The Study Of Variable Structure Control Based On Sliding Mode And Its Application To Inverted Pendulum Systems

In the 1950s, Emelyanov, a Soviet researcher, first proposed variable structure control (VSC) based on sliding mode(SM), then Utkin and Itkis et al. developed the theory. Significant interest on VSC with SM has been generated in the control research realm on account of its excellent robustness and complete adaptability to the uncertainties and external disturbance in the 1970s.So far, VSC with SM has been deeply studied as an important branch of nonlinear control theory. It has been employed to control discrete-time systems, distributed parameters systems and time-delay systems etc.. However, the chattering with high frequency in sliding mode control systems is a barrier for the application to the practice engineering problems. Therefore, many advanced control theories, such as adaptive control, fuzzy control, NN etc. have been applied to variable structure system to reduce the chattering.Considering the current developed VSC theory and the new requirements from the practice, some desiderated problems are studied and discussed. The single, double, parallel and triple inverted pendulums have been controlled by the sliding mode controller (SMC) successfully.An SM based identifier is presented to deal with the parameter identification problem for a class of parameter uncertain nonlinear dynamic systems with input nonlinearity. An SMC algorithm is employed to ensure the global reaching condition of the sliding mode for the nonlinear system, and an identifier is designed to identify the uncertain parameters of the nonlinear system. The asymptotical convergence of the identifier is proved.A discrete variable structure control algorithm with time-varying sliding surface is developed for a class of second-order uncertain discrete systems.IllThe time-varying sliding surface is obtained by rotating and/or shifting the initial sliding mode surface, and the existence of sliding mode with the time-varying sliding surface is proved. The rotating and/or shifting procedures are presented in detail, and the movement of the time-varying sliding surface is obtained quantitatively at every sampling time by taking advantage of the range of the sliding mode band. The states of the closed loop system moved in the sliding mode band of the time-varying sliding surface globally. Reaching mode is eliminated and robustness of the closed-loop system is enhanced.The sign function of the switching surface function is replaced by a saturate function to reduce the chattering. The chattering can be eliminated if there do not exist hasn't parameter uncertainties and external disturbance in the controlled system. An parameter of the saturate function can be adjusted to reduce the chattering if there are some parameter uncertainties and external disturbance, and how to select this parameter to reduce the chattering are introduced.An extended VSC is designed to make the single pendulum self erected and then keep it upright. Two loops are presented to swing the pendulum up. The outer loop, which is a positive feedback loop performs position control of the cart based on the position and rate of the pendulum. The inner loop make the cart track the position. The balance control part based on sliding mode keep the pendulum upright.The double inverted pendulum and the parallel inverted pendulum was successfully balanced by VSC with SM. Two different methods for these two systems are employed to reduce the chattering and excellent results are obtained.Triple inverted pendulum is a mechanical idealization which poses an interesting and difficult problem in control. In this paper, a robust control algorithm based on sliding mode is employed to control a triple inverted pendulum system with single input. The employment of such a techniqueIVappears necessary because the traditional linear design process cannot incorporate the nonlinear dynamics of such system and its physical limitations. The new controller satisfies the required dynamic characteristic of the triple inverted pendulum system and keep the system...