A Discrete-time Linearization Feedback Control for the Van der Pol Oscillator

被引：0

作者：

Oshima, Tatsuya ^{[1
]}

Kawai, Shin ^{[2
]}

Nguyen-Van, Triet ^{[2
]}

机构：

[1] Univ Tsukuba, Sch Sci & Engn, Coll Engn Syst, Ibaraki, Japan

[2] Univ Tsukuba, Grad Sch Sci & Technol, Intelligent & Mech Interact Syst, Ibaraki, Japan

来源：

2022 61ST ANNUAL CONFERENCE OF THE SOCIETY OF INSTRUMENT AND CONTROL ENGINEERS (SICE) | 2022年

关键词：

Van der Pol oscillator; nonlinear; discrete-time; linearization; forward difference; continualized discretization; STABILIZATION; SYSTEMS; MODEL;

D O I：

暂无

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper proposes a discrete-time feedback linearization for the Van der Pol oscillator, a well-known example for nonlinear systems. An approximate discrete-time model of the Van der Pol oscillator is derived by using a method called continualized discretization method. The discrete-time control input is a least-squares solution of an equation, which is derived by equating the discrete-time model of the Van der Pol oscillator and an exact discrete-time model of the desired linear system. The proposed method enables us to stabilize and suppress the self-oscillation of the Van der Pol system by the discrete-time controller. Simulation results show that the proposed controller has better performances than the conventional one derived by the forward-difference method in all the tested cases for system parameters and sampling period.

引用

页码：574 / 579

页数：6

共 11 条

[1]

AUSTIN G, 1962, CONFIN NEUROL, V22, P248

[2] Exact linearisation of the Van der Pol oscillator with fundamental linear differential equations for the tracking error [J].

Broecker, Markus .

IFAC PAPERSONLINE, 2019, 52 (03) :114-119

[3] Frequency demultiplication [J].

Dunsheath, P .

NATURE, 1927, 120 :363-365

[4]

Isidori A., 1985, Nonlinear Control Systems

[5]

James E. M., 1974, Journal of the Institute of Mathematics and Its Applications, V13, P67

[6]

Khalil H.K., 2002, Nonlinear Systems, Vthird

[7] A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models [J].

Nesic, D ;

Teel, AR .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2004, 49 (07) :1103-1122

[8] Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations [J].

Nesic, D ;

Teel, AR ;

Kokotovic, PV .

SYSTEMS & CONTROL LETTERS, 1999, 38 (4-5) :259-270

[9]

Nguyen -Van T., 2016, J COMPUT NONLIN DYN, V11

[10]

Triet NV, 2013, PROC SICE ANN CONF, P2560

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