Reset and switching control
Overcoming performance limitations of linear control!
It is well known that linear time-invariant (LTI) control system for LTI plants suffer from certain fundamental performance limitations imposed by Bode's gain-phase relationship, sometimes known as the "waterbed-effect."
To meet the ever increasing performance demands on throughput and accuracy, 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 reset and switching controllers.
A reset controller is 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 satised. These controllers were initially proposed to overcome the inherent performance limitations of linear feedback controllers imposed by Bode's gain-phase relationship. Indeed, due to the hybrid nature of reset control systems (RCSs) they can realize combinations of settling times, overshoot and asymptotic (steady-state) behavior that are unachievable by LTI controllers.
A switching controller is based on switching in a well-crafted manner between various LTI controllers (possibly based on disturbance information) to obtain a better overall closed-loop behavior compared to the case where single LTI control is used.
Many design questions are still open for reset and switching controllers. Through the HYPERMOTION project we are aiming to establish a systematic analysis and design framework for these types of hybrid controllers.
Related Publications
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A Small-Gain Approach to Incremental Input-to-State Stability Analysis of Hybrid Integrator-Gain Systems
2023
van den Eijnden, S., Heertjes, M., Nijmeijer, H., Heemels, W.P.M.H.
IEEE Control Systems Letters
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Existence and Completeness of Solutions to Extended Projected Dynamical Systems and Sector-bounded Projection-based Controllers
2023
W.P.M.H. Heemels and A. Tanwani
IEEE Control Systems Letters
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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
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Stability and Performance Analysis of Hybrid Integrator-Gain Systems: A Linear Matrix Inequality Approach
2022
S van den Eijnden, W.P.M.H. Heemels, H. Nijmeijer, M. Heertjes
Nonlinear Analysis: Hybrid Systems 45, p. 101192
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Filtered Split-Path Nonlinear Integrator: A Hybrid Controller for Transient Performance Improvement
March, 2022
B. Sharif, A. van der Maas, N. van de Wouw, and W.P.M.H. Heemels
IEEE Transactions on Control Systems Technology 30(2), p. 451-463
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On Convergence of Systems with Sector-Bounded Hybrid Integrators
2022
S. van den Eijnden, M. Heertjes, H. Nijmeijer, W.P.M.H. Heemels
IEEE Conference on Decision and Control (CDC) 2022, Cancun, Mexico, p. 7636-7641
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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
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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
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Projection-Based Integrators for Improved Motion Control:
Formalization,Well-posedness and Stability of Hybrid Integrator-Gain
Systems
2021
D.A. Deenen, B. Sharif, S. van den Eijnden, H. Nijmeijer, W.P.M.H. Heemels, M. Heertjes.
Automatica(133), p. 109830
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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
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On the Equivalence of Extended and Oblique Projected Dynamics with Applications to Hybrid Integrator-Gain Systems
2021
B. Sharif, M. Heertjes, H. Nijmeijer, W.P.M.H. Heemels
American Control Conference (ACC) 2021, New Orleans, USA, p. 3434-3439
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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
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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
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Oblique Projected Dynamical Systems and Incremental Stability under State Constraints
2020
W.P.M.H. Heemels, M.K. Camlibel, M. Heertjes
IEEE Control Systems Letters 4(4), p. 1060-1065
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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 Control Systems Letters 4(4), p. 1042 - 1047
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To stick or to slip: A reset PID control perspective on positioning systems with friction
2020
A. Bisoffi, R. Beerens, W.P.M.H. Heemels, H. Nijmeijer, N. van de Wouw, L. Zaccarian
Annual Reviews in Control 49, p. 37-63
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L2-gain Analysis of Periodic Event-Triggered Control and Self-Triggered
Control using Lifting
2020
N. Strijbosch, G.E. Dullerud, A.R. Teel, W.P.M.H. Heemels
IEEE Transactions on Automatic Control 66(8), p. 3749-3756
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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
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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
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Reset integral control for improved settling of PID-based motion systems with friction
2019
R. Beerens, A. Bisoffi, L. Zaccarian, W.P.M.H. Heemels, H. Nijmeijer, N. van de Wouw
Automatica 107, p. 483-492
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Extended Projected Dynamical Systems with Applications to Hybrid
Integrator-Gain System
December, 2019
B. Sharif, M.F. Heertjes, W.P.M.H. Heemels
IEEE Conference on Decision and Control (CDC) 2019, Nice, France, p. 5773-5778
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Hybrid Integral Reset Control with Application to a Lens Motion System
2019
Gruntjens, K., Heertjes, M., van Loon, S., van De Wouw, N., Heemels, W.P.M.H.
American Control Conference 2019, Philadelphia, USA, p. 2408-2413
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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
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Scheduled controller design for systems with varying sensor configurations: A frequency-domain approach
2018
R. van der Weijst, S.J.L.M. van Loon, M.F. Heertjes, W.P.M.H. Heemels
IEEE Transactions on Control Systems Technology 26(2), p. 523-534
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Bandwidth-on-demand motion control
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
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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
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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
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Frequency-domain tools for stability analysis of reset control systems
2017
S.J.L.M. van Loon, K. Gruntjens, M.F. Heertjes, N. van de Wouw, W.P.M.H. Heemels
Automatica 82, p. 101-108
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Linear Quadratic Regulation of Switched Systems Using Informed Policies
2017
D. Antunes, W.P.M.H. Heemels
IEEE Transactions on Automatic Control 62(6), p. 2675 - 2688
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Filtered Split-Path Nonlinear Integrator (F-SPANI) for Improved Transient Performance (Invited Paper)
2017
A. van der Maas, N. Van De Wouw, W.P.M.H. Heemels
American Control Conference 2017, Seattle (WA), USA. , p. 3500-3505
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Hybrid Integrator Design for Enhanced Tracking in Motion Control (Invited Paper)
2017
D.A. Deenen, M. Heertjes, W.P.M.H. Heemels, H. Nijmeijer
American Control Conference 2017, Seattle (WA), USA. , p. 2863-2868
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Set-point Control of Motion Systems with Uncertain Set-valued Stribeck Friction
2017
R. Beerens, H. Nijmeijer, W.P.M.H. Heemels, N. van de Wouw
IFAC World Congress 2017, Toulouse, France "[IFAC-PapersOnline]" 50-1, p. 2965–2970
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Split-Path Nonlinear Integral Control for Transient Performance
Improvement
April, 2016
S.J.L.M. van Loon, B. Hunnekens, W.P.M.H. Heemels,
N. van de Wouw, H. Nijmeijer
Automatica 66, p. 262-270
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L2-gain Analysis for a Class of Hybrid Systems with Applications to
Reset and Event-triggered Control: A Lifting Approach
October, 2016
W.P.M.H. Heemels, G.E. Dullerud, A.R. Teel
IEEE Transactions on Automatic Control 61(10), p. 2766-2781
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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
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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
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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
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A lifting approach to L2-gain analysis of periodic event-triggered and switching sampled-data control systems (invited paper)
2015
W.P.M.H. Heemels, G.E. Dullerud, A.R. Teel
IEEE Conference on Decision and Control (CDC) 2015, Osaka, Japan, p. 4176 - 4182
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Switching data-processing methods for feedback control: Breaking the speed versus accuracy trade-off
2015
E.P. van Horssen, D. Antunes, W.P.M.H. Heemels
IEEE Conference on Decision and Control (CDC) 2015, Osaka, Japan, p. 2313 - 2318
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DESIGN OF A VARIABLE GAIN INTEGRATOR WITH RESET
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
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Improved L2-gain analysis for a class of hybrid systems with applications to reset and event-triggered control
December, 2014
S.J.L.M. van Loon, W.P.M.H. Heemels and A.R. Teel
IEEE Conference on Decision and Control (CDC) 2014, Los Angeles, USA, p. 1221-1226
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Performance Analysis of a Class of Linear Quadratic Regulators for Switched Linear Systems
December, 2014
D. Antunes, W.P.M.H. Heemels
IEEE Conference on Decision and Control (CDC) 2014, Los Angeles, USA, p. 5475-5480
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Analyzing the non-smooth dynamics induced by a split-path nonlinear integral controller
July, 2014
S.J.L.M. van Loon, B. Hunnekens, W.P.M.H. Heemels, N. Van De Wouw and H. Nijmeijer
ENOC 2014, Vienna
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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
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Control of Mixing and Oscillations in Plasmas and Fluids
September, 2014
M. Lauret
Eindhoven University of Technology
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Switching Control in Vibration Isolation Systems
March, 2013
M.F. Heertjes, I.H. Sahin, N. van de Wouw and W.P.M.H. Heemels
IEEE Transactions on Control Systems Technology 21(3), p. 626-635
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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
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Disturbance Decoupling of Switched Linear Systems
January, 2012
E. Yurtseven, W.P.M.H. Heemels and M.K. Camlibel
Systems and Control Letters 61(1), p. 69-78
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Observer-Based Control of Discrete-Time LPV Systems with Uncertain Parameters
May, 2010
W.P.M.H. Heemels, J. Daafouz and G. Millerioux
IEEE Transactions on Automatic Control 55(9), p. 2130-2135
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Performance analysis of reset control systems
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
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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
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Design of observer-based controllers for LPV systems with unknown parameters
December, 2009
W.P.M.H. Heemels, J. Daafouz and G. Millerioux
IEEE Conference on Decision and Control (CDC) 2009, Shanghi, China, p. 1836-1841
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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
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Input-to-state stability and interconnections of discontinuous dynamical systems
December, 2008
W.P.M.H. Heemels and S. Weiland
Automatica 44(12), p. 3079-3086
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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
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Switching control in active vibration isolation
July, 2008
M.F. Heertjes, N. van de Wouw and W.P.M.H. Heemels
ENOC 2008, Saint-Petersburg, Russia, p. 1-6
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Nonlinear Control of Linear Motion Systems: An Exploratory Study
2008
W.H.T.M. Aangenent
Eindhoven University of Technology "PhD Thesis"
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Observer design for a class of piecewise linear systems
August, 2007
A.Lj. Juloski, W.P.M.H. Heemels and S. Weiland
International Journal of Robust and Nonlinear Control 17(15), p. 1387-1404
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H2 performance analysis of reset control systems
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
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Output-feedback Design for Non-Smooth Mechanical Systems: Control Synthesis and Experiments
2007
A. Doris
Eindhoven University of Technology "PhD Thesis"
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Stabilizing Model Predictive Control of Hybrid Systems
November, 2006
M. Lazar, W.P.M.H. Heemels, S. Weiland and A. Bemporad
IEEE Transactions on Automatic Control 51(11), p. 1813-1818
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On solution concepts and well-posedness of linear relay systems
December, 2003
A.Y. Pogromsky, W.P.M.H. Heemels and H. Nijmeijer
Automatica 39(12), p. 2139-2147
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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