Strojniški vestnik - Journal of Mechanical Engineering 66(2020)5, 337-347 © 2020 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2019.6499 Original Scientific Paper Received for review: 2019-12-06 Received revised form: 2020-04-06 Accepted for publication: 2020-04-14 Data-Driven Model-Free Control of Torque-Applying System for a Mechanically Closed-Loop Test Rig Using Neural Networks Aida Parvaresh1 - Mohsen Mardani2* !K.N. Toosi University of Technology, Iran 2ACECR, Sharif University of Technology Branch, Iran This paper presents a data-driven approach that utilizes the gathered experimental data to model and control a test rig constructed for the high-powered gearboxes. For simulating a wide variety of operational conditions, the test rig should be capable of providing different speeds and torques; this is possible using a torque-applying system. For this purpose, Electro-Hydraulic Actuators (EHAs) are used. Since applying accurate torque is a crucial demand as it affects the performance evaluation of the gearboxes, precise modelling of the actuation system along with a high-performance controller are required. In order to eliminate the need for to solve complex nonlinear equations of EHA that originate from friction, varying properties of flow and similar, a data-driven system based on neural networks is used for modelling. In this manner, the model of the system, which captures the whole dynamic of the system, can be obtained without any simplifying assumptions. The model is validated with experimental data, and the learning factors are set to zero to reduce the high computational costs. After that, another network of neurons is used as a controller. The performance of the proposed controller under normal conditions and in the presence of disturbances are investigated. The results show a good tracking of this controller for various reference inputs in different conditions with acceptable characteristics. Additionally, the obtained results are compared with a conventional proportional-integral-derivative (PID) controller results, and the superior features of the proposed scheme is concluded. Keywords: identification; data-driven system; closed-loop test rig; hydraulic actuator; neural networks Highlights • Presenting a straight-forward procedure for accurate modelling of the actuation system in the test rig for testing the high-powered gearboxes. • Eliminating the requirement for the application of simplifying assumptions to reach the linear analytical model. • Providing the possibility of applying different scenarios for testing the gearboxes performance under different operational conditions. • Achieving the precise control of the actuation system even in the presence of disturbances. 0 INTRODUCTION Ensuring safety and performance along with the reduced maintenance costs of high-powered gearboxes, which are mostly used in helicopters and wind turbines, are of great importance in industrial applications. Since in-field testing of such equipment is often impossible, time-consuming, and not cost-efficient, test rigs are developed [1] and [2], for primary assessment of the capability and performance of the components in industrial use. Full-sized test rigs can provide realistic conditions so that the performance and operation of the systems can be evaluated. These test rigs can be designed both in closed-loop or open-loop schemes. Test rigs operating based on the closed-loop principle can reduce energy consumption up to 95 % compared to open-loop schemes, so they are superior in testing high-powered gearboxes when a great amount of energy is required. Different types of test rigs have been developed to investigate different features based on desired parameters to be tested. In a study by Âkerblom [3], a closed-loop recirculating power test rig was developed for testing gearboxes under controlled environments. Different parameters, including noise, gearbox life, and efficiency, were studied in a gearbox system consisting of two similar gearboxes. In the studied system, one gearbox was tilted using a hydraulic cylinder. In [4], Arun et al. reviewed different test rigs; they also fabricated a new test rig. A novel test rig was proposed by Mihailidis and Nerantzis [5], which was consisted of a planetary gear box for applying variable torques and speeds. Palermo et al. [6] constructed a precise closed-loop test rig to evaluate the dynamic behaviour of gear pairs in different operational conditions. Their fabricated test rig consisted of a test side to test the desired gearbox and reaction side to close the power train. Mozafari et al. [7], represented the preliminary, conceptual, and detailed design of a test rig that was developed for high-powered gearboxes. Their rig was a closed-loop mechanical type and used hydraulic torque applying system for providing the desired torque. In order to reach the desired position of the hydraulic actuators, they implemented on-off and proportional-integral- *Corr. Author's Address: ACECR, Sharif University of Technology Branch, Iran, mardani@acecr.ac.ir 337 Strajniski vestnik - Journal of Mechanical Engineering 66(2020)5, 337-347 derivative (PID) controllers [8] as well as fractional order PID [9]. For conducting dynamic tests in high-powered gearboxes and for actuating the system, the torque should be applied automatically employing a torque-applying system. These systems should be able to provide variable torques and speeds to simulate the operational conditions of high-powered transmissions. Different systems can be used for this purpose, among which, hydraulic systems would be the best choice due to their superior features. Compared to the other equipment for applying torque, electro-hydraulic actuators (EHAs) can provide higher power-to-weight ratios considering the volume limitations, higher forces, reduced size of equipment as well as the robustness improvement. In addition, they are inherently more stiff and rigid so that the precise position control can be achieved. Also, they provide faster response, which is a desirable feature in industrial applications [10] and [11]. However, despite the noticeable advantages of these systems, their dynamic behaviour is highly nonlinear due to the nonlinear characteristics of flow and pressure, including varying bulk modulus, compressibility, and viscosity [12]. So, prior to the control of these systems, an accurate model, which represents the complete dynamic behaviour of the system should be developed. Despite the extensive published studies, a lack of precise and appropriate modelling is observed. Different methods have been utilized to overcome these problems. Some researchers attempt to overcome this problem via the linearization of equations and using linear control procedures to control these systems. However, by the use of linear control strategy, some portion of the dynamic system behaviour would be lost during the linearization of the system. Some researchers also used simplifying assumptions, such as neglecting leakage or flow compressibility. The obtained model by these approaches would be valid just in the adjacent of the linearization point. Additionally, the use of linear controllers would not lead to high-performance control. In some other researches, higher-order linear models were used to design controllers. However, these models also suffer from the validity problem in other points rather than operating points. In [13], a method for parameter identification of nonlinear terms in the model of the system was proposed. It was observed that considering the identified nonlinear effects, increases the accuracy of the model, significantly. In addition, in another study [14], the identification of the nonlinear effects, including friction coefficient was conducted using the input-output data. The control of EHAs and developing an appropriate controller to satisfy the desired requirements are of great importance regarding their various applications. The control scheme can be designed either in a force control mode or displacement control mode. Considering the easier implementation of displacement control mode from the practical point of view, better performance as well as disturbance rejection characteristics, this mode is widely used in controlling EHAs [15]. Many nonlinear adaptive control approaches were used for controlling EHA, among them, the usage of sliding mode controller [16], back-stepping [17] and [18], feedback linearization controller [19] and [20] and so on can be mentioned. Deticek and Zuperl [21], presented a novel hybrid-fuzzy control scheme for positioning the EHA in practical applications. Nonlinear control schemes are rarely utilized in industrial applications due to their need for a mathematical model as well as the complexity of tuning the parameters. Achieving high accuracies in the position tracking of hydraulic actuators are of great importance; however, parametric uncertainties, as well as nonlinearities, are the major problems in this field [22]. Parametric uncertainties can be compensated by the use of adaptive control schemes, while nonlinearities can be handled by robust controllers. To take advantage of these two schemes simultaneously, intelligent controllers are proposed. Guan and Pan [18] presented a nonlinear adaptive robust control procedure with unknown parameters for an EHA, by combining a back-stepping technique and a simple robust control. Haung et al. [17] used an incremental nonlinear dynamic inversion control technique for controlling a hydraulic actuator in the presence of system uncertainties. They implemented their proposed approach on a 6-degree-of-freedom (DOF) hexapod hydraulic robot. In industrial applications, sometimes the use of popular theoretical control methods, which represents superior performance, is not possible due to the occurrence of some unpredicted and unexpected effects [23]. Model-free controllers, which do not require an explicit model of the plant, are the best choice in these applications, such as classic PID controllers. In these types of controllers, high and intensive modelling work are not required. Among the advantages of model-free control schemes, easy implementation and tuning of the coefficients can be mentioned. The model-free procedure provides good control features without considering an accurate model of the system [24]. These models aim to approximate the system dynamics using the gathered information from the embedded sensors that are 338 Aida Parvaresh, A. - Mardani, M. Strajniski vestnik - Journal of Mechanical Engineering 66(2020)5, 337-347 estimated and updated in each time samples. It is evident that through using this control scheme, we can overcome the difficulties in mathematical modelling and improve the practical implementation. Some model-free control schemes were used for controlling EHA. Neural networks (NNs) are universal approximators, which means that they can be used as a black-box estimator applicable for the systems with parametric uncertainties and nonlinearities [25]. Tremendous interest has been devoted to NNs, according to their outstanding performances in learning, adaptation, generalization, optimization, and control [26]. From the theoretical point of view, a continuous function can be approximated to a desired accuracy, which enables the modelling of the complex nonlinear system using NNs. In many research studies, NNs are used for control and modelling [27]. These structures are used to learn the features and characteristics of the system, which can be used as the model, instead of obtaining the explicit dynamic of the system. According to some studies, these controllers can be classified as model-free controllers as they do not use the exact model of the system. The existing complexities in the control problem of industrial systems make the neural network approach as a popular method. Learning the control scheme using NNs was proposed for enhancing the trajectory tracking performance. Yao et al. [25] developed an advanced nonlinear controller for the hydraulic system to obtain position tracking in the presence of various disturbances. They used a neural network estimator to improve the disturbance compensation. In general, using these networks have significant advantages over other controllers. In this paper, we aim to take the advantages of NNs for modelling and controlling of a hydraulically-actuated test rig. The rest of the paper is organized as follows: In Section II, a brief introduction of the fabricated test rig, which is a mechanically closed-loop test rig with a hydraulically-driven torque applying system, is presented. Then, in Section III, the data acquisition procedure required for modelling of the system is explained. After that, in Section IV, the proposed algorithm for modelling and controlling the actuation system using neural networks is described. Then, the results of neural-network modelling and controlling for different conditions are presented in Section V. Finally, Section VI is dedicated to the conclusions derived from this research. 1 SYSTEM DEFINITION The studied test rig is a mechanically closed-loop test rig that was designed and fabricated in Sharif University of Technology branch of Academic Centre of Education, Culture and Research (ACECR). The mentioned test rig was designed so that it has low energy loss; it also provides wide ranges of torques and speeds. Therefore, it is appropriate for testing the high-powered gearboxes that are commonly used in aeronautic industries. The specification of the test rig and torque-applying system are provided in Table 1. In Fig. 1, the schematic and real test rig are depicted. To apply the required torque to the testing system, a torque-applying system that consists of a planetary gearbox is used. By rotating the ring of this planetary gearbox, the system is rotated. The rotation of the ring of this planetary gearbox is provided by the linear hydraulic actuators, which are depicted in Fig. 2. It is noteworthy that all criteria, including stresses, strains, safety fractures, and failure and similar, are provided in the design procedure [7]. For sensing the displacement of the actuator rod, two displacement sensors are utilized with the maximum measurement course of 75 mm, which is larger than the course length of the actuator. A hydraulic circuit is designed for controlling the hydraulic actuator; in addition, a 4/3 directional valve is used for changing the direction of the hydraulic actuator. The actuation system consists of a three-phase electrical motor, a positive displacement pump, a container, a safety valve, and a pressure indicator. More information about this test rig and actuation is provided in [28]. Table 1. Specifications of the test rig and torque applying system Specification Value Test Rig Max loading capacity 365 kW Max rotational speed 3000 rpm Max hydraulic actuator course 60 mm Torque applying Max required force 10 kN system Force applying arm 175 mm Max rotation 20 deg 2 DATA ACQUISITION The model obtained from the neural network structure does not require any mathematical relationships. It is a data-driven system, which uses input and output data of the system for training the desired network. Therefore, gathering data is an important step for modelling. The data collection procedure is depicted in Fig. 3. Data-Driven Model-Free Control of Torque-Applying System for a Mechanically Closed-Loop Test Rig Using Neural Networks 339 Strajniski vestnik - Journal of Mechanical Engineering 66(2020)5, 337-347 Fig. 1. The schematic and real test rig for high-powered gearboxes Fig. 2. The schematic and real test rig for high-powered gearboxes Fig. 3. Data- acquisition procedure According to Fig. 3, the generated excitation signal in the computer is converted to the current of Iv. Then, it is multiplied by Kv, which is the constant gain of the servo valve, to produce Xv, the signal for displacing the spool of 4/3 servo valve. By displacing the spool, the flow rate of QL would be changed; thus, the piston would be displaced. Then, this displacement is measured by the displacement sensors that are embedded in the system. The combination of sine signals is the best choice for excitation signal in the cases in which the system would be operated in determined frequencies, and the quality of the collected data in those signals are important. The frequency of the excitation signal should be selected according to the operational frequencies of the system [21]. In this research, the excitation signal is considered as follows: : ^at cos a.ts (1) where Sexc is the excitation signal, n is the number of sine signals that are summed together, ts is the sampling time, a, is the amplitude of ith sine signals, and m, is the frequency of the signals. The gathered input-output signal is depicted in Fig. 4. 340 Aida Parvaresh, A. - Mardani, M. = 1 Strajniski vestnik - Journal of Mechanical Engineering 66(2020)5, 337-347 10 -Input kç^r A M ilJL, rrWV Y\ 10 20 30 Time [s] 40 40 20 -20 -Output (\ A \ 1 V 0 10 20 30 40 Time [s] Fig. 4. Input-output data set for training the system 3 PROBLEM DEFINITION For obtaining the model of the actuation system for the torque-applying system, we aim to use a procedure that captures the system dynamics completely and uses no simplifying assumptions and can overcome the existing nonlinearities and uncertainties. Precise modelling is of great importance, as it directly affects the performance of the controller for the actuation system and consequently, the performance of the testing procedure for high-powered gearboxes. As mentioned, EHA is a single-input singleoutput (SISO) discrete-time nonlinear system. The system can be described using the following relation [23]. ^u(k), u(k -1),..., u(k - na ^x(k), x(k -1),..., x(k - nb) x(k +1) = M (2) This structure provides a nonlinear mapping from input space K" to output space Km and defined using [u(k) u(k- 1)... u(k-na)] and [u(k) u(k- 1)... u(k-nb)] vectors. In this relation, x(k) denotes the output of the system at time instant k, which is the rod displacement. M(.) e K is a function from K" ^ Km and represents the model structure of the system, which is a function of previous inputs and previous outputs of the system. The controller for this plant can be defined as: ^ u(k-1),u(k - 2),...,u(k - n ) ^ u(k ) = C ec (k +1), ec (k +1),..., ec (k - nd ) (3) In Eq. (3), u(k) is the current control signal, which is defined by the use of [u(k- 1) u(k- 2) ... u(k-nc)] and [ec(k- 1) ec(k-2)... ec(k-nd)]. [u(k- 1) u(k- 2) ... u(k-)] denotes the past control inputs, with the nc representing the maximum previous input; while [ec(k - 1) ec(k- 2) ... ec(k-nd)] denotes the past errors, with nd representing the maximum past errors. In addition, C(.) is a nonlinear function representing the controller structure. ec is the tracking error that is defined as: ec = x(k ) - xdes (k ), (4) where xdes(k) is the desired output. In order to obtain the model and controller structure practically, some assumptions should be considered as follows: Assumption 1: The partial derivatives of M(.) are continuous for k e N and M(.) e R is a smooth function of Rn ^ . This assumption is a general condition for nonlinear systems. Assumption 2: The model of the system as described in Eq. (2), is generalized Lipchitz; hence a positive constant C exists, so that the |AXX + 1)| < C||4||, {k = [Ar(k), Au(k)]. This assumption represents the direct influence of the inputs variation on variation rate of the system output. According to this assumption, the outputs of the system are bounded if the inputs are varied in the bounded region [29]. According to the above assumptions, Eq. (2) can be defined by the use of in the following form: x(k +1) = x(k ) + = = x(k ) + Ax(k k + Au(k (5) In Eq. (5) represents the nonlinear dynamic of the system. The main problem is the estimation of In this paper, the neural networks are used for approximating this function. A neural network is defined as a system of neurons locating at different layers. With the appropriate selection of the activation functions, bounding the input values to SB e Rn, as well as adjusting the hidden layers number, weights and biases, the M(x), which represents the model of the plant can be defined in the form of: M ( x) = H2TaM (HTx ) + s m ( x). (6) In the above equation, H1 is the matrix representing the weights (mn) and biases (bn) of the first hidden layer; while weights (mi2) and biases (bi2) of the second hidden layer are included in H2. Additionally, the vectors of activation functions are denoted by aM. Moreover, eM(x) is the approximation error by the neural network structure. With the use of a suitable NN for approximation, which means the appropriate selection of H1, H2 and aM, it is necessary 5 0 0 0 Data-Driven Model-Free Control of Torque-Applying System for a Mechanically Closed-Loop Test Rig Using Neural Networks 341 Strajniski vestnik - Journal of Mechanical Engineering 66(2020)5, 337-347 to obtain M(x) so that the approximation error (eMx)) becomes less or equal to the acceptable error: sM(x)