Research On Invertibility And Inverse Modeling Of Dynamical Systems

This Thesis mainly studied two problems of Adaptive Inverse Control, which was the invertibility and inverse modeling. The basic idea of Adaptive Inverse Control is that using the plant inverse as series controller controls dynamic characteristics of the system. Adaptive Inverse Control is an open-loop control method and can track the reference input. This method uses feedback in the process of adaptation, which avoid instability problems due to feedback and improve dynamic performance of system. Before using Adaptive Inverse Control, inverse model of system must be known, so invertibility of system is very important.For linear and nonlinear system, according to the structure of the Adaptive Inverse Control, the methods of judging the existence of invertibility were summarized, which provided the basis for inverse modeling of the system.Summarized the existing methods of inverse modeling for linear and nonlinear system. Because support vector machine (SVM) can approximate any function, it is widely used on inverse modeling of the system. However, it is uncertainty on choosing SVM’s kernel function and it is bad on handling outlier and disturbance. This thesis proposed a new method, which based on least squares support vector machine. This method choosing a fuzzy kernel function added the fuzzy membership in the least squares support vector machine, which make inverse model more accurate and promotional.Researching on multi-wire cutting system, direct inverse model control method was used based on SVM. This system used main motor as reference model, used FLS-SVM for inverse model identification of actinomycetes motor, and connected this inverse model with controlled object, making the static and dynamic characteristics be similar with the reference model, thus, the speed of the actinomycetes motor was the same as the main motor. Robustness was strengthen. The simulation results showed that this method is correct.