This work deals with the problem of choosing a controller for the production of biodiesel from the transesterification process through temperature control of the chemical reactor, from the point of view of automatic control, by considering such aspects as the performance metrics based on the error and the energy used by the controller, as well as the evaluation of the control system before disturbances. In addition, an improvement method is proposed via a neuro-fuzzy controller tuned with a metaheuristic algorithm to increase the efficiency of the chemical reaction in the reactor. A clear improvement is shown in the minimization of the integral of time multiplied squared error criterion (ITAE) performance index with respect to the proposed method (8.1657 $\times {10}^4$) in relation to the PID controller (7.8770 $\times {10}^7$). Moreover, the integral of the total control variation (TVU) performance index is also shown to evaluate the power used by the neuro-fuzzy controller (25.7697), while the PID controller obtains an index of (32.0287); this metric is especially relevant because it is related to the functional requirements of the system since it quantifies the variations of the control signal.

The inverse kinematics problem (IKP) is fundamental in robotics, but it gets harder to solve as the complexity of the mechanisms increases. For that reason, several approaches have been applied to solve it, including metaheuristic algorithms. This work presents a proposal for solving the IKP of a doubly articulated kinematic chain by means of a modified differential evolution (DE) algorithm. The novelty of the proposal is both in the modeling of the problem and the modification to the DE for solving it. The modeling is inspired by a technique used in animation software to recreate movements by dividing the complete trajectory in a number of segments. Each segment represents a single optimization problem linked to the IKP as a sequence that is solved by the modified DE where the initial population for each single problem is biased by using the solution of the previous one. The approach produces solutions for positioning the end effector in a specific point within the work space while minimizing the angular displacement between the initial and final poses. The proposal was able to obtain solutions requiring a fewer total execution cycles compared to the usual approach of solving only one optimization problem related to the inverse kinematics. Different trajectories were used to test the solutions generated by the proposed approach, and the set of conditions that must be covered to apply it to solve the IKP of a particular mechanism are presented.

This work presents a methodology to solve optimization problems with dynamic-size solution vectors containing continuous and integer variables. It is achieved by reformulating the original problem through a bilevel optimization approach and implementing metaheuristic techniques to solve it. In the selected case study, the optimization problem corresponds to tuning a neuro-fuzzy controller (NFC) that operates in a biodiesel production system for controlling temperature. The NFC performs well and is especially robust to disturbances, but due to its complexity, it is difficult to determine the best set of parameters for its use. This has led to biased searches based on criteria such as the experiences of designers. With the proposed method, it was possible to obtain a tuning that—when implemented in a simulation—led to results that surpassed those documented in the literature. Finally, the proposal offers flexibility for implementation with other controllers that have similar architectures and can be integrated into various other plants or processes.

Heat exchangers are widely used process equipment in industrial sectors, making the study of their temperature dynamics particularly appealing due to the nonlinearities involved. Model-free approaches enable the use of input and output data to generate specific and accurate estimations for each proposed system. In this work, a model-free identification strategy is proposed using a convolutional neural network to estimate the system’s behavior. Notably, the model does not rely on direct temperature measurements; instead, temperature is inferred from other system signals such as reference, flow, and control inputs. This data-driven approach offers greater specificity and adaptability, often outperforming manufacturer-provided coefficients whose performance may vary from design expectations. The results yielded an $R^2$ index of 0.9951 under nominal conditions and 0.9936 when the system was subjected to disturbances.

This paper demonstrates that biodiesel production processes can be optimized through implementing a controller based on fuzzy logic and neural networks. The system dynamics are identified utilizing convolutional neural networks, enabling tests of the reactor temperature response under different control law proposals. In addition, a sensorless technique using a convolutional neural network to replace the sensor/transmitter signal in case of failure is implemented. Two optimization functions are proposed utilizing a metaheuristic algorithm based on differential evolution, where the aim is to minimize the use of cooling for the control of the reactor temperature. Finally, the control system proposals are compared, and the results show that a neuro-fuzzy controller without optimization restrictions generated unviable ITAE ($1.9597\times {10}^7$) and TVU (22.3993) performance metrics, while the restriction proposed in this work managed to minimize these metrics, improving both the ITAE ($3.3928\times {10}^6$) and TVU (17.9132). These results show that combining the sensorless technique and our optimization method for the cooling stage enables energy saving in the temperature control processes required for biodiesel production.