Review and new theoretical perspectives on active disturbance rejection control for uncertain finite-dimensional and infinite-dimensional systems

The active disturbance rejection control (AD RC), first proposed by Jingqing Han in late 1980s, is a powerful control technology being able to deal with external disturbances and internal uncertainties in large scale for control systems in engineering applications. This survey paper will articulate, from a theoretical perspective, the origin, ideology and progress of ADRC for not only uncertain finite-dimensional systems but also uncertain infinite-dimensional ones. Some recent theoretical developments, general framework and unsolved problems of ADRC for finite-dimensional systems with mismatched disturbances and uncertainties by output feedback, uncertain finite-dimensional stochastic systems, uncertain infinite-dimensional systems described by both the wave equation and the fractional-order partial differential equation are successively addressed, from which we see the challenges and opportunities for this remarkable emerging control technology to various types of control systems.

[1]  Feiqi Deng,et al.  Divided State Feedback Control of Stochastic Systems , 2015, IEEE Transactions on Automatic Control.

[2]  Sen Chen,et al.  Analytical design of active disturbance rejection control for nonlinear uncertain systems with delay , 2019, Control Engineering Practice.

[3]  Wei Xing Zheng,et al.  Sampled-Data-Based Event-Triggered Active Disturbance Rejection Control for Disturbed Systems in Networked Environment , 2019, IEEE Transactions on Cybernetics.

[4]  George Weiss,et al.  Admissibility of unbounded control operators , 1989 .

[5]  Haitao Gao,et al.  Airship horizontal trajectory tracking control based on Active Disturbance Rejection Control (ADRC) , 2014 .

[6]  Jingqing Han,et al.  From PID to Active Disturbance Rejection Control , 2009, IEEE Trans. Ind. Electron..

[7]  Jie Huang,et al.  Parameter convergence and minimal internal model with an adaptive output regulation problem , 2009, Autom..

[8]  Zhiqiang Gao,et al.  Scaling and bandwidth-parameterization based controller tuning , 2003, Proceedings of the 2003 American Control Conference, 2003..

[9]  Bao-Zhu Guo,et al.  Approximate decoupling and output tracking for MIMO nonlinear systems with mismatched uncertainties via ADRC approach , 2018, J. Frankl. Inst..

[10]  Ibraheem Kasim Ibraheem,et al.  Improved Sliding Mode Nonlinear Extended State Observer based Active Disturbance Rejection Control for Uncertain Systems with Unknown Total Disturbance , 2016 .

[11]  Hassan K. Khalil,et al.  High-gain observers in the presence of measurement noise: A switched-gain approach , 2009, Autom..

[12]  Zhe Gao,et al.  Active disturbance rejection control for nonlinear fractional‐order systems , 2016 .

[13]  Bao-Zhu Guo,et al.  On the convergence of an extended state observer for nonlinear systems with uncertainty , 2011, Syst. Control. Lett..

[14]  Yuanqing Xia,et al.  Compound Control Methodology for Flight Vehicles , 2013 .

[15]  Li Sun,et al.  Direct energy balance based active disturbance rejection control for coal-fired power plant. , 2017, ISA transactions.

[16]  Wenxiang Deng,et al.  Active Disturbance Rejection Adaptive Control of Hydraulic Servo Systems , 2017, IEEE Transactions on Industrial Electronics.

[17]  Xu Yang,et al.  Active disturbance rejection control for high pointing accuracy and rotation speed , 2009, Autom..

[18]  Wei Xue,et al.  Active Disturbance Rejection Control for a Flywheel Energy Storage System , 2015, IEEE Transactions on Industrial Electronics.

[19]  Bao-Zhu Guo,et al.  Sliding Mode and Active Disturbance Rejection Control to Stabilization of One-Dimensional Anti-Stable Wave Equations Subject to Disturbance in Boundary Input , 2012, IEEE Transactions on Automatic Control.

[20]  Bao-Zhu Guo,et al.  A Novel Extended State Observer for Output Tracking of MIMO Systems With Mismatched Uncertainty , 2018, IEEE Transactions on Automatic Control.

[21]  Zhiqiang Gao,et al.  On the centrality of disturbance rejection in automatic control. , 2014, ISA transactions.

[22]  Wang Honglun,et al.  Back-stepping active disturbance rejection control design for integrated missile guidance and control system via reduced-order ESO. , 2015, ISA transactions.

[23]  Zhiqiang Gao,et al.  On stability analysis of active disturbance rejection control for nonlinear time-varying plants with unknown dynamics , 2007, 2007 46th IEEE Conference on Decision and Control.

[24]  José Ángel Acosta,et al.  Stability of active disturbance rejection control for uncertain systems: A Lyapunov perspective , 2017 .

[25]  Mingwei Sun,et al.  Output feedback control for aircraft at high angle of attack based upon fixed-time extended state observer , 2019 .

[26]  Alberto Isidori,et al.  Nonlinear control systems: an introduction (2nd ed.) , 1989 .

[27]  Hua-Cheng Zhou,et al.  Output Feedback Exponential Stabilization for One-Dimensional Unstable Wave Equations with Boundary Control Matched Disturbance , 2018, SIAM J. Control. Optim..

[28]  Dan Wu,et al.  Design and Analysis of Precision Active Disturbance Rejection Control for Noncircular Turning Process , 2009, IEEE Transactions on Industrial Electronics.

[29]  Li Sun,et al.  On Tuning and Practical Implementation of Active Disturbance Rejection Controller: A Case Study from a Regenerative Heater in a 1000 MW Power Plant , 2016 .

[30]  Choon Ki Ahn,et al.  Cooperative disturbance rejection control of vibrating flexible riser systems , 2019 .

[31]  Zhiqiang Gao,et al.  On the conceptualization of total disturbance and its profound implications , 2019, Science China Information Sciences.

[32]  Wen-Hua Chen,et al.  Disturbance observer based control for nonlinear systems , 2004, IEEE/ASME Transactions on Mechatronics.

[33]  Mohammad Haeri,et al.  Linear Active Disturbance Rejection Control From the Practical Aspects , 2018, IEEE/ASME Transactions on Mechatronics.

[34]  Weihai Zhang,et al.  Finite Horizon $H_{2}/H_{\infty}$ Control for Discrete-Time Stochastic Systems With Markovian Jumps and Multiplicative Noise , 2010, IEEE Transactions on Automatic Control.

[35]  Bao-Zhu Guo,et al.  On convergence of active disturbance rejection control for a class of uncertain stochastic nonlinear systems , 2019, Int. J. Control.

[36]  Jun Yang,et al.  Disturbance Observer-Based Control: Methods and Applications , 2014 .

[37]  Lei Guo,et al.  How much uncertainty can be dealt with by feedback? , 2000, IEEE Trans. Autom. Control..

[38]  Bao-Zhu Guo,et al.  Active Disturbance Rejection Control Approach to Output-Feedback Stabilization of a Class of Uncertain Nonlinear Systems Subject to Stochastic Disturbance , 2016, IEEE Transactions on Automatic Control.

[39]  Li Sun,et al.  Combined feedforward and model-assisted active disturbance rejection control for non-minimum phase system. , 2016, ISA transactions.

[40]  Chaoyang Dong,et al.  Backstepping active disturbance rejection control: a delayed activation approach , 2017 .

[41]  Zhiqiang Gao,et al.  Predictive active disturbance rejection control for processes with time delay. , 2014, ISA transactions.

[42]  Zhiqiang Gao,et al.  A DSP-based active disturbance rejection control design for a 1-kW H-bridge DC-DC power converter , 2005, IEEE Trans. Ind. Electron..

[43]  Yangmin Li,et al.  Development and Active Disturbance Rejection Control of a Compliant Micro-/Nanopositioning Piezostage With Dual Mode , 2014, IEEE Transactions on Industrial Electronics.

[44]  Jun-Min Wang,et al.  ADRC Dynamic Stabilization of an Unstable Heat Equation , 2020, IEEE Transactions on Automatic Control.

[45]  Bao-Zhu Guo,et al.  Weak Convergence of Nonlinear High-Gain Tracking Differentiator , 2013, IEEE Transactions on Automatic Control.

[46]  Lei Guo,et al.  Active Disturbance Rejection Control for the Ranger Neutral Buoyancy Vehicle: A Delta Operator Approach , 2017, IEEE Transactions on Industrial Electronics.

[47]  Yuanqing Xia,et al.  Active disturbance rejection and predictive control strategy for a quadrotor helicopter , 2016 .

[48]  Genqi Xu,et al.  Stabilization of an Euler-Bernoulli beam with a tip mass under the unknown boundary external disturbances , 2017, J. Syst. Sci. Complex..

[49]  Nariman Sepehri,et al.  Active disturbance rejection control applied to automated steering for lane keeping in autonomous vehicles , 2018 .

[50]  Li Sun,et al.  Tuning of Active Disturbance Rejection Control with application to power plant furnace regulation , 2019, Control Engineering Practice.

[51]  Bao-Zhu Guo,et al.  Active disturbance rejection control: Old and new results , 2017, Annu. Rev. Control..

[52]  Lei Guo,et al.  Disturbance-Observer-Based Control and Related Methods—An Overview , 2016, IEEE Transactions on Industrial Electronics.

[53]  A. Isidori.  Nonlinear Control Systems: An Introduction , 1986 .

[54]  Hua-Cheng Zhou,et al.  Disturbance estimator based output feedback exponential stabilization for Euler-Bernoulli beam equation with boundary control , 2018, Autom..

[55]  Zhijia Zhao,et al.  Boundary Adaptive Robust Control of a Flexible Riser System With Input Nonlinearities , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[56]  Genqi Xu,et al.  Stabilization of an Euler-Bernoulli beam system with a tip mass subject to non-uniform bounded disturbance , 2017, IMA J. Math. Control. Inf..

[57]  Zhiqiang Gao,et al.  Fractional active disturbance rejection control. , 2016, ISA transactions.

[58]  Bao-Zhu Guo,et al.  Output Feedback Stabilization for One-Dimensional Wave Equation Subject to Boundary Disturbance , 2015, IEEE Transactions on Automatic Control.

[59]  Bao-Zhu Guo,et al.  Active Disturbance Rejection Control for Rejecting Boundary Disturbance from Multidimensional Kirchhoff Plate via Boundary Control , 2014, SIAM J. Control. Optim..

[60]  Yuanqing Xia,et al.  Active Disturbance Rejection Attitude Control for a Dual Closed-Loop Quadrotor Under Gust Wind , 2018, IEEE Transactions on Control Systems Technology.

[61]  Bao-Zhu Guo,et al.  Output tracking for a class of nonlinear systems with mismatched uncertainties by active disturbance rejection control , 2017, Syst. Control. Lett..

[62]  Jie Li,et al.  On the Robust Stability of Active Disturbance Rejection Control for SISO Systems , 2017, Circuits Syst. Signal Process..

[63]  Peter Kuster,et al.  Nonlinear And Adaptive Control Design , 2016 .

[64]  Jianqiang Yi,et al.  A Class of Adaptive Extended State Observers for Nonlinear Disturbed Systems , 2015, IEEE Transactions on Industrial Electronics.

[65]  Huaping Liu,et al.  Nonlinear sampled-data ESO-based active disturbance rejection control for networked control systems with actuator saturation , 2019 .

[66]  Choon Ki Ahn,et al.  Boundary Antidisturbance Control of a Spatially Nonlinear Flexible String System , 2020, IEEE Transactions on Industrial Electronics.

[67]  Bao-Zhu Guo,et al.  Active disturbance rejection control to MIMO nonlinear systems with stochastic uncertainties: approximate decoupling and output-feedback stabilisation , 2020, Int. J. Control.

[68]  David J. N. Limebeer,et al.  Linear Robust Control , 1994 .

[69]  Qing Wang,et al.  Active Disturbance Rejection Control for Uncertain Nonaffine-in-Control Nonlinear Systems , 2017, IEEE Transactions on Automatic Control.

[70]  Yi Huang,et al.  On extended state based Kalman filter design for a class of nonlinear time-varying uncertain systems , 2018, Science China Information Sciences.

[71]  Ning Yang,et al.  A generalized active disturbance rejection control method for nonlinear uncertain systems subject to additive disturbance , 2016 .

[72]  Lincong Chen,et al.  Stationary response of strongly non-linear oscillator with fractional derivative damping under bounded noise excitation , 2012 .

[73]  Bao-Zhu Guo,et al.  Extended state observer for MIMO nonlinear systems with stochastic uncertainties , 2018, Int. J. Control.

[74]  R Sanz,et al.  Enhanced extended state observer-based control for systems with mismatched uncertainties and disturbances. , 2017, ISA transactions.

[75]  YangQuan Chen,et al.  Mittag‐Leffler stabilization for an unstable time‐fractional anomalous diffusion equation with boundary control matched disturbance , 2019, International Journal of Robust and Nonlinear Control.

[76]  Bao-Zhu Guo,et al.  A New Active Disturbance Rejection Control to Output Feedback Stabilization for a One-Dimensional Anti-Stable Wave Equation With Disturbance , 2017, IEEE Transactions on Automatic Control.

[77]  J. Han,et al.  NONLINEAR TRACKING-DIFFERENTIATOR , 1994 .

[78]  A. Schaft.  L/sub 2/-gain analysis of nonlinear systems and nonlinear state-feedback H/sub infinity / control , 1992 .

[79]  Bao-Zhu Guo,et al.  Sliding mode and active disturbance rejection control to stabilization of one-dimensional anti-stable wave equations subject to disturbance in boundary input , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[80]  Yi-Qing Ni,et al.  STOCHASTIC AVERAGING OF STRONGLY NON-LINEAR OSCILLATORS UNDER BOUNDED NOISE EXCITATION , 2002 .

[81]  Isaac Chairez,et al.  Robust Trajectory Tracking of a Delta Robot Through Adaptive Active Disturbance Rejection Control , 2015, IEEE Transactions on Control Systems Technology.

[82]  Wenxiang Deng,et al.  Active disturbance rejection adaptive control of uncertain nonlinear systems: theory and application , 2017 .

[83]  Sen Chen,et al.  On Active Disturbance Rejection Control for a Class of Uncertain Systems With Measurement Uncertainty , 2021, IEEE Transactions on Industrial Electronics.

[84]  Bao-Zhu Guo,et al.  Boundary Feedback Stabilization for an Unstable Time Fractional Reaction Diffusion Equation , 2018, SIAM J. Control. Optim..

[85]  Sen Chen,et al.  Observers and observability for uncertain nonlinear systems: A necessary and sufficient condition , 2019 .

[86]  Jin Tao,et al.  Altitude control for flexible wing unmanned aerial vehicle based on active disturbance rejection control and feedforward compensation , 2019, International Journal of Robust and Nonlinear Control.

[87]  Zhiqiang Gao,et al.  An energy saving, factory-validated disturbance decoupling control design for extrusion processes , 2012, Proceedings of the 10th World Congress on Intelligent Control and Automation.

[88]  B. Pasik-Duncan,et al.  Adaptive Control , 1996, IEEE Control Systems.

[89]  Lihua Xie,et al.  Active disturbance rejection control for uncertain time-delay nonlinear systems , 2020, Autom..

[90]  M. Krstić,et al.  Stochastic nonlinear stabilization—I: a backstepping design , 1997 .

[91]  Mario Ramírez-Neria,et al.  On the Linear Control of Underactuated Nonlinear systems via tangent Flatness and Active Disturbance Rejection Control: The Case of the Ball and Beam System , 2016 .

[92]  Hua-cheng Zhou,et al.  Output‐based disturbance rejection control for 1‐D anti‐stable Schrödinger equation with boundary input matched unknown disturbance , 2017 .

[93]  Doreen Meier,et al.  Introduction To Stochastic Control Theory , 2016 .

[94]  Alain Haraux.  The Wave Equation in a Bounded Domain , 2018 .

[95]  Feiqi Deng,et al.  Mittag-Leffler Stabilization of an Unstable Time Fractional Hyperbolic PDE , 2019, IEEE Access.

[96]  Zhiqiang Gao,et al.  On the conditions of exponential stability in active disturbance rejection control based on singular perturbation analysis , 2017, Int. J. Control.

[97]  Donghai Li,et al.  Active disturbance rejection control for the ALSTOM gasifier benchmark problem , 2013 .

[98]  Bruce A. Francis,et al.  The internal model principle of control theory , 1976, Autom..

[99]  Zhihao Cai,et al.  Quadrotor trajectory tracking and obstacle avoidance by chaotic grey wolf optimization-based active disturbance rejection control , 2019, Mechanical Systems and Signal Processing.

[100]  Bao-Zhu Guo,et al.  Performance output tracking for one-dimensional wave equation subject to unmatched general disturbance and non-collocated control , 2017, Eur. J. Control.

[101]  Weiqiu Zhu,et al.  Stochastic averaging of quasi-integrable Hamiltonian systems under bounded noise excitations , 2004 .

[102]  Bao-Zhu Guo,et al.  On convergence of nonlinear active disturbance rejection control for MIMO systems , 2012, Proceedings of the 31st Chinese Control Conference.

[103]  Zhiqiang Gao,et al.  On active disturbance rejection based control design for superconducting RF cavities , 2011 .

[104]  Jun-Min Wang,et al.  The active disturbance rejection control of the rotating disk–beam system with boundary input disturbances , 2016, Int. J. Control.

[105]  Yi Huang,et al.  On comparison of modified ADRCs for nonlinear uncertain systems with time delay , 2018, Science China Information Sciences.

[106]  Lihua Xie,et al.  On robust control invariance of Boolean control networks , 2016, at - Automatisierungstechnik.

[107]  Lei Guo,et al.  Control of uncertain nonlinear systems based on observers and estimators , 2015, Autom..

[108]  Bao-Zhu Guo,et al.  Active disturbance rejection control: Theoretical perspectives , 2015, Commun. Inf. Syst..

[109]  J. E. Gibson,et al.  ANALYSIS AND DESIGN OF NONLINEAR CONTROL SYSTEMS. , 1965 .

[110]  Bao-Zhu Guo,et al.  The Active Disturbance Rejection Control to Stabilization for Multi-Dimensional Wave Equation With Boundary Control Matched Disturbance , 2015, IEEE Transactions on Automatic Control.

[111]  Jie Li,et al.  On the Necessity, Scheme, and Basis of the Linear–Nonlinear Switching in Active Disturbance Rejection Control , 2017, IEEE Transactions on Industrial Electronics.

[112]  Shengyuan Xu,et al.  Delay-Dependent $H_{\infty }$ Control and Filtering for Uncertain Markovian Jump Systems With Time-Varying Delays , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[113]  Peter S. Maybeck,et al.  Stochastic Models, Estimation And Control , 2012 .

[114]  Zhiqiang Gao,et al.  Modified active disturbance rejection control for time-delay systems. , 2014, ISA transactions.

[115]  Carlos García-Rodriguez,et al.  On the Control of the Permanent Magnet Synchronous Motor: An Active Disturbance Rejection Control Approach , 2014, IEEE Transactions on Control Systems Technology.

[116]  Bao-Zhu Guo,et al.  Stabilization of ODE with hyperbolic equation actuator subject to boundary control matched disturbance , 2019, Int. J. Control.

[117]  Bao-Zhu Guo,et al.  Sliding mode control and active disturbance rejection control to the stabilization of one‐dimensional Schrödinger equation subject to boundary control matched disturbance , 2014 .

[118]  R. Villamizar,et al.  Linear active disturbance rejection control for a raceway photobioreactor , 2019, Control Engineering Practice.

[119]  Feng-Fei Jin,et al.  The active disturbance rejection and sliding mode control approach to the stabilization of the Euler-Bernoulli beam equation with boundary input disturbance , 2013, Autom..

[120]  J. Doyle,et al.  Essentials of Robust Control , 1997 .

[121]  Yi Huang,et al.  The selection criterion of nominal model in active disturbance rejection control for non-affine uncertain systems , 2020, J. Frankl. Inst..

[122]  Guang-Hong Yang,et al.  New Results on Output Feedback $H_{\infty} $ Control for Linear Discrete-Time Systems , 2014, IEEE Transactions on Automatic Control.

[123]  Bao-Zhu Guo,et al.  Active Disturbance Rejection Control for Nonlinear Systems: An Introduction , 2017 .

[124]  Gernot Herbst,et al.  Practical Active Disturbance Rejection Control: Bumpless Transfer, Rate Limitation, and Incremental Algorithm , 2016, IEEE Transactions on Industrial Electronics.

[125]  Bao-Zhu Guo,et al.  Performance Output Tracking for Multidimensional Heat Equation Subject to Unmatched Disturbance and Noncollocated Control , 2020, IEEE Transactions on Automatic Control.

[126]  Jessica Daecher,et al.  Robust Control Of Nonlinear Uncertain Systems , 2016 .

[127]  Zeyu Song,et al.  Study on active disturbance rejection control with actuator saturation to reduce the load of a driving chain in wind turbines , 2019 .

[128]  Wenchao Xue,et al.  On performance analysis of ADRC for a class of MIMO lower-triangular nonlinear uncertain systems. , 2014, ISA transactions.

[129]  Van,et al.  L2-Gain Analysis of Nonlinear Systems and Nonlinear State Feedback H∞ Control , 2004 .

[130]  Caifen Fu,et al.  Linear Active Disturbance-Rejection Control: Analysis and Tuning via IMC , 2016, IEEE Transactions on Industrial Electronics.

[131]  Chaoyang Dong,et al.  Disturbance rejection control of morphing aircraft based on switched nonlinear systems , 2019, Nonlinear Dynamics.

[132]  Yi Huang,et al.  ADRC With Adaptive Extended State Observer and its Application to Air–Fuel Ratio Control in Gasoline Engines , 2015, IEEE Transactions on Industrial Electronics.

[133]  Bao-Zhu Guo,et al.  Distributed disturbance estimator and application to stabilization for multi-dimensional wave equation with corrupted boundary observation , 2016, Autom..

[134]  Qinglin Sun,et al.  Active disturbance rejection control (ADRC)-based autonomous homing control of powered parafoils , 2016 .

[135]  Bao-Zhu Guo,et al.  A nonlinear extended state observer based on fractional power functions , 2017, Autom..

[136]  Wenchao Xue,et al.  Active disturbance rejection control: methodology and theoretical analysis. , 2014, ISA transactions.

[137]  Bao-Zhu Guo,et al.  On convergence of tracking differentiator and application to frequency estimation of sinusoidal signals , 2011, 2011 8th Asian Control Conference (ASCC).

[138]  T. Basar,et al.  Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[139]  Bao-Zhu Guo,et al.  Active disturbance rejection control approach to output‐feedback stabilization of lower triangular nonlinear systems with stochastic uncertainty , 2017 .

[140]  Lei Guo,et al.  Anti-disturbance control theory for systems with multiple disturbances: a survey. , 2014, ISA transactions.

[141]  Bao-Zhu Guo,et al.  Output feedback stabilization for multi-dimensional Kirchhoff plate with general corrupted boundary observation , 2016, Eur. J. Control.