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 satis ed. 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

2023

  • 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 7, p. 1590-1595

  • 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

  • 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]"

  • On the relationship between control barrier functions and projected dynamical systems

    2023
    G. Delimpaltadakis, W.P.M.H. Heemels
    IEEE Conference on Decision and Control (CDC) 2023, Singapore

  • 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]"

  • 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

  • Projection-based Controllers with Inherent Dissipativity Properties

    2023
    H. Chu, S. van den Eijnden, W.P.M.H. Heemels
    IEEE Conference on Decision and Control (CDC) 2023, Singapore

2022

  • 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

  • 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

  • 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

  • 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

  • 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

2021

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

2020

  • 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

  • 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

  • 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

  • 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

  • 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

2019

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

2017

  • 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

  • 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

  • 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

  • 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

  • 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

2016

  • 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

  • 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

  • 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

  • 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

2015

  • 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

  • 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

  • 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

  • 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

2014

  • 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

  • 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

  • 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

  • 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

  • Control of Mixing and Oscillations in Plasmas and Fluids

    September, 2014
    M. Lauret
    Eindhoven University of Technology

2013

  • 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

  • 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

2012

  • 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

2010

  • 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

  • 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

2009

  • 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

  • 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

2008

  • 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

  • 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

  • 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

  • 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

  • Nonlinear Control of Linear Motion Systems: An Exploratory Study

    2008
    W.H.T.M. Aangenent
    Eindhoven University of Technology "PhD Thesis"

2007

  • 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

  • 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

  • Output-feedback Design for Non-Smooth Mechanical Systems: Control Synthesis and Experiments

    2007
    A. Doris
    Eindhoven University of Technology "PhD Thesis"

2006

  • 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

2003

  • 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

1999

  • 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