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Research Papers

Zhang-Gradient Controllers for Tracking Control of Multiple-Integrator Systems

[+] Author and Article Information
Yunong Zhang

School of Information Science and Technology,
Sun Yat-sen University,
Guangzhou 510006, China;
SYSU-CMU Shunde International
Joint Research Institute,
Shunde 528300, China;
Key Laboratory of Autonomous Systems and
Networked Control,
Ministry of Education,
Guangzhou 510640, China
e-mail: zhynong@mail.sysu.edu.cn

Sitong Ding, Dechao Chen, Mingzhi Mao, Keke Zhai

School of Information Science and Technology,
Sun Yat-sen University,
Guangzhou 510006, China;
SYSU-CMU Shunde International
Joint Research Institute,
Shunde 528300, China;
Key Laboratory of Autonomous Systems and
Networked Control,
Ministry of Education,
Guangzhou 510640, China

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 5, 2015; final manuscript received July 21, 2015; published online September 2, 2015. Assoc. Editor: Ming Xin.

J. Dyn. Sys., Meas., Control 137(11), 111013 (Sep 02, 2015) (11 pages) Paper No: DS-15-1005; doi: 10.1115/1.4031148 History: Received January 05, 2015; Revised July 21, 2015

In this paper, the tracking-control problem of multiple-integrator (MI) systems is considered and investigated by combining Zhang dynamics (ZD) and gradient dynamics (GD). Several novel types of Zhang-gradient (ZG) controllers are proposed for the tracking control of MI systems (e.g., triple-integrator (TI) systems). As an example, the design processes of ZG controllers for TI systems with a linear output function (LOF) and/or a nonlinear output function (NOF) are presented. Besides, the corresponding theoretical analyses are elaborately given to guarantee the convergence performance of both z3g0 controllers (ZG controllers obtained by utilizing the ZD method thrice) and z3g1 controllers (ZG controllers obtained by utilizing the ZD method thrice and the GD method once) for TI systems. Numerical simulations concerning the tracking control of MI systems with different types of output functions are further performed to substantiate the feasibility and effectiveness of ZG controllers for tracking-control problems solving. Besides, comparative simulation results of the tracking control for MI systems with NOFs (e.g., y=cos(x1),y=x12+x22) substantiate that controllers of zmg1 type can resolve the singularity problem effectively with m being the times of using the ZD method.

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Figures

Grahic Jump Location
Fig. 1

Output trajectories and control inputs for system (2) synthesized by z3g0 controller (3) and z3g1 controller (4), respectively, with yd(t)=sin(2t)cos(2t)

Grahic Jump Location
Fig. 5

|e| of the quadruple-integrator system synthesized by z4g0 controller and z4g1 controller, respectively, with yd(t)=sin(t)

Grahic Jump Location
Fig. 6

Performance of the quintuple-integrator system synthesized by z4g0 controller (27) and z4g1 controller (28), respectively, with yd(t)=cos(t)+2

Grahic Jump Location
Fig. 2

Tracking errors for system (2) synthesized by z3g0 controller (3) and z3g1 controller (4), respectively, with yd(t)=sin(2t)cos(2t)

Grahic Jump Location
Fig. 3

Tracking performances of system (2) synthesized by z3g0 controller (6) and z3g1 controller (7), respectively, with yd(t)=sin(t)

Grahic Jump Location
Fig. 4

Tracking performance of system (2) synthesized by z2g1 controller (25) with y=x12+x22 and z1g1 controller (26) with y=x1x2x3, respectively, for tracking path yd(t)=sin(t)exp(−0.1t)+2

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