Optimal Design of Multivariable Controller for Nonlinear Systems Using Variable Population Artificial Bee Colony Algorithm

Artificial bee colony algorithms belong to the paradigm of bio-inspired, population-based, algorithms that have been widely used to solve optimization problems. These algorithms use population of individuals/particles/bees/ants in order to explore a search space of potential solutions to a given problem and to be able to quickly converge to a global solution, or at least to a good solution. The proposed paper uses a variable population of bees in order to improve the converge rate of the algorithm, as well as a dynamic control of the inertia of the bees in order to better control the exploration of the search space. The balance between exploitation and exploration of the search space is a well-known key feature for such optimization methods and many works have been devoted to improving the management of this balance: managing population, operators, and fitness functions. To evaluate the performance of the proposed algorithm, a comparison is made with the classic artificial bee colony and genetic algorithms in tuning the multivariable the proportional-integral-derivative (PID) controllers. The proposed experimental study is the Distillation Column System (DCS) which represent control systems of complex industrial processes. Moreover, the DCS is known to be multivariable, time variant, nonlinear MIMO system with time delays. The experimental results show that the new algorithm performs better than classic approaches such as genetic algorithm and classic artificial bee colony algorithm. Key–Words: Multivariable PID Controller, Variable Population Size, Artificial Bee Colony,Nonlinear Systems, Distillation Column System.