Wavelet, PID control, MIMO, Metaheuristic, Particle swarm optimization, Genetic algorithm, Firefly algorithm

The control of dynamic systems is a challenge, the methods traditionally used in tuning present the difficulty in expressing the desired specifications and being able to find controllers that produce these requirements, especially when the case requires more complex controllers, it is the case of  Multiple Input Multiple Output (MIMO) problems. Due to the increasing competitiveness in the industry, it becomes imperative to use more efficient tuning techniques and that in fact can find controllers with the desired performance. For this, one can use metaheuristics, such as Particle Swarm Optimization (PSO), Genetic Algorithm (AG) and Vagalume Algorithm to obtain the parameters of the controller according to a fitness function, which should in fact code how good a given controller is, adequately expressing the desired specifications, so that the metaheuristic employed can find the optimal controller, which best satisfies the chosen fitness function. Therefore, it is proposed to use the multilevel wavelet analysis, already present in the literature, focused on other applications, especially in the analysis of signals, sounds and images, for the creation of an index to be used as a fitness function in control optimization. Wavelet analysis allows to capture information on the behavior and shape of the signal by informing the frequency of a signal over time, a characteristic that may be desirable, in the evaluation and design of controllers and, thus, it is possible to separately evaluate the performance transitional and permanent arrangements. A case study will be done, finding control of a MIMO system of four coupled tanks. A comparative study was made with other fitness functions presented in the literature and with the Root Locus  method. The implemented controllers presented the expected performance, and the one found using the proposed index presented better performance.