Evaluation of Fractional-Order Sliding Mode Control Applied to an Energy Harvesting System

The use of fractional operators in control theory is recent and new approaches are emerging more and more. The existing literature shows improvement in control performance when using fractional controllers. One of the main reasons for this improvement is due to the greater number of control parameters, inserted by the exponents that represents the fractional-order of the integral or derivative operators. Another interesting feature of fractional calculus is that it is often used to describe phenomena with memory. In this context, this paper proposes a comparison between Sliding Mode Controls of Integer-Order (SMC) and Fractional-Order (FOSMC). Sliding Mode Control is one of the most successful approaches in dealing with uncertainties and one of the most efficient in nonlinear dynamics. The problem chosen for the application of the controllers is a nonlinear bi-stable vibration energy harvesting system, since controlling this system makes the relationship between generated energy and consumed energy (control effort) very important, being an ideal situation to evaluate and compare the performance of the two methods. A novelty in this paper is the use of the Cross Entropy optimization method to obtain the set of optimal parameters (best performance) in the SMC and FOSMC controllers. The result of the optimization tests reinforces the improvement in the use of the fractional operator reducing the control effort by up to 93% when compared to the integer-order controller. The Cross Entropy method was also very effective for controllers with a large number of adjustment parameters.