High-order Sliding Mode Control of a Bioreactor Model through Non-Commensurate Fractional Equations

A higher-order sliding approach to control a bioreactor model is proposed by non-commensurate fractional equations. According to existing conditions and chattering reduction, a high-order sliding mode approach has been chosen to design the controller. A mathematical problem is a barrier to use the high-order sliding mode approach for fractional order systems. The contribution of the paper is to choose proper sliding surfaces. High-order sliding mode controllers have been taken in accordance with the structure of integer order system. Thus, in order for the system to apply more precise calculations, fractional systems should somehow turn to integer order. The sliding surfaces have been selected so appropriately that we can benefit from the structure of integer order controllers for fractional order system. The sliding surface in both controllers has also been the same so as to provide conditions for comparison. The model outputs are reached the desired values using two controllers. Finally, the comparison in simulations indicates that the proposed approach has a great impact on chattering reduction.