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Barrier Function-Based Integral Sliding Mode Controller Design for a Single-Link Rotary Flexible Joint Robot Cover

Barrier Function-Based Integral Sliding Mode Controller Design for a Single-Link Rotary Flexible Joint Robot

Open Access
|May 2024

Figures & Tables

Figure 1:

Rotary flexible joint platform.
Rotary flexible joint platform.

Figure 2:

Schematic diagram of the FJR system.
Schematic diagram of the FJR system.

Figure 3:

Overall block diagram of the proposed control system.
Overall block diagram of the proposed control system.

Figure 3:

The sliding variable of unactuated controller vs. time.
The sliding variable of unactuated controller vs. time.

Figure 4:

The sliding variable of actuated controller vs. time.
The sliding variable of actuated controller vs. time.

Figure 5:

Tracking response (x1) of the FJR and vibration angle (α) vs. time. FJR, flexible joint robot.
Tracking response (x1) of the FJR and vibration angle (α) vs. time. FJR, flexible joint robot.

Figure 6:

Vibration angle of the FJR vs. time. FJR, flexible joint robot.
Vibration angle of the FJR vs. time. FJR, flexible joint robot.

Figure 7:

Position tracking error e1 vs. time.
Position tracking error e1 vs. time.

Figure 8:

Controlled voltage (Vm) vs. time.
Controlled voltage (Vm) vs. time.

Figure 9:

Tracking response (x1) of the FJR and vibration angle (α) vs. time. FJR, flexible joint robot.
Tracking response (x1) of the FJR and vibration angle (α) vs. time. FJR, flexible joint robot.

Figure 10:

Vibration angle of the FJR vs. time. FJR, flexible joint robot.
Vibration angle of the FJR vs. time. FJR, flexible joint robot.

Nominal parameters of the FJR manipulator

SymbolDescriptionValue
JeqEquivalent moment of inertia of servo motor (kg ∙ m2)0.0018
JarmMoment of inertia of the link (kg ∙ m2)0.0033
BeqThe viscous friction coefficient of the manipulator (Nms /rad)0.015
KsJoint stiffness (N/m)1.3
KmMotor back-EMF constant N/(rad/s)0.0077
KgHigh gear ratio70
KtMotor torque constant (NM/A)0.00767
RmMotor torque constant (Ω)2.6
ηmMotor efficiency0.69
ηgGearbox efficiency0.90

Controllers and observer parameters

ControllersDesign parameters
Unactuated controller (virtual controller)ε1 = 0.01, λ1 = 1, c1 = 16, c2 = 8
Actuated controllerε2 = 0.01, λ2 = 0.01, c3 = 12, c4 = 7
ObserverKo = 1000, γo = 100, τo = 0.0001
Language: English
Submitted on: Sep 13, 2023
Published on: May 4, 2024
Published by: Professor Subhas Chandra Mukhopadhyay
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2024 Ahmed Mohsen Mohammad, Shibly Ahmed AL-Samarraie, Alaa Abdulhady Jaber, published by Professor Subhas Chandra Mukhopadhyay
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.