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Active magnetic bearing (AMB) system has been recently employed widely as an ideal equipment for high-speed rotating machines. The inherent challenges to control the system include instability, nonlinearity and constricted range of operation. Therefore, advanced control technology is essential to optimize AMB system performance. This paper presents an application of model predictive control (MPC) based on linear parameter-varying (LPV) models to control an AMB system subject to input and state constraints. For this purpose, an LPV model representation is derived from the nonlinear dynamic model of the AMB system. In order to provide stability guarantees and since the obtained LPV model has a large number of scheduling parameters, the parameter set mapping (PSM) technique is used to reduce their number. Based on the reduced model, a terminal cost and an ellipsoidal terminal set are determined offline and included into the MPC optimization problem which are the essential ingredients for guaranteeing the closed-loop asymptotic stability. Moreover, for recursive feasibility of the MPC optimization problem, a slack variable is included into its cost function. The goal of the proposed feedback control system is twofold. First is to demonstrate high performance by achieving stable levitation of the rotor shaft as well as high capability of reference tracking without violating input and state constraints, which increases the overall safety of the system under disturbances effects. Second is to provide a computationally tractable LPVMPC algorithm, which is a substantial requirement in practice for operating the AMB system with high performance over its full range. Therefore, we propose an LPVMPC scheme with frozen scheduling parameter over the prediction horizon of the MPC. Furthermore, we demonstrate in simulation that such frozen LPVMPC can achieve comparable performance to a more sophisticated LPVMPC scheme developed recently and a standard NL MPC (NMPC) approach. Moreover, to verify the performance of the proposed frozen LPVMPC, a comparison with a classical controller, which is commonly applied to the system in practice, is provided.

This paper presents a nonparametric method for identification of MIMO linear parameter-varying (LPV) models in state-space form. The states are first estimated up to a similarity transformation via a nonlinear canonical correlation analysis (CCA) operating in a reproducing kernel Hilbert space (RKHS). This enables to reconstruct a minimal-dimensional inference between past and future input, output and scheduling variables, making it possible to estimate a state sequence consistent with the data. Once the states are estimated, a least-squares support vector machine (LS-SVM)-based identification scheme is formulated, allowing to capture the dependency structure of the matrices of the estimated state-space model on the scheduling variables without requiring an explicit declaration of these often unknown dependencies; instead, it only requires the selection of nonlinear kernel functions and the tuning of the associated hyper-parameters. 2017 Elsevier Ltd This paper has presented a nonparametric method for identification of LPV-SS models. The proposed technique relies only on the inputs, outputs, and scheduling variables data. The states are estimated up to a similarity transformation by using correlation analysis between the past and future data. Once estimated, an LS-SVM-based non-parametric scheme is used to identify the underlying LPV model. The proposed scheme solves a convex optimization problem and provides encouraging results on a MIMO numerical example with challenging nonlinearities in the presence of noise. The proposed algorithm is further validated on the model of a continuous stirred tank reactor process, and results are compared with an earlier study that assumes complete knowledge of the states. We find that kernel CCA provides encouraging state reconstruction results, which can then be augmented with the measured data in order to build an LPV-SS model. The main contribution of this paper lies in formulating the kernel CCA and LS-SVM solution for this identification problem by preserving the linearity structure in parameter-dependent state-space models. The proposed method also does not impose any dependency structure on the matrix functions, affine or otherwise. Since LPV-SS models are important for LPV control synthesis purposes, we believe that this work has the potential to pave the way for efficient low-order LPV modeling for control synthesis. Syed Zeeshan Rizvi obtained his B.E. in Electronics Engineering from N.E.D. University of Engineering & Tech., Pakistan and his M.S. in Electrical Engineering from King Fahd University of Petroleum & Minerals, Saudi Arabia, in years 2006 and 2008, respectively. In January 2013, he joined the Complex Systems Control Laboratory at The University of Georgia in Athens, GA, where he focused on system identification, model reduction, and control synthesis methods for linear parameter-varying models. He obtained his Ph.D. focusing on LPV system identification and control in December 2016. He is currently working as a process control scientist with Corning Inc. in Corning, NY, focusing on data analytics and advanced process control solutions for specialty glass and ceramic manufacturing processes. Javad Mohammadpour Velni received B.S. and M.S. degrees in electrical engineering from Sharif University of Technology and University of Tehran, Iran, respectively, and Ph.D. degree in mechanical engineering from University of Houston, TX. He joined the University of Georgia as an assistant professor of electrical engineering in August 2012. Prior to that, he was with the University of Michigan, where he worked in the naval architecture & marine engineering department from October 2011 to July 2012. He was also a Research Assistant Professor of mechanical engineering at University of Houston from October 2008 to September 2011 and a Research Associate at the same institution from January 2008 to September 2008. He has published over 100 articles in international journals and conference proceedings, served in the editorial boards of ASME and IEEE conferences on control systems and edited two books on control of large-scale systems (published in 2010) and LPV systems modeling, control and applications (published in 2012). His current research interests are in secure control of cyber physical systems (and in particular, smart grids), coverage control of heterogeneous multi-agent systems, and data-driven approaches for model learning and control of complex distributed systems. Farshid Abbasi received his B.Sc. and M.Sc. degrees in Mechanical Engineering both from University of Tabriz in 2007 and 2010, respectively. In January 2013, he joined Complex Systems Controls Lab at the University of Georgia, where he received a Ph.D. in dynamic system and controls in December 2016. His research interests include multi-agent systems, cooperative control, machine learning and system identification methods focusing on complex nonlinear processes. He is currently with ASML as a controls and system identification research scientist where his research focuses on developing new control and data analysis techniques to enhance rapidly changing semiconductor technologies. Roland T?th was born in 1979 in Miskolc, Hungary. He received the B.Sc. degree in Electrical Engineering and the M.Sc. degree in Information Technology in parallel with distinction at the University of Pannonia, Veszpr�m, Hungary, in 2004, and the Ph.D. degree (cum laude) from the Delft Center for Systems and Control (DCSC), Delft University of Technology (TUDelft), Delft, The Netherlands, in 2008. He was a Post-Doctoral Research Fellow at DCSC, TUDelft, in 2009 and at the Berkeley Center for Control and Identification, University of California Berkeley, in 2010. He held a position at DCSC, TUDelft, in 2011�2012. Currently, he is an Assistant Professor at the Control Systems Group, Eindhoven University of Technology (TU/e). He is an Associate Editor of the IEEE Conference Editorial Board, the IEEE Transactions on Control Systems Technology and the International Journal of Robust and Nonlinear Control. His research interests are in linear parameter-varying (LPV) and nonlinear system identification, machine learning, process modeling and control, model predictive control and behavioral system theory. He received the TUDelft Young Researcher Fellowship Award in 2010, the VENI award of The Netherlands Organisation for Scientific Research in 2011 and the Starting Grant of the European Research Council in 2016. Nader Meskin received his B.Sc. from Sharif University of Technology, Tehran, Iran, in 1998, his M.Sc. from the University of Tehran, Iran in 2001, and obtained his Ph.D. in Electrical and Computer Engineering in 2008 from Concordia University, Montreal, Canada. He was a postdoctoral fellow at Texas A&M University at Qatar from January 2010 to December 2010. He is currently an Associate Professor at Qatar University and Adjunct Associate Professor at Concordia University, Montreal, Canada. His research interests include Fault Detection and Isolation (FDI), multi-agent systems, active control for clinical pharmacology, and linear parameter varying systems. He has published more than one hundred refereed journal and conference papers and he is a coauthor (with K. Khorasani) of the book Fault Detection and Isolation: Multi-Vehicle Unmanned Systems (Springer 2011). Scopus

Modeling is recognized to be one of the toughest and most time-consuming tasks in modern nonlinear control engineering applications. Linear parameter-varying (LPV) models deal with such complex problems in an effective way, by exploiting well-established tools for linear systems while, at the same time, being able to accurately describe highly nonlinear and time-varying plants. When LPV models are derived from experimental data, it is difficult to estimate a priori how modeling errors will affect the closed-loop performance. In this work, a method is proposed to directly map data onto LPV controllers. Specifically, a hierarchical structure is proposed both to maximize the system performance and to handle signal constraints. The effectiveness of the approach is illustrated via suitable simulation tests.