A Multiobjective Genetic Algorithm Applied to Multivariable Control Optimization

Many control problems involve simultaneous optimization of multiple performance measures that are often noncommensurable and competing with each other. Traditionally, classical optimization algorithms based on nonlinear programming or optimal control theory is applied to obtain the solution of such problems using different scalar approaches. The presence of multiple objectives in a problem usually gives rise to a set of optimal solutions, largely known as Pareto-optimal solutions. In this context, the Non-dominated Sorting Genetic Algorithm (NSGA-II) has been successfully applied to solving many multiobjective problems. This paper presents the design and the tuning of two PID (Proportional-Integral-Derivative) controllers through NSGA-II. Simulation numerical results of multivariable PID control and convergence of the NSGA-II is presented and discussed with application in a robotic manipulator of two-degree-of-freedom. The proposed optimization method based on NSGA-II offers an effective way to implement simple but robust solutions providing a good reference tracking performance in closed loop.