Hybrid Integrator-Gain Systems: Analysis, Design and Applications

This book introduces the hybrid integrator-gain system (HIGS) as a promising approach for overcoming fundamental limitations of linear time-invariant (LTI) control systems. These limitations pose significant challenges in meeting the ever-increasing demands for accuracy, speed and reliability in high-precision positioning systems, including wafer scanners and other advanced mechatronic platforms. The working principle of the HIGS relies on switching dynamics that avoid hard state resets and produce continuous control signals, resulting in phase advantages over LTI integrators and offering practical performance benefits. Hybrid Integrator-Gain Systems contributes a comprehensive set of practical tools for the design and analysis of HIGS-based controllers with the aim of enabling substantial performance improvements beyond what is achievable with conventional LTI control. The material is organized into three parts:

• Part I formally introduces the concept of the HIGS and uses numerical examples to demonstrate that genuine performance advantages over LTI control can be achieved;
• Part II develops rigorous time- and frequency-domain tools for analysing robust stability and performance of feedback interconnections between LTI plants and HIGS-based controllers, addressing the challenges in closed-loop analysis and design introduced by the hybrid nature of these systems; and
• Part III focuses on practical design considerations and experimental validation of HIGS-based controllers applied to LTI systems.

Hybrid Integrator-Gain Systems presents a framework for the design and analysis of HIGS-based control architectures for LTI systems. It demonstrates how appropriately designed HIGS controllers can push the performance of high-tech systems to levels unattainable with purely LTI approaches. Researchers and practitioners working in high-precision motion control, hybrid and switched control and related fields will find this book of considerable interest for its potential to advance control performance.

Sebastiaan van den Eijnden (1991) received the M.Sc. degree and Ph.D. degree (Cum Laude) from the Eindhoven University of Technology (TU/e) in 2017 and 2022, respectively. From 2022-2023 He has been working as a Mechatronics and Control Engineer at ASML, the Netherlands. Currently, Sebastiaan is an Assistant Professor at the Mechanical Engineering department, TU/e. He was a recipient of the 2023 Hybrid Systems CSS TC Outstanding Student Paper Prize and the 2023 Automatica Paper Prize. His current research includes the analysis and design of nonlinear/hybrid systems using graphical techniques, and the development of nonlinear control paradigms for realizing performance beyond the limitations of linear time-invariant control, with application to high-precision industrial systems.

Marcel Heertjes (1969) received the M.Sc. and Ph.D. degrees from the Eindhoven University of Technology, Eindhoven, The Netherlands, in 1995 and 1999, respectively. After being with the Philips Center for Industrial Technology from 2000-2005, he joined ASML in 2006 where he currently is appointed Sr. principle mechatronics architect. He was a recipient of the IEEE Control Systems Technology Award 2015 for variable gain control and its applications to wafer scanners and the 2023 Automatica Paper Prize on projection-based integrators for improved motion control, among others. In 2019, he was appointed (part-time) full Professor on Industrial Nonlinear Control for High-Precision Systems at Eindhoven University of Technology. He acts as an Associate Editor for IFAC Mechatronics since 2016.

Maurice Heemels (1972) received the M.Sc. (mathematics) and Ph.D. (EE, control theory) degrees (summa cum laude) from the Eindhoven University of Technology (TU/e) in 1995 and 1999, respectively. From 2000 to 2004, he was with the Electrical Engineering Department, TU/e, as an assistant professor, and from 2004 to 2006 with the Embedded Systems Institute (ESI) as a Research Fellow. Since 2006, he has been with the Department of Mechanical Engineering, TU/e, where he is currently a Full Professor and Vice-Dean. He held visiting professor positions at ETH, Switzerland (2001), UCSB, USA (2008) and University of Lorraine, France (2020). He is a Fellow of the IEEE and IFAC, and was the chair of the IFAC Technical Committee on Networked Systems (2017-2023). He served/s on the editorial boards of Automatica,  Nonlinear Analysis: Hybrid Systems (NAHS), Annual Reviews in Control, and IEEE Transactions on Automatic Control, and is the Editor-in-Chief of NAHS as of 2023. He was a recipient of a personal VICI grant awarded by NWO (Dutch Research Council) and recently obtained an ERC Advanced Grant. He was the recipient of the 2019 IEEE L-CSS Outstanding Paper Award and the Automatica Paper Prize 2020-2022. He was elected for the IEEE-CSS Board of Governors (2021-2023).   His current research includes hybrid and cyber-physical systems, networked and event-triggered control systems and model predictive control.

Henk Nijmeijer (1955) is a professor emeritus in Dynamics and Control at the Department of Mechanical Engineering of the Eindhoven University of Technology. His research field encompasses nonlinear dynamics and control and applications thereof. He is a fellow of the IEEE since 2000 and was awarded in 1990 the IEE Heaviside premium. He is appointed honorary knight of the ‘Golden Feedback Loop’ (NTNU, Trondheim) in 2011. He has been scientific director of the Dutch Institute of Systems and Control (DISC) in the period 2014-2023. He is recipient of the 2015 IEEE Control Systems Technology Award and a member of the Mexican Academy of Sciences. He has been Graduate Program director of the TU/e Automotive Systems program in the period 2016-2021. He is an IFAC Fellow since 2019 and as of January 2021 an IEEE Life Fellow. He has been awarded various best paper awards, including the Automatica best paper award for the period 2020-2022. He is Chief Field editor of the newly established journal Frontiers in Control Engineering. He chaired the Dutch Mechanical Engineering Council till 2024 and is a core member of the ICMS with focus area ‘complexity and soft robotics’.