Article Transactions of the Institute of Measurement and Control 1–14 Ó The Author(s) 2020 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/0142331220909597 journals.sagepub.com/home/tim Neuro-fuzzy iterative learning control for 4-poster test rig Ufuk Dursun 1,2 , Galip Cansever 2 and _ Ilker U ¨ stog ˘lu 3 Abstract In this paper, a new control method is presented for the 4-poster test systems. The primary aim of the paper is to improve the convergence speed and decrease the error rate for model-based iterative learning control (ILC), a widely used method as a tracking control. First, the dynamic equations of the system are generated, and the control problem is formulated. Then, an inverse model of the system is established directly through the adaptive neuro-fuzzy inference system (ANFIS) with auxiliary parameter (piston position) as a serial combination of two sub-models. In order to construct a neuro-fuzzy ILC (NFILC) structure, these sub-models are integrated into the neuro-fuzzy inverse controller (NFIC). Because of this new structure, the modified ILC rule has two layers. In the first layer, the controlled parameter, namely, the acceleration is iterated, whereas, in the second layer, the auxili- ary parameter is iterated. The outcomes of the proposed control method are scrutinized by testing through a numerical simulation. Finally, it is demon- strated that the modified ILC rule dramatically increase the convergence speed and reduce the final error rate. Keywords ANFIS, iterative learning control, road simulator, test rig, 4-poster Introduction The purpose of test systems is to determine the performance and durability of a product. Based-on intended use(s) and purpose(s), there exist pseudo-static and dynamic (fatigue) test systems. While the pseudo-static test systems are mainly applied to type approval and durability tests, the dynamic test systems are used for the determination of fatigue and lifetime of a product. Before performing a fatigue test, the loads to be applied on a product by the test system are analyzed in terms of fatigue and lifetime (Grubisic, 1994), and then reference signals of limited time duration are created. Being referred to as the magnitudes of location, force, acceleration and so on, these reference signals are applied to the test system as sine, trapezoid or random signals, and so forth. During the fatigue tests, the aim is to track the reference signal by means of a real system with minimum error. For the control of the test systems that are mostly performed by the hydraulic actuators, a variety of control methods have been developed in accor- dance with test purposes. Accordingly, Plummer (2007) dis- cussed the details of the related control methods. For example, Proportinal Integral Derivative (PID) type classical control methods or most of the other control methods can be utilized based on the requirements of the application. Thanks to the conventional feedback controller structure, especially the moving cylinder to the working location or the force off- set settings can be achieved. There are also several other algo- rithms such as self-tuning PID (Hinton, 1992, 1996), which can adapt itself according to the test sample before the test, and offline (Clarke, 1996; Plummer and Vaughan, 1996) or online (Clarke, 1998; Jacazio and Balossini, 2007; Langdon, 2007) adaptive control algorithms sensitive to the changes and the disturbances during the test. In the same vein, to eliminate the system-led (e.g. nonlinear) or external distur- bances and improve the tracking performance, repetitive con- trol methods are available for tracking periodical reference signals (Plummer et al., 2005; Thoen, 1992). Yao et al. (2013) and Yao et al. (2017) established control methods to cancel acceleration harmonics that occur based on hydraulic nonli- nearities. Chen et al. (2017) offer a cerebellar model articula- tion controller for material strength testing to reduce the nonlinearity effect of the system. The test systems, as mentioned above, play an essential role in many kinds of industries, including the automotive industry. For example, a specific sub-field of the test systems used in the automotive sector, the road/load simulators, allow to perform fatigue tests on the whole vehicle and/or its com- ponents (Chindamo et al., 2017). The test designs in which the entire vehicle is tested are called 4-poster test systems and hereafter referred to as 4-poster. In these tests, the vehicles 1 Ford Otosan, Istanbul, Turkey 2 Department of Control and Automation Engineering, Yıldız Technical University, Turkey 3 Department of Control and Automation Engineering, Istanbul Technical University, Turkey Corresponding author: Ufuk Dursun, Ford Otosan, Akpınar, Hasan Basri Cd. No:2, 34885 Sancaktepe, Istanbul, 34885, Turkey. Email: udursun1@ford.com.tr; ufuk.dursun@std.yildiz.edu.tr