# Design and Optimization of a Neuro-Fuzzy System for the Control of an Electromechanical Plant
## 1 Introduction
Currently, advanced techniques are applied to traditional controls such as the Field-Oriented Control (FOC) and Direct Torque Control (DTC). Authors in [13] evaluate traditional FOC and DTC compared to two additional fuzzy and predictive controllers. Concerning robotic applications using fuzzy logic, reference [14] employs a fuzzy control Proportional Integral (PI) in a robotic driving system for hybrid electric vehicles in a way that allows a reliable evaluation of energy efficiency. This depicts the relevance of the efficiency of fuel in hybrid vehicles. Thus, reliable measurements are required in order to have an accurate analysis of fuel efficiency; whereby, the authors propose a robotic system to perform driving tests to reduce the deviation when such tests are carried out by humans. Moreover, reference [15] proposes a Knowledge-Based Neural Fuzzy Controller (KNFC) for navigation control in mobile robots. Knowledge-Based Cultural Multi-Strategy Differential Evolution (KCMDE) is employed here to adjust the parameters of the KNFC. This is applied in mobile robots PIONEER 3-DX for automatic navigation systems and obstacle avoidance, employing the existing angle between the obstacle and the robot to determine if the robot enters in specific reference points to modify its behavior and thus skip dead ends. A related work is presented in [16] using a neuro-fuzzy system in path planning for a service robot in complex environments with the presence of humans as in a retirement home. As inputs for path planning, the system uses a 3D depth camera and multiple sonar sensors. Meanwhile, reference [17] proposes a simple and practical decoupled control structure for a parallel robot positioning control using the Cable-Driven Parallel Robot (CDPR). This structure is employed with a non-linear Proportional Integral Derivative (PID) and classic PID controllers. In addition, the control system structure is proposed through an analysis of cables involved in End-Effector (EE) robot's movement when operating independently for each axis; later, an adjustment of rules for fuzzy PID controllers was carried out and the Ziegler-Nichols method was applied to PID classic controllers. Regarding recent research of neuro-fuzzy control systems, in [18] is developed a Terminal Sliding-Mode Control (TSMC) using a Fuzzy Double Hidden Layer Recurrent Neural Network (FDHLRNN). According to authors, the neuro-fuzzy system proposed is a combination of a radial basis neural network and a fuzzy neural network. To reduce the switching gain (associated with the TSMC), the FDHLRNN is employed to approximate the nonlinear sliding-mode equivalent control term. In order to observe the dynamic response and robustness, the control scheme is tested using a second-order nonlinear system. An additional work is observed in [19], where is designed a TSMC using FDHLRNN for a single-phase Active Power Filter (APF). Authors propose the TSMC to allow the tracking error converges to zero (in a finite time). The system is used in harmonic suppression first to approximate the equivalent control and second to suppress unknown disturbances. The equations to update the adaptive parameters of the FDHLRNN are obtained using a Liapunov function in order to ensure asymptotic stability. Finally, in [20] is displayed an approximation-based adaptive fractional sliding mode control. For approximating the system uncertainties and disturbance we used a Double Loop Recurrent Fuzzy Neural Network (DLRFNN). In this development, a fractional order term is incorporated into the sliding surface having the benefits of sliding mode control and fractional calculus. The DLRFNN uses the advantages of fuzzy systems to handle uncertain information and the neural networks to learn using data measured from the process. In this work, the designed neuro-fuzzy controller uses the structure of a compact fuzzy system based on Boolean relations as presented in [21], which can be used for the identification and control of dynamic systems.