identification scheme usually used for smoothly linear dynamic systems is extended to the case of non-smoothly dynamic systems. Moreover, both the simulation and the modeling of the X-Y moving positioning stage demonstrate the effectiveness of the proposed method.Secondly, based on the key term separation principle, we developed a parametrical model to describe the characteristic of the backlash. In the proposed scheme, the multi-valued mapping between the input and output of the backlash is transformed into a one-to-one mapping. Then, a MRGIA method is proposed for the identification of such kind of systems. The corresponding convergence of the algorithm is analyzed and the looser convergent conditions of the algorithm are obtained. Moreover, the extensions of the identification method to the Hammerstein, Wiener and sandwich systems with backlash are discussed respectively.A gradient based recursive identification method is proposed for sandwich systems with dead zones or backlash. As the sandwich systems with dead zone or backlash are non-smooth systems, the gradients cannot exist at the nonsmooth points of the system. Thus, the Clarke subgradient and Clarke subdifferential are introduced to approximate the gradients at the nonsmooth points. The bundle method based recursive algorithm is proposed to search for the subgradient direction. The method to handle the case for nonsmooth and nonconvex systems is also investigated. The presented simulation results illustrate the effectiveness of the proposed method. This provides us with one of the new options for the identification and control of the nonsmooth sandwich systems.Due to the complexity of hysteresis, it is hard for us to apply the above-mentioned recursive identification method to the modeling of the behavior of hysteresis. Hence, in this dissertation, we consider hysteresis as a black box. A modified Prandtl-Ishlinksii (PI) model is presented. In the modified PI model, an asymmetrically generalized backlash operator is used as the elementary operator of the PI model. In order to estimate the weights of the operators as well as the thresholds and slopes of the operators, the Levenberg-Marquardt algorithm based on the bundle method is developed. Compared with the other types of PI models which usually specify the parameters of the models by time-consuming empirical procedure, the proposed modified PI modeling method can determine the optimizing parameters of the model automatically. Moreover, the proposed modeling method can obtain a simplified model structure as well as the accurate model. The experimental results respectively on a piezoceramic actuator and an ultrasonic motor have shown the proposed method has achieved satisfactory modeling results.As the performance of the hysteresis usually depends on the frequency of the input, especially the frequency of the input is increased to a certain value. This kind of hysteresis is called as rate-dependent hysteresis. In order to obtain the information of the frequency change of the input on-line, in his dissertation, we give the proof that the derivative of the input with respect to time has a certain relationship with the input frequency. Moreover, the movement direction of the hysteresis is estimated by using the derivative of the input based on the bundle method. Then, the Clarke subgradient of the hysteresis output with respect to its inputs is used to approximate the gradients at the nonsmooth points. By introducing the derivative of the input and the Clarke subgradient of the hysteresis output with respect to its input, an expanded input space is constructed to transform the multi-valued mapping of the hysteresis to a one-to-one mapping. Based on the expanded input space, the neural networks can be used to model the behavior of the rate-dependent hysteresis. Similarly, this method can also be utilized to identify and predict the sandwich systems with hysteresis. Furthermore, the experimental results on modeling of a piezoceramic actuator and an X-Y ultraprecise positioning stage are presented respectively to illustrate the performance of the proposed approach.Finally, the modified discrete-time internl model control method for a class of sandwich system with backlash is discussed. In this sort of systems, the output of the first linear subsystem can be measured directliy. In the control scheme, an inverse model based compensator is introduced to compensate for the effect of the first linear subsystem. Therefore, the sandwich systems with backlash can be simplified as the Hammerstein systems with backlash. Then, a novel form of the system model and the corresponding inverse model are constructed respectively. Thus, the model errors caused by both linear part and the backlash are included into the consideration of the control design. As the backlash model is switched among the different operating zones, the piecewise robust filters are proposed to improve the robust stability and transient performance of the control system. Finally, the simulation results based on the proposed method are also presented.