Power rate exponential reaching law for enhanced performance of sliding mode control

In Sliding Mode Control (SMC), the control action can be split into two regions- the reaching phase and the sliding phase. Considerable research attention has been given to improve the reaching time so as to best utilize the benefit of robustness property of sliding mode motion. Attention has also been on alleviating and/or eliminating chattering during sliding mode motion so that smooth control is obtained which will not hinder practical applications. Exponential Reaching Law (ERL) is one of the methods reported in the literature for alleviating chattering in sliding mode. This paper proposes a Power Rate Exponential Reaching Law (PRERL) whereby substantial improvement both in reaching time and chattering alleviation are achieved compared to ERL. With ERL, the states do not settle at its desired position due to high frequency low magnitude chattering, thus limiting its practical utility. This drawback has been overcome in the PRERL method. Thus the benefits of the proposed method is many fold: reducing reaching time, improving chattering alleviation and ensuring settling of the states at its final position with considerable improvement in speed of response.