Vol.:(0123456789) 1 3 Journal of the Brazilian Society of Mechanical Sciences and Engineering (2021) 43:248 https://doi.org/10.1007/s40430-021-02957-y TECHNICAL PAPER A neural network‑based inversion method of a feedback linearization controller applied to a hydraulic actuator Fábio Augusto Pires Borges 1  · Eduardo André Perondi 2  · Mauro André Barbosa Cunha 3  · Mario Roland Sobczyk 2 Received: 10 February 2020 / Accepted: 18 March 2021 / Published online: 10 April 2021 © The Brazilian Society of Mechanical Sciences and Engineering 2021 Abstract In this work, we use a neural network as a substitute for the traditional analytic functions employed as an inversion set in feedback linearization control algorithms applied to hydraulic actuators. Although very efective and with strong stability guarantees, feedback linearization control depends on parameters that are difcult to determine, requiring large amounts of experimental efort to be identifed accurately. On the other hands, neural networks require little efort regarding parameter identifcation, but pose signifcant hindrances to the development of solid stability analyses and/or to the processing capabili- ties of the control hardware. Here, we combine these techniques to control the positioning of a hydraulic actuator, without requiring extensive identifcation procedures nor losing stability guarantees for the closed-loop system, at reasonable comput- ing demands. The efectiveness of the proposed method is verifed both theoretically and by means of experimental results. Keywords Hydraulic actuator control · Neural network-based identifcation · Feedforward multilayer perceptron · Feedback linearization 1 Introduction Due to their high force/size ratios, hydraulic actuators are widely used in tasks combining high forces with limited dimensions. On the other hands, their dynamics depend on strongly nonlinear phenomena such as valve saturation, behavior of the fow rates through the valve orifces and friction forces in the piston [1]. Moreover, their open-loop dynamics present low damping, and their mathematical modeling sufers from signifcant uncertainties in many key parameter values, such as leakages and dead zones in the control valves. These are challenging characteristics for their corresponding controllers to cope with, making it difcult to use such actuators in high-precision applica- tions. Several control strategies have been proposed with the goal of enhancing the precision of hydraulic actuators, e.g., backstepping [2–6], feedback linearization [7–9] and sliding mode control [10–12]. Many other algorithms are based on combinations of these and other techniques, as illustrated in [13–15], for instance. An important feature of these model-based control approaches lies in the possibil- ity of using Lyapunov methods for analyzing the controlled plants, providing stability guarantees even when nonlinear efects are explicitly taken into account. All of the afore- mentioned papers include some strategy to overcome the parametric uncertainties and external disturbances present in hydraulic actuators. Many works include online learning methods, where parameters and disturbances are estimated in real time, such as adaptive control [6, 10, 13], extended state observer (ESO) [2, 6], extended disturbance observer (EDO) [4] and extended diferentiator [3]. Even though they Technical Editor: Victor Juliano De Negri. * Fábio Augusto Pires Borges fborges@furg.br Eduardo André Perondi eduardo.perondi@ufrgs.br Mauro André Barbosa Cunha maurocunha@ifsul.edu.br Mario Roland Sobczyk mario.sobczyk@ufrgs.br 1 N2E Research Group, Engineering School, Federal University of Rio Grande, Av Italia, km 8, Rio Grande, RS 96203-900, Brazil 2 Federal University of Rio Grande Do Sul, Rua Sarmento Leite 425, Porto Alegre, RS 90050-170, Brazil 3 Automation and Control Research Group, Sul-Rio-Grandense Federal Institute for Education, Science, and Technology, Praça Vinte de Setembro, 455, Pelotas CampusPelotas, RS 96015-360, Brazil