Identification And Control Of Non-smooth Nonlinear Dynamic System Using Sandwich Model

With the development of industry, the higher requirements of control accuracy andsensitivity must be achieved, and the plant becomes more and more complicated andmore characteristics have to be modeled and compensated. If a component existnonlinearity, such a system will no longer be treated as the linear dynamic system.Further, if the nonlinearity is also non-smooth, i.e. dead-zone, backlash, hysteresis, etc.,and is surrounded by other components, it is difficult to use the traditional methods toidentify or control such a system. Further analysis showed that the non-smoothnonlinearity often exists in one or a few components. However, the main difficulties toidentify and control this kind of the systems are how to deal with the unmeasurednon-smooth nonlinearity. In this dissertation, based on the various experimental resultsof the multi-dimensional ultra-precision stage, the identification and control problemson the non-smooth sandwich system with dead-zone, backlash and hysteresis areinvestigated. In order to improve the trajectory accuracy and sensitivity of stage, atwo-stage identification method based on degeneration input and the correspondingnon-smooth sandwich controllers are proposed. The main contributions are brieflydescribed as follows:First, the macro-platform driven by the motor and the ball screw is studied.According to the experimental results, its trajectory accuracy and sensitivity areseverally degraded by dead-zone caused by friction. Moreover, dead-zone is locatedbetween the motor and the load so that it cannot be measured or compensated directly,which such a system is defined as the sandwich system with dead-zone. In this chapter,based on the local stimulation idea for the nonlinearity, a special signal calleddegeneration input is designed to excite boths end of linear sub-systems enough anddegenerate dead-zone into a linear function simultaneously. Consequently, using thekey terms separation principle, its degenerated sandwich model is reconstructed and aspecial form that is linearized in coefficients can be obtained. Besides, considering anadditional independent constraint on the static gain of system, the parameters of twolinear subsystems are firstly estimated by Recursive General Identification Algorithm(RGIA). After that, the new input signal is re-designed to excite dead-zone enough andtwo internal variables are reconstructed using two identified linear sub-models. Thus,the parameters of dead-zone sub-model can be estimated. Finally, simulation andexperimental results verify the effectiveness of the proposed identification scheme. Further experiments showed that: backlash cannot be ignored when the trajectorymovement with micron-level precision is performed. Backlash is also generated amongthe transmission system so that it cannot be measured directly, which such a system iscalled as the sandwich system with backlash. As backlash is a non-smooth, multi-valuemapping and local memory feature, it is more difficult to identify such a system. In thischapter, a monotonic independently incremental random signal is design tosimultaneously excite boths end of linear sub-models and eliminate the unexpectedfeatures of backlash, i.e. local memory, multi-value mapping, non-smoothness, etc.. Inthis case, backlash subsystem is degenerated into a linear function. Then, similar to theidentification process of the sandwich system with dead-zone, boths end of linearsub-models and nonlinear backlash sub-model is identified, respectively.In general, the trajectory with nanometer-level precision is achieved by thepiezoelectric actuator (PEA). Further, if the trajectory accuracy and sensitivity of PEAneed to achieved simultaneously, the dynamic feature of the filter amplifier and flexiblehinge cannot be ignored. In this case, PEA has to be treated as the sandwich systemwith hysteresis. It is a new challenge to identify such a system because hysteresis alsohas others features, i.e. global memory, rate-dependency and mirror-loop. Fortunately,based on the experimental results and analysis, hysteresis will be degenerated into astatic, smooth and one-to-one mapping nonlinear curve and can be approximated by thepolynomial when it is excited by a monotonic input signal. Therefore, a two-stageidentification scheme is proposed in this chapter. First, a special input is designed todegenerate hysteresis into a nonlinear curve. Then, boths end of linear subsystems arefirstly estimated by the key terms separation technique and RGIA. Second, anotherinput is designed to excite hysteresis enough and both input and output signals ofhysteresis are reconstructed by two obtained linear sub-models. In this case, a neuralnetwork based model to describe the hysteresis sub-model can be obtained using theexpanded input space method.Next, the above-mentioned identification schemes are summarized and asystematic method called the two-stage identification method based on degenerationinput is proposed in this chapter. The key to the proposed scheme is the degenerationinput, which usually consists of the frequency and amplitude component. In general,according to the specific characteristics of the non-smooth nonlinearity and thefundamental reason generated the non-smooth nonlinear phenomena, the degenerationinput can be designed to excite boths end of linear subsystems enough and locally stimulate the non-smooth nonlinearity simultaneously. In this case, the parameters oftwo linear subsystems can be first estimated because the unexpected nonlinear feature isavoided in this identification stage. Besides, several key issues on the identificationprocess of the proposed methods are discussed.Finally, based on the sandwich identification results, several non-smooth sandwichcontrollers are designed to control the multi-dimension ultra-precision stage. If the firstinternal variable of the sandwich system can be truly reconstructed by the obtainedsandwich model, the sandwich controller based on the inverse-model compensator isproposed. In this scheme, an internal-loop controller is first developed to eliminate theeffect of the first linear subsystem, and then the nonlinear inverse model cancompensate the nonlinear subsystem directly. In this case, the non-smooth sandwichsystem is equivalent considered as a linear system with disturbance. On the other hand,if the first internal variable cannot be truly reconstructed by the identified sandwichmodel, the non-smooth sandwich controller with feed-forward compensation andinternal model are proposed, respectively. In these schemes, the non-smoothnonlinearities are eliminated or suppressed by the identified sandwich model, and thenthe robust control scheme is designed and employed. Moreover, for the multi-dimensionPEA stage with the interaction disturbance between axes, the robust design scheme withan inverse sandwich compensator and a neural network based nonlinear decouplingcontroller is proposed to guarantee the system to achieve the desired performance. Theexperimental results verify the effectiveness of the proposed control scheme.