Research Papers

Adaptive Boundary Control for a Flexible Manipulator With State Constraints Using a Barrier Lyapunov Function

[+] Author and Article Information
Tingting Jiang

Jiangsu Automation Research Institute of CSIC,
Lianyungang 222061, China;
School of Automation Science and
Electrical Engineering,
Beihang University (Beijing University of
Aeronautics and Astronautics),
Beijing 100191, China

Jinkun Liu

School of Automation Science
and Electrical Engineering,
Beihang University (Beijing University of
Aeronautics and Astronautics),
Beijing 100191, China
e-mail: ljk@buaa.edu.cn

Wei He

Key Laboratory of Knowledge Automation
for Industrial Processes,
Ministry of Education,
School of Automation and
Electrical Engineering,
University of Science and Technology Beijing,
Beijing 100083, China

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received March 15, 2017; final manuscript received November 16, 2017; published online March 30, 2018. Assoc. Editor: Davide Spinello.

J. Dyn. Sys., Meas., Control 140(8), 081018 (Mar 30, 2018) (7 pages) Paper No: DS-17-1152; doi: 10.1115/1.4039364 History: Received March 15, 2017; Revised November 16, 2017

In this paper, the problem of state constraints control is investigated for a class of output constrained flexible manipulator system with varying payload. The dynamic behavior of the flexible manipulator is represented by partial differential equations. To prevent states of the flexible manipulator system from violating the constraints, a barrier Lyapunov function which grows to infinity whenever its arguments approach to some limits is employed. Then, based on the barrier Lyapunov function, boundary control laws are given. To solve the problem of varying payload, an adaptive boundary controller is developed. Furthermore, based on the theory of barrier Lyapunov function and the adaptive algorithm, state constraints and output control under vibration condition can be achieved. The stability of the closed-loop system is carried out by the Lyapunov stability theory. Numerical simulations are given to illustrate the performance of the closed-loop system.

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Fig. 1

Configuration of the flexible manipulator

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Fig. 2

Schematic illustration of a symmetrical barrier Lyapunov function

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Fig. 8

Boundary deflection speed regulation (y˙(L,t)=0)

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Fig. 9

Elastic deflection of the flexible manipulator

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Fig. 10

Control inputs: (a) control input τ(t) and (b) control input F(t)

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Fig. 3

Angle and its speed constraints: (a) angle constraint and (b) angle speed constraint

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Fig. 4

Boundary deflection and its speed constraints: (a) boundary deflection constraint and (b) boundary deflection speed constraint

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Fig. 5

Angle regulation (θ(t))

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Fig. 6

Angle speed regulation (θ˙(t))

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Fig. 7

Boundary deflection regulation (y(L,t)=0)

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Fig. 11

α and α̂ under different conditions



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