Modified Nondominated Sorting Genetic Algorithm-Based Multiobjective Optimization of a Cross-Coupled Nonlinear PID Controller for a Twin Rotor System

This paper presents an innovative nonlinear PID control scheme based on a modified nondominated sorting genetic algorithm validated using a laboratory helicopter model called the Twin Rotor System. The concepts of controlled elitism and dynamic crowding distance are incorporated into the proposed algorithm to progress towards the best solution from the entire population in order to solve the multiobjective optimization problem with good convergence characteristics. The addition of nonlinear functions to the cross-coupled PID controller structure initiates better error tracking and facilitates smooth output under changing input conditions. The design objective is to implement an optimal nonlinear PID control scheme for the angular displacements of the twin-rotor system, with integral square error and control energy taken as the multiobjective problems. The statistical performance of the controller is analyzed by considering the best, worst, mean, and standard deviations of ISE. In this work, simultaneous control of pitch and yaw angles is considered to get rid of the coupling effect between the two rotors. The results indicate the advantage of the MNGSA-based tuning for the two degrees of freedom MIMO control with standard reference trajectories as per the TRMS330-10 model.