Adaptive disturbance observer‐based control for stochastic systems with multiple heterogeneous disturbances

Antidisturbance control problem is discussed for stochastic systems with multiple heterogeneous disturbances, which include the white noise and the disturbance with unknown frequencies and amplitudes. An adaptive disturbance observer is designed to estimate the disturbance with unknown frequencies and amplitudes, based on which, an adaptive disturbance observer‐based control scheme is proposed by combining adaptive technique and linear matrix inequality method. It is proved that the closed‐loop system is asymptotically bounded in mean square when multiple heterogeneous disturbances exist simultaneously and that the equilibrium is globally asymptotically stable in probability as additive disturbance disappears. Finally, two simulation examples, including a wind turbine system, are given to show the effectiveness of the proposed scheme.

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

[2]  Cemal Tugrul Yilmaz,et al.  Output feedback control for unknown LTI systems driven by unknown periodic disturbances , 2019, Autom..

[3]  Xiaohua Liu,et al.  Elegant anti-disturbance control for uncertain discrete-time stochastic systems , 2015, The 27th Chinese Control and Decision Conference (2015 CCDC).

[4]  Liang Cai,et al.  Resilient control based on disturbance observer for nonlinear singular stochastic hybrid system with partly unknown Markovian jump parameters , 2018, J. Frankl. Inst..

[5]  Feng Ding,et al.  Identification of non-uniformly sampled-data systems with asynchronous input and output data , 2017, J. Frankl. Inst..

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

[7]  José de Jesús Rubio,et al.  Uniform stable observer for the disturbance estimation in two renewable energy systems. , 2015, ISA transactions.

[8]  S. Shreve,et al.  Stochastic differential equations , 1955, Mathematical Proceedings of the Cambridge Philosophical Society.

[9]  Petros A. Ioannou,et al.  Robustness and Performance of Adaptive Suppression of Unknown Periodic Disturbances , 2015, IEEE Transactions on Automatic Control.

[10]  Yang Wang,et al.  Identification of multi-sinusoidal signals with direct frequency estimation: An adaptive observer approach , 2019, Autom..

[11]  Jun Yang,et al.  Disturbance rejection of ball mill grinding circuits using DOB and MPC , 2010 .

[12]  Lei Guo,et al.  Composite disturbance‐observer‐based control and H∞ control for complex continuous models , 2010 .

[13]  Nathan van de Wouw,et al.  Friction compensation in a controlled one-link robot using a reduced-order observer , 2004, IEEE Transactions on Control Systems Technology.

[14]  Hamid Reza Karimi,et al.  Composite hierarchical antidisturbance control for a class of discrete‐time stochastic systems , 2018 .

[15]  Carl J. Kempf,et al.  Disturbance observer and feedforward design for a high-speed direct-drive positioning table , 1999, IEEE Trans. Control. Syst. Technol..

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

[17]  Hamid Reza Karimi,et al.  Disturbance observer-based disturbance attenuation control for a class of stochastic systems , 2016, Autom..

[18]  Juan Li,et al.  On the rejection of internal and external disturbances in a wind energy conversion system with direct-driven PMSG. , 2016, ISA transactions.

[19]  Lei Guo,et al.  Optimal control for networked control systems with disturbances: a delta operator approach , 2017 .

[20]  B. Øksendal.  Stochastic differential equations : an introduction with applications , 1987 .

[21]  Christopher I. Byrnes,et al.  Output regulation for nonlinear systems: an overview , 2000 .

[22]  Zhengtao Ding,et al.  Output-based disturbance rejection control for non-linear uncertain systems with unknown frequency disturbances using an observer backstepping approach , 2016 .

[23]  Jian Han,et al.  Disturbance observer-based elegant anti-disturbance saturation control for a class of stochastic systems , 2020, Int. J. Control.

[24]  V. O. Nikiforov,et al.  Nonlinear servocompensation of unknown external disturbances , 2001, Autom..

[25]  Shuzhi Sam Ge,et al.  Vibration Control of a Nonuniform Wind Turbine Tower via Disturbance Observer , 2015, IEEE/ASME Transactions on Mechatronics.

[26]  Shihua Li,et al.  Attitude synchronization control for a group of flexible spacecraft , 2014, Autom..

[27]  Peng Shi,et al.  Robust Constrained Control for MIMO Nonlinear Systems Based on Disturbance Observer , 2015, IEEE Transactions on Automatic Control.

[28]  Gun-Woo Moon,et al.  A current control for a permanent magnet synchronous motor with a simple disturbance estimation scheme , 1999, IEEE Trans. Control. Syst. Technol..

[29]  Miroslav Krstic,et al.  Stabilization of stochastic nonlinear systems driven by noise of unknown covariance , 2001, IEEE Trans. Autom. Control..

[30]  Arkadi Nemirovski,et al.  Lmi Control Toolbox For Use With Matlab , 2014 .

[31]  Linlin Hou,et al.  Disturbance attenuation and rejection for stochastic Markovian jump system with partially known transition probabilities , 2018, Autom..

[32]  Shankar P. Bhattacharyya,et al.  Controllability, observability and the solution of AX - XB = C , 1981 .

[33]  Haiying Dong,et al.  Voltage and Reactive Power Control of Front-end Speed Controlled Wind Turbine via H∞ Strategy , 2013 .

[34]  Huibert Kwakernaak,et al.  Linear Optimal Control Systems , 1972 .

[35]  Nan Chen,et al.  Composite hierarchical anti‐disturbance control for nonlinear systems with DOBC and fuzzy control , 2014 .

[36]  Gang Feng,et al.  Robust adaptive output feedback control to a class of non-triangular stochastic nonlinear systems , 2018, Autom..

[37]  Xinjiang Wei,et al.  Elegant anti-disturbance control for discrete-time stochastic systems with nonlinearity and multiple disturbances , 2018, Int. J. Control.

[38]  Xuerong Mao,et al.  Stochastic Differential Equations With Markovian Switching , 2006 .

[39]  Songyin Cao,et al.  Anti-Disturbance Control for Systems with Multiple Disturbances , 2013 .

[40]  Zhengtao Ding,et al.  Adaptive consensus output regulation of a class of nonlinear systems with unknown high-frequency gain , 2015, Autom..

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

[42]  Jian Han,et al.  Robust adaptive tracking control for a class of mechanical systems with unknown disturbances under actuator saturation , 2019, International Journal of Robust and Nonlinear Control.