Improvement tracking performances of adaptive model following control systems with unknown disturbances

In this paper, an approach to Adaptive Model Following Control systems (AMFC) based on PID controller is proposed and analyzed for a class of Multi-Input Multi-Output (MIMO) linear time varying plant with unknown disturbances. This approach of design adaptive controller improved the performances of conventional AMFC schemes considerably, by incorporating an additional Proportional-Integral-Derivative (PID) action in the closed loop of hyper-stable AMFC systems. The controller parameters are designed under assumptions of unknown bounded disturbances, to a proper choice that satisfies the Popov stability criteria. Specifically, a control law is constructed of two essential components, the first one corresponds to AMFC systems without disturbances and the second one is responsible to reduce the effects of unknown load disturbances. Therefore, it's important to note that the method does not use any estimation algorithm and can guarantee an asymptotically stable state error for bounded disturbances. Finally, a numerical example is presented to show applicability and performances of the proposed approach.