Overcoming performance limitations of linear control!
It is well known that linear time-invariant (LTI) control system for LTI plants suffer from fundamental performance limitations both in time-domain and frequency-domain, e.g., the "waterbed-effect." These limitations always call for design comprises and trade-offs.
To meet the ever increasing performance demands on throughput and accuracy in high-tech systems, these limitations have to be overcome. Therefore, we propose a paradigm shift to hybrid feedback controllers with the aim to remove these limitations. To enable this paradigm shift, we are developing performance analysis and synthesis techniques for hybrid controllers for linear motion systems. Examples of hybrid controllers include projection-based controllers, including our own successful hybrid-integrator gain system (HIGS) and reset controllers.
A projection-based controller (PBC) is an LTI controller combined with a projection element in the loop that ensures that specific signals are kept in well-chosen constraint sets inducing direct performance-enhancing benefits. This key idea can be used, for instance, to build a projection-based integrator (aka HIGS) in which the sign of its input and output are always the same. This leads to a direction reduction in phase lag (38,15 degrees in terms of its describing function), which is instrumental for overcoming fundamental performance limitations. In my ERC Advanced grant PROACTHIS we are developing the analysis and design toolkit for PBC and HIGS-based controllers in order for them to be embraced by the broader control engineering community and industry.
Reset controllers aim for the same objective as the HIGS mentioned above only not by projection on certain input-output sets, but by resetting controller states. Typically, reset controllers consist of a linear time-invariant (LTI) control system whose states, or subset of states, are reset to zero whenever certain conditions on its input and output are satisfied. These controllers were initially proposed in the 1950's to overcome the inherent performance limitations due to the 90 degrees phase lag of linear integrators. Indeed, due to the hybrid nature of reset control systems (RCSs), just as PBCs they can realize combinations of settling times, overshoot and asymptotic (steady-state) behavior that are unachievable by LTI controllers. PBCs might have the advantages of continuous control signals (and no resets, only swtiching of dynamics) as opposed to RCS results in discontinuous control signals (due to the resets). Due to this difference, it. might be easier for PBCs to build up a comprehensive toolkit much closer to the strong analysis and design tools for LTI control.
Many analysis and design questions are still open for projection-based control, reset controllers and more general hybrid and switching controllers (such as split-path nonlinear integrators). Through the ERC AdG PROACTHIS we are aiming to establish a systematic analysis and design framework for these types of hybrid controllers.
Incremental Stability of Discrete-Time First-Order Projection Elements
2024 R. Bertollo, S. van den Eijnden, W.P.M.H. Heemels 8th IFAC Conference on Analysis and Design of Hybrid Systems (ADHS) 2024, Boulder, Colorado, USA
Stability analysis of hybrid integrator-gain systems using linear programming
2024 J.J. Palacios Roman, S. Hafstein, S. van den Eijnden, M. Heertjes, W.P.M.H. Heemels 8th IFAC Conference on Analysis and Design of Hybrid Systems (ADHS) 2024, Boulder, Colorado, USA
Stability and performance analysis of hybrid integrator-gain systems: An LMI approach
2024 S. van den Eijnden, W.P.M.H. Heemels, H. Nijmeijer, W.P.M.H. Heertjes 8th IFAC Conference on Analysis and Design of Hybrid Systems (ADHS) 2024, Boulder, Colorado, USA
A Small-Gain Approach to Incremental Input-to-State Stability Analysis of Hybrid Integrator-Gain Systems
2023 S. van den Eijnden, M. Heertjes, H. Nijmeijer, W.P.M.H. Heemels IEEE Conference on Decision and Control (CDC) 2023, Singapore "IEEE Control Systems Letters [joint with CDC]", p. 2443-2448
Frequency-Domain Stability Conditions for Split-Path Nonlinear Systems
January, 2023 S.J.A.M. van den Eijnden, B. Sharif, M. F. Heertjes. W.P.M.H. Heemels 12th IFAC Symposium on Nonlinear Control Systems (NOLCOS) 2022 "IFAC PapersOnLine 301–306" 56(1), p. 301-306
Existence and Completeness of Solutions to Extended Projected Dynamical Systems and Sector-bounded Projection-based Controllers
2023 W.P.M.H. Heemels, A. Tanwani IEEE Conference on Decision and Control (CDC) 2023, Singapore "ieee Control Systems Letters [joint with CDC]", p. 1590-1595
Reset PID design for motion systems with Stribeck friction
January, 2022 R. Beerens, A. Bisoffi, L. Zaccarian, H. Nijmeijer, W.P.M.H. Heemels, N. van de Wouw IEEE Transactions on Control Systems Technology 30(1), p. 294-310
A Discrete-Time Approach to Analysis of Sampled-Data Hybrid Integrator-Gain Systems
2022 B. Sharif, D.W.T. Alferink, M.F. Heertjes, H. Nijmeijer, W.P.M.H. Heemels IEEE Conference on Decision and Control (CDC) 2022, Cancun, Mexico, p. 7612-7617
Control allocation for an industrial high-precision transportation and positioning system
2021 R. Beerens, S.C.N. Thissen, W.C.M. Pancras, T.M.P. Gommans, N. van de Wouw, W.P.M.H. Heemels IEEE Transactions on Control Systems Technology 29(2), p. 876-883
A solution to gain loss in hybrid integrator-gain systems
2021 M. Heertjes, S. van den Eijnden, W.P.M.H. Heemels, H. Nijmeijer IEEE Conference on Control Technology and Applications (CCTA), San Diego, USA, 2021, p. 1179-1184
Overcoming Performance Limitations of Linear Control with Hybrid Integrator-Gain Systems
2021 D. van Dinther, B. Sharif, S. van den Eijnden, H. Nijmeijer, M. Heertjes, W.P.M.H. Heemels
IFAC Conference on Analysis and Design of Hybrid Systems (ADHS) 2021, Brussels, Belgium "IFAC PapersOnline" 54(4), p. 289-294
Frequency-Domain Tools for Stability Analysis of Hybrid Integrator-Gain Systems
2021 S. van den Eijnden, M. Heertjes (23277), W.P.M.H. Heemels, H. Nijmeijer European Control Conference, Rotterdam, The Netherlands, 2021, p. 1895-1900
Oblique Projected Dynamical Systems and Incremental Stability under State Constraints
2020 W.P.M.H. Heemels, M.K. Camlibel, M. Heertjes
IEEE Conference on Decision and Control (CDC) 2020, Jeju Island, Republic of Korea "IEEE Control Systems Letters" 4(4), p. 1060-1065
Hybrid Integrator-Gain Systems: A Remedy for Overshoot Limitations in Linear Control?
2020 S. van den Eijnden, M. Heertjes, W.P.M.H. Heemels, H. Nijmeijer IEEE Conference on Decision and Control (CDC) 2020, Jeju Island, Republic of Korea "IEEE Control Systems Letters [joint with CDC]", p. 1042-1047
Hybrid Integrator-Gain System for Active Vibration Isolation with Improved Transient Response
2019 M. Heertjes, S. van den Eijnden, B. Sharif, W.P.M.H. Heemels, H. Nijmeijer
Joint 8th IFAC Symposium on Mechatronic Systems and 11th IFAC Symposium on Nonlinear Control Systems 2019, Vienna, Austria "IFAC PapersOnLine" 52(15), p. 454-459
2018 S.J.L.M. van Loon, B.G.B. Hunnekens, A.S. Simon, N. van de Wouw, W.P.M.H. Heemels IEEE Transactions on Control Systems Technology 26(1), p. 265 - 273
Hybrid PID control for transient performance
improvement of motion systems with friction
2018 Ruud Beerens, Andrea Bisoffi, Luca Zaccarian, W.P.M.H. Heemels, Hendrik Nijmeijer, Nathan Van De Wouw American Control Conference 2018, Milwaukee, USA , p. 539-544
A switched system approach to optimize mixing of fluids
July, 2018 V.S. Dolk, M. Lauret, D.A. Antunes, P. Anderson, W.P.M.H. Heemels IFAC Conference on Analysis and Design of Hybrid Systems (ADHS) 2018, Oxford, UK "[IFAC-PapersOnline]" 51-16, p. 31–36
Reference-dependent variable-gain control for a nano-positioning motion system
2016 S.J.L.M. van Loon, B.G.B. Hunnekens, A.S. Simon, N. van de Wouw, W.P.M.H. Heemels 12th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing 2016, Eindhoven, Netherlands "(IFAC-PapersOnLine, Volume 49, Issue 13, 2016, Pages 70-75)", p. 70-75
Experimental Evaluation of Reset Control for Improved Stage Performance
2016 M.F. Heertjes, K.G.J. Gruntjens, S.J.L.M. van Loon, N. van de Wouw, W.P.M.H. Heemels
12th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing 2016, Eindhoven, Netherlands "(IFAC-PapersOnLine, Volume 49, Issue 13, 2016, Pages 93-98)", p. 93-98
Scheduled Controller Design for Systems with Two Switching Sensor Configurations: A Frequency-Domain Approach
2015 S.J.L.M. van Loon, R. van der Weijst, M. Heertjes, W.P.M.H. Heemels IFAC Conference on Analysis and Design of Hybrid Systems (ADHS) 2015, Atlanta, USA. "(IFAC-PapersOnLine, Volume 48, Issue 27, 2015, Pages 99-104)", p. 99-104
2015 M.F. Heertjes, K.G.J. Gruntjens, S.J.L.M. van Loon, N. Kontaras, W.P.M.H. Heemels American Control Conference (ACC) 2015, Chicago, USA, p. 2155-2160
Transient Performance Improvement of Linear Systems Using a Split-Path Nonlinear Integrator
June, 2014 S.J.L.M. van Loon, B. Hunnekens, W.P.M.H. Heemels, N. Van De Wouw and H. Nijmeijer American Control Conference (ACC) 2014, Portland, Oregon, p. 341-346
Hybrid Control of the Boost Converter: Robust Global Stabilization
December, 2013 T.A.F. Theunisse, R.G. Sanfelice, J. Chai and W.P.M.H. Heemels IEEE Conference on Decision and Control (CDC) 2013, Florence, Italy, p. 3635-3640
June, 2010 W. Aangenent, G. Witvoet, W.P.M.H. Heemels. M.J.G. van de Molengraft, M. Steinbuch International Journal of Robust and Nonlinear Control 20(11), p. 1213-1233
Control of mechanical motion systems with non-collocation of actuation and friction: a Popov criterion approach for input-to-state stability and set-valued nonlinearities
February, 2009 J.C.A. de Bruin, A. Doris, N. van de Wouw, W.P.M.H. Heemels and H. Nijmeijer Automatica 45(2), p. 405-415
Robust control of piecewise linear systems: a case study in sheet flow control
August, 2008 J.J.T.H. de Best, B.H.M. Bukkems, M.J.G. van de Molengraft, W.P.M.H. Heemels and M. Steinbuch Control Engineering Practice 16(8), p. 991-1003
An LMI-based L2 gain performance analysis for reset control systems
June, 2008 W.H.T.M. Aangenent, G. Witvoet, W.P.M.H. Heemels, M.J.G. van de Molengraft and M. Steinbuch American Control Conference (ACC) 2008, Seattle, USA, p. 2310-2315
December, 2007 G. Witvoet, W.H.T.M. Aangenent, W.P.M.H. Heemels, M.J.G. van de Molengraft and M. Steinbuch IEEE Conference on Decision and Control (CDC) 2007, New Orleans, USA, p. 3278-3284
Positive feedback stabilization of surge in a centrifugal compressor
December, 1999 F. Willems, W.P.M.H. Heemels, B. de Jager and A.A. Stoorvogel IEEE Conference on Decision and Control (CDC) 1999, Phoenix, USA, p. 3295-3300
