# Design and Optimization of a Neuro-Fuzzy System for the Control of an Electromechanical Plant
## 1 Introduction  
In control systems, fuzzy logic offers broad applicability given its flexibility to implement control strategies through a set of rules using membership functions [1; 2; 3]. It is possible to use training algorithms with neural networks when representing the fuzzy system as a neural network that grants higher accuracy in the fuzzy system performance. When representing a fuzzy system as a neural network, a neuro-fuzzy system is obtained [4; 5]. An interesting application of fuzzy logic is the aided design process. In this regard, a remarkable application is observed for compliant mechanism design used in soft robotics, space, and bioengineering due to the advantages of free friction, monolithic structure, and minimal assembly. Considering this area, a hybrid methodology is presented in [6] for solving the multi-objective optimization design. Authors propose a hybridization through a combination of a finite element method, statistical technique, desirability function approach, fuzzy logic system, Adaptive Neuro-Fuzzy Inference System (ANFIS), and Lightning Attachment Procedure Optimization (LAPO). A bistable compliant mechanism is designed, where desirability values of two performance metrics are calculated and transferred into the fuzzy logic system to obtain the output in a single objective function. A related workis presented in [7], proposing a method using statistics, numerical simulation, computational intelligence, and metaheuristics. A two-degree of freedom compliant mechanism is designed, where numerical datasets are collected by simulations. The sensitivity of design parameters is studied by analysis of variance and Taguchi technique. The results of sensitivity are employed to separate populations for lightning attachment procedure optimization. The values of two output mechanism performances are the inputs of the fuzzy logic model, and the output of this system is a single objective function, that is optimized using LAPO algorithm. Other advanced work is presented in [8], presenting an optimization framework to provide a systematic design method for a flexure gripper. The optimization strategy includes the topology, modeling, and size optimization phases. The gripper topology is determined via the solids isotropic material with penalization method considering stress constraint and force distribution. The modeling of the performances is implemented via an Enhanced Adaptive Neuro-Fuzzy Inference System (EANFIS). The optimization is performed to search for the best model parameters. Finally, a hybrid procedure of the Taguchi method is described in [9], using fuzzy logic, response surface method, and Moth-flame optimization algorithm to solve the design optimization of a flexure hinge to enhance three quality characteristics. Fuzzy modeling is proposed to interpolate the three objective functions into a unified objective function. An integrated regression equation is determined via response surface method and flexure hinge is optimized using Moth-flame optimization algorithm. Regarding fuzzy control applications for electromechanical systems, there are relevant developments in electric engines control and robotics. With regard to fuzzy logic for motor control, reference [10] carries out a review of multi-motor control, which are multiple input and multiple output systems. The main purpose of the multiple motor control variators consists of achieving a coordinated operation in all motors. The literature reviewed shows that fuzzy systems are widely employed in multi-motor control. Meanwhile, in [11] a fuzzy controller is proposed using a motion capture system to operate the speed and orientation of a wheelchair considering the model of a Direct Current (DC) motor for the design process. Further, a fuzzy logic controller is used in [12], for an image-based navigation system of an autonomous underwater vehicle with a DC motor. According to [13], due to high robustness and simple maintenance, Induction Motors (IM) are commonly used in household appliances and industries.