Edge Theorem-Based 2-DOF Controller Design for MIMO System

Abstract

The designing and implementation of controllers on multiple-input multiple-output (MIMO) plants for achieving a robust performance are always a promising problem for design engineers. Decoupler is one of the vital applied algorithms to minimize the undesirable effect of cross couplings present in MIMO plants for improving the plant performance. However, the inclusion of a decoupler makes the resulting decoupled system more complex, thereby increasing the computational complexity of designing the controller. To enhance performance, this paper aims to design a controller without incorporating any decoupling technique. This approach is intended to make the compensated system effectively track the desired path while treating coupling effects as a disturbance. The two degrees of freedom (2-DOF) proportional integral derivative (PID) control method is employed including a filter coefficient in derivative part based on edge theorem considering the MIMO system as different single-input single-output subsystems on which the cross couplings act as a disturbance to each other. The optimum value of controller parameter is searched in between the range determined through edge theorem using particle swarm optimization technique. The designed controller is implemented to the twin rotor MIMO system in which the designed method is quite capable of minimizing the disturbances occur for the reason of cross coupling. It is seen that in 2-DOF PID control method, the maximum overshoots are found to be 0% and 8% for main and tail rotor, respectively which are superior as compared to the conventional PID controller with decoupler designed for same system where the maximum overshoots are found as 30% for both main and tail rotors. The robust performance of compensated plant is studied by plant parameter variation, output disturbance rejection and changing the nature of input signals to the plant.