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Robust Backstepping Control for a Four-Bar Linkage Mechanism Driven by a DC Motor

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Abstract

Four-bar linkage mechanisms have dragged the attention of many specialists due to its importance in the academic and industrial sectors. Hence, a lot of research work has been conducted to understand their complex behavior and explore various control techniques. In fact, such mechanisms possess highly nonlinear dynamics that require advanced nonlinear control methods. In addition, the four-bar linkage mechanism is exposed to significant dynamic fluctuations at high speeds due to the system inertias. In this paper, a backstepping control algorithm with a robust scheme is designed and applied on the four-bar linkage mechanism to investigate and explore its dynamical performance under various operating conditions and without a priori knowledge of the model parameters. Five operating conditions are introduced and tested in numerical simulations to show that the proposed nonlinear controller successfully regulates and tracks the speed of the driving link of the mechanism and shows a satisfactory performance.

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Abbreviations

B :

vicious damping at motor bearing

C :

torsional damping coefficient

c m i :

center of mass of the ith link

i a :

motor armature current

J :

moment of inertia of the motor rotor and gear

J i :

moment of inertia of the ith link

K :

torsional spring constant

k b :

motor electromotive force voltage constant

k e :

positive control gain

k m :

motor torque constant

k o :

positive control gain

k η :

positive control gain

L a :

motor armature inductance

L i :

length of inertia of the ith link

m i :

mass of inertia of the ith link

n :

gear ratio

R a :

motor rotor armature resistor

r i :

location of the center of mass of the ith link

T :

total applied torque on the leading link (i.e., link 2)

T L :

mechanical load torque

T m :

motor output torque

V a :

applied armature voltage

ε 1 :

arbitrary small positive constant

ε 2 :

arbitrary small positive constant

ε i :

arbitrary small positive constant

ε x :

arbitrary small positive constant

λ 1 :

positive constant

λ 2 :

positive constant

λ 3 :

positive constant

σ :

small positive constant

\(\ddot {{\phi }}_{i}\) :

angular acceleration of the ith link

\(\dot {{\phi }}_{i}\) :

angular velocity of the ith link

ϕ i :

angular displacement of the ith link

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Acknowledgments

Work of E. Tatlicioglu is partially supported by The Scientific and Technological Research Council of Turkey via grant number 116M272.

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Authors and Affiliations

  1. Mechatronics Engineering Department, The Hashemite University, Zarqa, 13115, Jordan

    Mohammad Salah, Ahmad Al-Jarrah & Suleiman Banihani

  2. Electrical and Electronics Engineering Department, Izmir Institute of Technology, Izmir, 35430, Turkey

    Enver Tatlicioglu

Authors
  1. Mohammad Salah
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  2. Ahmad Al-Jarrah
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  3. Enver Tatlicioglu
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  4. Suleiman Banihani
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Correspondence to Mohammad Salah.

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Salah, M., Al-Jarrah, A., Tatlicioglu, E. et al. Robust Backstepping Control for a Four-Bar Linkage Mechanism Driven by a DC Motor. J Intell Robot Syst 94, 327–338 (2019). https://doi.org/10.1007/s10846-018-0811-y

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