An Approach to Design MIMO FO Controllers for Unstable Nonlinear Plants

This paper develops an approach to control unstable nonlinear multi-inputs multi-output (MIMO) square plants using MIMO fractional order (FO) controllers. The controller design uses the linear time invariant (LTI) state space representation of the nonlinear model of the plant and the diagonal closedloop transfer matrix (TM) function to ensure decoupling between inputs. Each element of the obtained MIMO controller could be either a transfer function (TF) or a gain. A TF is associated in turn with its corresponding FO TF. For example, a D (Derivative) TF is related to a FO TF of the form D^δ, δ = [0, 1]. Two applications were performed to validate the developed approach via experimentation: control of the angular positions of a manipulator, and control of the car and arm positions of a translational manipulator.