Comparative Study of Integer and Fractional Order Sliding Mode Control

Abstract

A comparative study of integer order sliding mode control (IOSMC) and fractional order sliding mode control (FOSMC) is outlined on two different systems. The numerical example of first system is subjected to non-linear sinusoidal disturbance while the second numerical example considered being a marginally stable system. Sliding mode control (SMC) theory is a category of variable structure control system (VSCS). SMC generates discontinuous control action that generates a high frequency ON or OFF states which forces the system state to converge to zero. However, this switching at high frequency produces chattering phenomenon that is supposed to be eliminated or minimized. The Lyapunov function is being considered that provides global asymptotic stability in finite time. The integer order sliding surface (IOSS) and fractional order sliding surface (FOSS) is designed for both the numerical examples representing two different systems and a control input law is determined such that it provides asymptotic convergence in finite amount of time span and is supposed to ensure zero steady state error. The fractional order (FO) is varied in between zero to one and various responses of both the systems are observed. For the system exposed to sinusoidal disturbance, FOSMC provides stability faster than the IOSMC scheme for values of FO that are close to one. In the case of marginal stable system, IOSMC adds stability to the system faster than the linear feedback control law. The performance of FOSMC on marginal stable system is not so better than compared to IOSMC method. The settling time of plant trajectories are large than produced by IOSMC. However, FOSMC performs better when values of FO are selected very close to one but responses are not so good when FO values are placed close to zero. Overall the simulation results prove the nucleus notion of SMC theory that provides finite time stability as well as robustness against external disturbances and perturbations and are insensitive to system parameters.