Based On The Parameters Of The Hamiltonian System Stability Study And Its Application In All-digital Fuzzy Control System

In the analysis of nonlinear systems, the traditional approach generally treat the existence of equilibria and their stability separately and assumes that the equilibrium remains fixed for the entire range of parameters. In most of the practical applications, however, it is not realistic to make such assumption. The variations of system parameters might result in a moving equilibrium whose stability properties can vary substantially. It is reported that the equilibrium even disappears in some cases. Hence, parametric stability becomes the first concern for systems with moving equilibrium. This thesis investigates parametric stability of nonlinear systems by Hamiltonian method and applies it to the control of permanent magnet synchronous motor (PMSM).At first, a kind of energy-based method of analysis for parametric stability is proposed. The core idea of this method is to find a suitable energy function and represent the system as a dissipative Hamiltonian form with an energy function changing with the variations of the parameters. Parametric stability can then be established if the energy function always reaches its minimum at the equilibrium determined by parameters. In addition, adaptive dissipative Hamiltonian realization method is adopted to study how to use the matching equation to get the parametric stabilizer. This method firstly chooses appropriate energy function. Then in order to guarantee the solvability of the matching equation, the closed-loop structure matrix is properly configured. Lastly parameter adaptive law and parametric stabilizer are directly obtained by solving the matching equation. On the basis of the study above, parametric L2-gain control problem is also studied.Secondly, the impact of unknown load torque and flux on the equilibrium location of PMSM is investigated. According to the physical meaning of the system, an appropriate energy function is selected and then the system is changed into the Hamiltonian form. By solving the matching equation, an adaptive estimation of load torque and a speed regulator are obtained. How the closed-loop equilibrium varies with the change of the load torque and flux is analyzed. In the case of varying flux linkage, L2-gain control problem of PMSM is also studied. The simulation results show the effectiveness of the proposed controller.At last, using the energy shaping method, the speed regulation problem of PMSM is investigated under the circumstances of the system being affected by unknown periodic load disturbance and flux being unknown. By choosing appropriate Casimir function, the energy function of the system is modified. Estimators of interference amplitude and flux and a parametric stabilizer are obtained. The numerical simulation results show that the design is effective.