Research Of Sliding Mode Control Based On Fractional Calculus

Fractional calculus is a theory on the research and application of derivatives and integral of arbitrary real or complex order. It is a natural extension of the classical integer order calculus. Control theory of fractional calculus is a novel topic. It has developed rapidly on the recent 30 years and become the focus of so many researchers.In this paper, fractional sliding mode control method will be researched. Firstly, a brief introduction is given about the sliding mode control and the basic knowledge and properties of fractional calculus. Then the fundamental linear fractional-order differential equation will be introduced, and fractional-order exponential differential equation curves are got and studied by changing the parameters regularly. According to the variations of curves with the change of parameters regularly, the fractional exponential curve and the integral exponential curve is compared and it supplies the basis of theory of next studies. The fractional calculus is introduced in the classical integer-order exponential sliding mode control law, called fractional-order exponential sliding mode control law. This law is proved the generalization of the classical sliding mode control law and can lead the state of systems into the sliding mode. Then it will be used in designing the control law in the synchronization of two chaos systems. By SIMULINK, the result of the fractional-order law method and the integer-order law method will be compared and the fractional-order law method is proved much more better. At the end of this paper, another fractional-order sliding mode control law is studied. It is called sliding mode control law based on the fractional compensation. People can much more easily deduce that the state of the system will reach the sliding mode by this method. It is another way of generalizing the classic sliding mode control law. It is used in designing the observer of the fractional skyhook damping semi-active suspension. The designed fractional-order observer improves the performance of the optimized fractional-order skyhook damping semi-active suspension. So one can conclude that the fractional-compensation sliding mode control method is better than integral-compensation one.