Stability Analysis and Fractional Order Controller Design for Control System

In this paper, a new approach to stability for fractional order control system is proposed. Here a dynamic system whose behavior can be modeled by means of differential equations involving fractional derivatives. Applying Laplace transforms to such equations, and assuming zero initial conditions, causes transfer functions with no integer powers of the Laplace transform variable s to appear. In recent time, the application of fractional derivatives has become quite apparent in modeling mechanical and electrical properties of real materials. Fractional integrals and derivatives have found wide application in the control of dynamical systems when the controlled system and the controller are described by a set of fractional order differential equations. In the existing work, a fractional order system has been signified by a higher integer order system. Fractional calculus provides an excellent instrument for the description of memory and hereditary properties of various materials and processes. Fractional derivatives have better flexibility as the comparison to classical integer order models, in which system dynamics not taken into account. Modern times have a wide use of field fractional derivatives and integral as well in the field of dynamic control systems, where the controlled system and the controller are defined by a set of fractional differential equations. Here the stability of fractional order system is checked at the different level and it is found that the stability region is large in the complex plane. This large stability region provides the more flexibility for system implementation in the control engineering.