This paper provides a nonlinear technique that uses a fuzzy inference system and neural networks for the identification purposes of heat flow transfer in the chamber. Firstly, linear models are obtained by transfer functions with delay using Matlab identification tools for heat exchange. Three different transfer functions are provided (for three sensors in different positions along the chamber), and after it has been concluded that the second model has the smallest error, it is tested using different input. In this case, the linear model failed to represent the behaviour of the system precisely, making the error more than 1.5 C in the steady state. This was expected because linear models are trustworthy only around certain operating ranges. In order to make the new model, which will be unique and valid in the whole state space, another identification method using an adaptive neuro-fuzzy inference system (ANFIS) was presented. Furthermore, for the best performance, the ANFIS architecture was found using one of the most famous population-based optimizations: the genetic evolutionary algorithm. With two inputs and 70 parameters found by optimization (40 premises and 30 consequent) ANFIS greatly outperforms standard identification technique in terms of the mean square error. This nonlinear model was also tested on the different input, which was not used in the training process, and it was concluded that the nonlinear model identifies the real object with a neglectable error, which is 45 times smaller than the linear one.

The aim of this study is to investigate nonlinear DC motor behavior and to control velocity as output variable. The linear model is designed, but as it is experimentally verified that it does not describe the system well enough it is replaced by the nonlinear one. System’s model has been obtained taking into account Coulomb and viscous friction in the firmly nonlinear environment. In the frame of the paper the dynamical analysis of the nonlinear feedback linearizing control is carried out. Furthermore, a metaheuristic optimization algorithm is set up for finding the coefficient of the proportional-integral feedback linearizing controller. For this purpose Gray wolf optimization technique is used. Moreover, after the introduction of the control law, analysis of the pole placement and stability of the system is establish. Optimized nonlinear control signal has been applied to the real object with simulated white noise and step signal as disturbances. Finally, for several desired output signals, responses with and without disruption are compared to illustrate the approach proposed in the paper. Experimental results obtained on the given system are provided and they verify nonlinear control robustness.

This paper presents the proportional-derivative fuzzy controller for trajectory tracking of the gripping mechanism with two degrees of freedom. Aiming to achieve movement of the gripping mechanism without sudden starting and stopping, a polynomial velocity profile is utilized. The African vultures optimization, as one of the latest metaheuristic algorithms, is used to obtain the optimal input/output scaling gains of the proposed fuzzy controller according to the selected fitness function. The results obtained by this algorithm are compared with the other three new and popular metaheuristic algorithms: the whale optimization, the ant lion optimization and the sine cosine algorithm. Moreover, a simulation study was done for the defined initial position and for the scenario where there is a certain deviation because the gripping mechanism is not at its original initial position. Finally, the robustness of the controller is tested for the case when the masses of the segments increase three times. The results revealed that the suggested controller was capable of dealing with nonlinearities of the gripping mechanism, initial position and parameter changes. The movement of the gripping mechanism is smooth and follows the defined trajectory.

Adaptive Neural Fuzzy Inference Systems ANFIS have an increasing tendency to be used in scientific research and practical applications. The digitization of production and the emergence of Industry 4.0 enabled the development of this trend, primarily due to the ability to adapt to the task by integrating artificial neural networks and fuzzy logic, which can potentially use the advantages of both techniques in unique frameworks. This approach facilitated the modeling, data analysis, classification and control processes. The advantage of the ANFIS, compared to conventional methods, is reflected in the ability to predict the output based on a set of inputs and on the rule base. Also, these systems are suitable, because they provide the possibility to adjust the parameters of the control system. This paper presents the structure of the ANFIS system and gives a detailed review of the achievements so far, through a comparative analysis, where some possible spheres of interdisciplinary application are highlighted. Possibilities for variations, improvements and innovations of the algorithm, as well as reducing the complexity of the network architecture itself, are discussed. Proposals for some new, as yet unused combinations with metaheuristic optimization methods are presented. Finally, important guidelines are provided on when and where it is useful to apply ANFIS systems.

The production industries have repeatedly combated the problem of system modelling. Successful control of a system depends mainly on the exactness of the mathematical model that predicts its dynamic. Different types of studies are very common in the complicated challenges involving the estimations and approximations in describing nonlinear machines are based on a variety of studies. This article examines the behaviour and stability of holonomic mechanical system in the arbitrary parameter sets and functional configuration of forces. Differential equations of the behaviour are obtained for the proposed system on the ground of general mechanical theorems, kinetic and potential energies of the system. Lagrange?s equations of the first and second kind are introduced, as well as the representation of the system in the generalized coordinates and in Hamilton?s equations. In addition to the numerical calculations applied the system, the theoretical structures and clarifications on which all of the methods rely on are also presented. Furthermore, static equilibriums are found via two different approaches: graphical and numerical. Above all, stability of motion of undisturbed system and, later, the system that works under the action of an external disturbance was inspected. Finally, the stability of motion is reviewed through Lagrange-Dirichlet theorem, and Routh and Hurwitz criteria. Linearized equations are obtained from the nonlinear ones, and previous conclusions for the stability were proved.