Hierarchical Fuzzy Sliding Mode Control For A Class Of Underactuated Systems

Underactuated systems are the systems which have fewer actuators than the degreesof freedom to be controlled. Because of the lack of the drive devices, the control ofunderactuated systems is far more complex than of actuated systems. So far, there’s nogeneral method that can be used to control underactuated systems. Meanwhileunderactuated systems can be found in many fields, including fields of aerospace, ships,transportation and robots. So it is of great theoretical and practical value to study thecontrol of underactuated systems.In recent years, the sliding mode control (SMC) developed rapidly because of itsadvantage of robust, fast responsibility and easy realization. Based on SMC, hierarchicalsliding mode control (HSMC) attracted extensive attention immediately when it came up.The sliding mode surfaces in HSMC are designed in hierarchical structure which iscomposed of a total surface and two sub-sliding surfaces. Two sub-sliding planes aredesigned respectively for underactuated sub-system and actuated sub-system, and then thetotal sliding plane is constructed from these two sub-sliding planes. A control law which isderived from the total sliding surface can make the system asymptotically stable.The main work in my paper is as follows:(1) Since the exact mathematical model is always unknown, the control law which isdesigned based on the theory of HSMC can not be obtained. In addition, there are manyparameters in the controller, and it is hard to adjust the parameters using trial method.Therefore, a hierarchical fuzzy sliding mode control method based on genetic algorithm(HFSMC) is proposed in this paper, which combines the HSMC, fuzzy control and geneticalgorithm. Adaptive fuzzy logic systems are used to approximate the unknown nonlinearfunctions and genetic algorithm is used to find the optimal parameters. The validity andefficiency of this method are verified by theoretical analysis and simulation.(2) Based on the HFSMC, a hierarchical fuzzy terminal sliding mode control method(HFTSMC) is proposed in the rest of the paper. This method replaces the linear sliding surface with global fast terminal sliding surface which is faster than linear sliding surfacein this whole process of sliding because of the introducing of higher order term. Thesimulation results shows the validity and superiority of this method.