Fractional order nonlinear model predictive control using RIOTS_95

Abstract

RIOTS_95 is a Matlab toolbox for solving integer order optimal control problems in general form. In this paper, using RIOTS_95, fractional order nonlinear model predictive control for fractional order system in a very general setting is presented. Problems of single-input single-output (SISO) and Multi-input multi-output (MIMO) with or without state/input constraints can be solved within this software platform. First, the fractional order transfer function is approximately converted into integer order transfer function with Oustaloup's recursive approximation approach. Then a Luenberger observer designed according to the obtained integer order transfer function is used to estimate the intermediate states of the approximated integer-order system. With the integer order model and the estimated states, the original fractional order nonlinear system can then be controlled with integer order Model Predictive Control using RIOTS_95 (RMPC). Three examples are given to show the effectiveness of the RMPC to control fractional order system and its ability to handle constraints. Step disturbance is added on the system outputs to show the achieved robustness of RMPC.