The Genetic algorithms (GAs) are considered as a global and stochastic search technique that based on the principles of Darwinian evolution as given in (Gen, M., & Cheng, R., 2000). During the last decades, the Genetic algorithms have been utilized in a wide range of fields with multiple degrees of success within each. It has arisen from a grow to model the biological processes of natural selection and population genetics, with the creative aim of designing autonomous learning and decision- making systems (Holland, J. H, 1975). Since the introduction and subsequent popularization of GA as introduced in (Goldberg, D. E.,1989), it has been commonly used as an alternative optimization tool to usual methods.
Genetic algorithms use some variation of the following procedure to search for an optimal solution such as initialization, selection, crossover, mutation, and repeat (Holland, J. H, 1975; Goldberg, D. E.,1989). In the first step (Initialization), an initial population of solutions is randomly generated, and the objective function is estimated for each member of this initial generation as described in (Gen, M., and Cheng, R., 2000) while in the selection step, the individual members are chosen stochastically either to parent the next generation or to be passed on to it. The parent or the passing will occur in the members whose fitness is higher. The solution of fitness based on its objective value which the better objective value means higher fitness. Whereas the crossover means that some of the selected solutions are passed to a crossover operator. The crossover operator combines two or more parents to produce new offspring solutions for the next generation. The crossover operator tends to produce new offspring that keep the common characteristics of the parent solutions while combining the other behavior in new ways. In this way new areas of the search space are explored, hopefully, while retaining optimal solution characteristics (Gen, M., and Cheng, R., 2000). In mutation step, some of the next-generation solutions are passed to a mutation operator, which introduces random variations in the solutions. The purpose of the mutation operator is to ensure that the solution space is adequately searched to prevent premature convergence to a local optimum (Holland, J. H, 1975). Finally, the current generation of solutions is replaced by the new generation. If the stopping criterion is not satisfied, the process returns to the selection phase. The flowchart of GA is given in Fig. 5.
The use of GAs in control can generally be categorized into two different areas: offline and online optimization. Furthermore, offline applications have confirmed to be mainly popular and successful. However, the difficulties that associated with using the GA in real time and directly influencing the operation of the system will give a limited range of using the on-line optimization (Fogarty, T. C, 1989; Tammam, M. A., 2013).
The performance criterion for the designed controllers with the optimization technique is compared in terms of tracking error which the integral time absolute error (ITAE) is used as an objective function.
With take into consideration, a good tracking response will give a small value of ITAE and give optimal tuning parameters. In addition, the performance of the chosen problem with the designed control strategy depends on the control parameters. All these control parameters are obtained through GA technique by giving the system the tracking error. This algorithm will operate in order to minimize its objective function and in the final step, will produce the optimal parameters. The objective function is the same as mentioned in Equation (14). As a result of taking into account the fast system dynamics of the studied problem, the sampling period in the simulation and experimental routines is selected to be 0.01 sec.