Journal of Robotics and Control (JRC) Volume 6.
Issue 4, 2025 ISSN: 2715-5072.
DOI: 10.
18196/jrc.
Advanced Sliding Mode Control with Disturbance Rejection Techniques for Multi-DOF Robotic Systems Mohamed Abdelhakim Basal 1* Faculty of Engineering.
Menoufia University.
Egypt Email: 1 mohamedabdelhikeem@yahoo.
*Corresponding Author AbstractAiFor the control of complex and non-linear systems such as robotic arms, especially in sensitive systems such as medical applications and chemical industries, it becomes necessary to improve the performance considering the balance between fast response and smooth, vibration-free, in addition to overcoming disturbances and model uncertainty.
These and other reasons may be the reason for the failure of some linear and classical control systems.
This research presents a hybrid control system that combines sliding mode control (SMC) with an active disturbance rejection controller (ADRC) for a threedegree-of-freedom .
-DOF) robotic arm.
The research contributes to developing a robust control system that reduces the vibrations caused by the classical SMC and utilizes its advantages to achieve smooth, fast, high dynamic response.
The proposed method combines the benefits of SMC stiffness for regulating the angular velocities and ADRC in disturbance compensation to regulate the angular positions, ensuring smooth and accurate control despite its relative complexity.
The simulation results show that the classical SMC methodology provides superior performance compared to the traditional PIDC in terms of low settling time, but suffers from higher overshoot and large vibrations that sometimes cause a large value of tracking error.
In contrast, the proposed control methodology contributes to the improvement of the robotic arm performance, achieving higher tracking accuracy, tracking error minimization, very low settling time, and clear vibration cancellation in both the output signals and the applied control The proposed system has clear advantages, so it can provide a promising solution for robotic arms, particularly in industries demanding high performance, fast tracking and minimal vibrations.
KeywordsAi3-DOF Robotic Manipulator.
Sliding Mode Control.
Disturbance Observer Design.
Tracking Error Minimization.
MATLAB/Simulink.
INTRODUCTION
Manipulative robotic arms are gaining increasing popularity due to their excellent performance and ability to perform tasks accurately and quickly in various applications.
In addition, robotic arms contribute to reducing errors and improving the quality of industrial processes.
These applications include multiple tasks such as picking and placing materials in specific locations, welding processes, automated painting, and automatic assembly of electronic and mechanical components.
Automotive, aerospace, medical, and even research and home applications.
This diversity of uses reflects the flexibility of these systems and their ability to meet the requirements of precise and complex tasks .
Achieving efficiency in these processes requires advanced control strategies that ensure precise coordination between different degrees of freedom, with the ability to handle different loads and adapt to changing conditions .
Robotic arm control engineering focuses on designing controllers that perform at the highest quality, with high dynamics and stability, and achieve the lowest tracking error.
To improve stability and performance, advanced controllers and various modern technologies are used, such as enhanced proportional-integral-differential (PID) controllers or PID controllers integrated with intelligent control technologies .
This is because classical control systems only cover linear systems.
in addition to that, they suffer from some drawbacks, such as low dynamics and may not be effective for multiple-input, multiple-output (MIMO) The state feedback methods like linear quadratic regulator (LQR) are an effective solution for controlling MIMO systems, improving the system performance and stability, it has been used in a number of published literature for robotic and manipulator systems such as in .
Modern control systems for robotic and manipulator systems have proven their effectiveness in providing high stability and reliable dynamic performance even in the presence of various disturbances or uncertainties and changes in system parameters.
These systems include different techniques such as nonlinear control systems such as sliding mode control (SMC) .
and back step control (BSC) .
, artificial intelligence techniques (AIT) such as fuzzy logic and neural network .
and other approaches such as active disturbance rejection controller (ADRC) .
or fractional proportional-integraldifferential (FOPID) control systems .
, .
The hybridization of control systems is very effective in obtaining high stability and dynamic performance while maintaining a static error at a minimum value without the presence of various defects such as vibration or being affected by various disturbances, despite the control system design being based on a questionable model or the presence of various other challenges.
Therefore, much research has been done in this regard, such as .
which proposed an adaptive fuzzy control system for a three-degree-of-freedom hydraulic arm position, designed to handle large load Journal Web site: http://journal.
id/index.
php/jrc Journal Email: jrc@umy.
Journal of Robotics and Control (JRC) ISSN: 2715-5072 The system combined backscatter-based slip control, a fuzzy logic system, and a nonlinear disturbance The slip control adjusts the dynamics of the arm and actuators, while the fuzzy logic is used to adjust the control gain based on the output of the disturbance controller, allowing for effective compensation of load variations.
two-link arm control methodology is proposed in .
that includes the design of a nonlinear disturbance controller supported by a neural network, using an integrated sliding manifold and backtracking techniques to ensure the system's efficiency and stability.
In .
the dynamics model is precisely compensated in the SMC by proposing a parallel artificial intelligence network.
In .
, a control algorithm based on fuzzy logic and SMC was presented to address the control errors and input jitter problem encountered by conventional control methods for controlling underwater One common type of robotic controller is the three-degree-of-freedom (DoF) articulated controller.
typically has three rotary joints, allowing for threedimensional movement.
Tasks requiring simple spatial positioning, such as pick-and-place actions, simple assembly tasks, vehicle assemblies, or educational purposes, frequently require this type of controller.
Based on the structure of this arm, it is characterized by the following .
Articulated structure: A large range of motion is provided by the arrangement of the joints in a chain.
Three degrees of freedom: Three levels of motion can be performed using the three rotary joints, which typically correspond to:
Base rotation.
Shoulder movement.
Elbow movement.
Workspace: The end controller can reach positions within a certain range and direction thanks to the spherical workspace of the design.
By reviewing some of the published literature on controlling this type of arm-robot, it was found that during the two researches .
, .
, an LQR methodology was used to regulate the angular positions of the three joints, while in the research .
, the performance of LQR was improved by using adaptive control techniques.
In .
, .
, a state feedback control system and PID regulators were used to track the path in three-dimensional space.
In line with this goal, the authors in .
designed controllers using neural networks to improve the positioning and orientations of the end effector and simplify the forward and Inverse Kinematics In .
, a robust Hinf controller was designed based on a simplified model of the arm-robot and the results were compared with PID controllers, with only the logarithmic features of the results being presented.
In .
, the sliding mode technique is used to improve the tracking of the angular positions of the three joints, relying on the optimization algorithm to adjust the parameters of the control Some of the drawbacks of different control techniques used in previous literature can be summarized as follows:
PID-based control systems may fail to control some complex multi-degree-of-freedom robot systems when the performance criteria are stringent and strong, especially when the number of inputs does not match the number of outputs or when strong coupling effects exist between different variables.
LQR-based control systems performance may not be adequate as it has a linear control law like PID controller.
Using control systems based on a specific technology may cause the control system to lose some of the positive advantages offered by another technology.
It is known that the sliding mode control system is characterized by strength and robustness, but it suffers from the phenomenon of chatter.
In contrast, the backstepping control system may not provide the same robustness as the sliding mode, but it is characterized by the absence of Also, some control systems, such as FOPID.
AIT, and Hinf controllers suffer from a high degree of computational complexity, difficulty in practical implementation, and the need for extensive calibration and adjustment to obtain strong and effective Considering the above-mentioned drawbacks and the importance and effectiveness of hybrid control systems for robotic arms mentioned in .
, this research aims to design a hybrid control system based on SMC and ADRC controllers that has a lower degree of complexity compared to other hybrid systems and achieves efficient performance and high dynamics to overcome various disturbances and achieve efficient and continuous tracking of reference values.
Contributions that the Research Seeks to Achieve In systems with sensitive missions such as medical applications, chemical industries, and aviation systems.
Tracking speed and accuracy are of utmost importance, but a balance must be struck between fast response and vibrational In addition to improving overall performance in terms of reducing tracking error and overcoming various disturbances that may result from model non-linearity or The research contribution focuses on developing a robust control system that combines SMC and ADRC, and is characterized by the following:
Efficient performance: enhancing the system's time response characteristics .
educing both settling time, overshoot and steady-state erro.
High dynamics: ensuring that the control system responds quickly and smoothly to time-varying reference signals .
racking a circular path for exampl.
Disturbance rejection and uncertainty overcoming:
dealing effectively with various disturbances, and ensuring robust operation despite the inaccuracy of the mathematical model adopted during the design of the control system.
Reference tracking: maintaining accurate and effective tracking of the required reference values, even in difficult Mohamed Abdelhakim Basal.
Advanced Sliding Mode Control with Disturbance Rejection Techniques for Multi-DOF Robotic Systems Journal of Robotics and Control (JRC) ISSN: 2715-5072 Structure of the Paper The rest of this paper is organized as follows.
Section 2 describes the dynamic model of the robotic arm, and also presents the linear model of it, which is essential for the design of the proposed controllers.
Section 3 discusses the strategies of the control systems.
Section 4 presents the simulation results comparing the performance of different control strategies.
Finally.
Section 5 concludes the paper by summarizing the results and suggesting future research II.
ycA11 ycA=[ 0 TABLE I.
THE ARM PARAMETER VALUES
Length of the first link Length of the second link Length of the third link Mass of the first link Mass of the second link Mass of the third link The Euler-Lagrange Formulation is the standard and basic method for obtaining the second-order dynamic equations of the studied robotic arm, where the Lagrange equation is expressed as the difference between the total kinetic energy .
and the total potential energy .
cEyc.
of each joint of the This approach enables an accurate and systematic representation of the robot's dynamic behaviour, accounting for the interplay of inertia, gravity, and joint interactions.
The equation of the Lagrange function is given as follows:
After obtaining Lagrange's equation, the equations of the moments acting on the rotary joints can be obtained as ya = Oc yaycn Oe Oc ycEycn yuaycn = .
ycA23 ] ycA33 ycA22 = 1/3 yca22 yco2 yca22 yco3 1/3yca32 yco3 yca2 yca3 yco3 ycaycuyc yuE3 ycA23 = ycA32 = 1/3 yca32 yco3 yca22 yco3 1/3yca2 yca3 yco3 ycaycuyc yuE3 ycA33 = 1/3 yca32 yco3 uE, yuEN) = .
cO2 ] ycO3 ycO1 = [Oe 4AE3 yco2 yca22 ycycnycu 2yuE2 Oe 1AE3 yco3 yca32 ycycnycu 2.
uE2 yuE3 ) Oe yco3 yca2 yca3 ycycnycu.
yuE2 yuE3 )]yuE1N yuE2N [Oe 1AE3 yco3 yca32 ycycnycu 2.
uE2 yuE3 ) Oe yco3 yca2 yca3 ycaycuyc yuE2 ycycnycu.
uE2 yuE3 )]yuE1N yuE3N ycO2 = [Oeyco3 yca2 yca3 ycycnycu yuE3 ]yuE2N yuE3N [Oe0.
5yca2 yca3 ycycnycu yuE3 ]yuE3N [ yco2 yca22 ycycnycu 2yuE2 yco3 yca32 ycycnycu 2.
uE2 yuE3 ) 0.
5yco3 yca22 ycycnycu 2yuE2 0.
5yco3 yca2 yca3 ycycnycu.
yuE2 yuE3 )] yuE1N ycO3 = .
5yco3 yca2 yca3 ycycnycu yuE3 ]yuE22N .
AE6 yco3 yca32 ycycnycu 2.
uE2 yuE3 ) 0.
5yco3 yca2 yca3 ycaycuyc yuE2 ycycnycu.
yuE2 yuE3 )]yuE1N .
uE) = .
5yco3yciyca3 ycaycuyc.
uE2 yuE.
5yco2 yciyca2 ycaycuyc yuE2 yco3yciyca2 ycaycuyc yuE.
5yco3 yciyca3 ycaycuyc.
uE2 yuE3 ) ycc yuiya , ycn = 1,2,3 yccyc yuiyuEycn yuiyuEycn yuAycn is the torque acting on joint ycn, yuEycn is the angle of joint ycn, yuEycnN is the angular velocity of joint ycn.
The general dynamic equation for robotic arms with nDOF rotary joints is given as:
yua = ycA.
uE)yuEO ycO.
uE, yuEN) ya.
uE) .
In the above equation, ycA represents the inertia matrix, while the matrix ycO includes both the carioles and centrifugal forces and finally, the matrix ya represents the Earth's gravity.
For the considered robotic arm with three rotary joints, the matrices ycA, ycO, and ya are given as .
ycA11 = 0.
5yco1 yca12 0.
5yco1 yca22 ca22 ycaycuycyuE22 1/3yca32 ycaycuyc.
uE2 yuE3 )2 yca2 yca3 ycaycuyc.
uE2 yuE3 ) ycaycuyc yuE2 ) 1/3yco2 yca22 ycaycuycyuE22 SYSTEM DESCRIPTION AND DYNAMIC MODEL .
Robotic arms have become a cornerstone of modern automation and industrial applications.
The depicted robotic arm consists of multiple articulated joints as shown in Fig.
each allowing rotational motion around specific axes.
This design enables the arm to perform precise and complex movements within three-dimensional space, making it ideal for tasks that require dexterity and accuracy.
The values of the arm parameters are shown in Table I.
ycA22 ycA32 Fig.
The 3dof robotic arm .
, .
Mohamed Abdelhakim Basal.
Advanced Sliding Mode Control with Disturbance Rejection Techniques for Multi-DOF Robotic Systems .
Journal of Robotics and Control (JRC) ISSN: 2715-5072 The System's Linear Model To obtain the linear model of the robotic arm, some approximations such as .
will be made.
= 1, ycycnycu.
= 0
By substituting .
in the equations .
and substituting them in the equation .
, the following is yua1 ua2 ] yua3 yuEO1 yco22 yco23 ] .
uEO2 ] =[ 0 yco32 yco33 yuEO .
5yco3 yciyca3 0.
5yco2 yciyca2 yco3 yciyca2 ] 5yco3 yciyca3 Where:
m11 = 0.
5m1 a21 0.
5m1 a22 m3 .
22 1/3a23 a 2 a 3 ) 1/3m2 a22 m22 = 1/3 a22 m2 a22 m3 1/3a23 m3 a 2 a3 m3 m23 = M32 = 1/3 a23 m3 a22 m3 1/3a 2 a 3m3 m33 = 1/3 a23 m3 After substituting the parameters listed in Table I, the linear model containing three input signals .
he three torques transmitted to the joint.
and six state variables .
he three joint angles and the angular velocitie.
can be rewritten in the state space formally as follows after negotiating the G:
yuE1N yuE2N yuE3N = 0 yc1N yc2N .
c3N ] i.
0 yuE1 0 yuE2 1 yuE3 0 yc1 0 yc2 .
[ yc3 ] yua1 .
ua2 ] yua3 Oe0.
[ 0
94 Oe1.
MIMO SYSTEM CONTROL OF THE ARM ROBOT
It is noted in relation .
that the matrix B of the system includes a link between the input signals, to build a controller system capable of dealing with SISO systems, so a transformation matrix must be added so that the input of this matrix is the output signals of the three SISO controllers that will be placed to regulate the three positions of the joints while the output of this matrix is the three torque signals affecting the joints.
This matrix is calculated as follows:
If it is assumed that we have three control signals .
a, ub, u.
representing the output of the three controllers and that the system has become of the SISO type, then relation .
can be fixed so that it is written as .
yuE1N yuE2N yuE3N = 0 yc1N yc2N .
c3N ] .
0 yuE1 0 yuE2 1 yuE3 0 yc1 0 yc2 .
[ yc3 ] .
0 yc yca 0 yc [ yc.
0 yc yca By matching relations .
, we find:
yua1 ycyca yc yua [ yc.
= [ 0 Oe0.
94 ] [ 2 ]
ycyca 94 Oe1.
96 yua3 Thus, the transformation matrix required to calculate the required torques of the actuators can now be easily obtained from the control signals generated by the SISO controllers as yua1 = 0.
yua2 = 0.
yua3 = 0.
PIDC of the Arm Robot Considering the relationships .
- .
It is noted that the torque of the second and third motors is impacted by the control signal that governs the movement of the second joint, and the torque of the second and third motors is impacted by the control signal that governs the movement of the third Thus, it is possible to say that the control system has evolved into a SISO-based MIMO system.
Fig.
2 shows the block diagram of the MIMO control system based on PIDC.
Fig.
Block diagram of the MIMO control system of the arm robot based on PIDC SMC of the Arm robot SMC is a robust control method that works well in dynamic or unpredictable contexts because it can tolerate system uncertainties, parameter fluctuations, and external Using a sliding surface that is specifically made to depict the intended system behaviour is the fundamental concept of SMC.
Consistent and dependable performance results from the controller making sure that the system states converge to and stay on this surface.
The system maintains stability and meets the intended control goals after it reaches the sliding surface, when it becomes essentially insensitive to uncertainties and disturbances .
For the state space described by the relation .
, the following relation can be written expressing the relationship between the state variable and the control signal:
ycuN = yc To make the state variable ycu track the reference value, the sliding surface function can be written as .
Mohamed Abdelhakim Basal.
Advanced Sliding Mode Control with Disturbance Rejection Techniques for Multi-DOF Robotic Systems Journal of Robotics and Control (JRC) ISSN: 2715-5072 ycI = ycuycyceyce Oe ycu By deriving the equation .
, we get ycIN = ycuycyceyce N Oeyc To attract the state variable ycu to the sliding surface, the switching law can be written as:
ycIN = OeycoycIyciycu.
cI) Oe ycycI The constants yco presents the switching gain, and yc presents the proportional term.
By substituting relation .
into relation .
, the control law for the regulation ycu can be obtained as:
yc = ycuycyceyce N ycoycIyciycu.
cI) ycycI For a Lyapunov function according to the relation:
ycO = 0.
5ycI 2 For the system to be stable, it must be achieved:
ycON = ycINycI < 0 By substitution the switching law from .
, we find:
ycON = OeycoycIyciycu.
cI)ycI Oe ycycI 2 This confirms the necessity for the constants yco and yc to be positive values.
A higher value of them speeds up the convergence but may cause vibrations.
The constants .
ca2 , yca4 , yca6 , yca8 , yca10 , yca12 ) correspond to the constant yc in .
A higher value enhances stability but may cause saturation of the transient control signal and drift away from the slip surface.
Experimental analysis or simulation should be performed to choose the best .
caCA, yca3 , yca5 , yca7 , yca9 , yca11 ) .
ca2 , yca4 , yca6 , yca8 , yca10 , yca12 ) to achieve a fast response without excessive vibrations.
Fig.
3 shows the block diagram of robot control using the sliding mode methodology.
ADRC of the Arm Robot To estimate and correct for disturbances and uncertainties in the models, a contemporary control technique called Active Disturbance Rejection Control (ADRC) has been The Extended State Observer (ESO), which forms the basis of ADRC, continuously monitors the system to estimate its states and the total disturbances affecting it.
The control law created using these estimates dynamically adjusts the systemAos behaviour to compensate for the uncertainty and Among the improvements that this controller brings are the elimination of vibrations resulting from the use of the sliding pattern methodology and the smoothing of the transient and steady state of the system, which contributes to improving the stability and performance of the robotAos threelink control system .
SMC Laws of Arm Robot By applying the methodology in section 3-2, the control laws for regulating the angular positions of the robot are obtained as in .
and the control laws for regulating the angular velocities as in .
after taking the relations .
into account.
N yca1 ycIyciycu.
uE1ycyceyce Oe yuE1 ) yc1ycyceyce = .
uE1 ycyceyce yca2 .
uE1ycyceyce Oe yuE1 ) N yca3 ycIyciycu.
uE2ycyceyce Oe yuE2 ) yc2ycyceyce = .
uE2 ycyceyce yca4 .
uE2ycyceyce Oe yuE2 ) N yca5 ycIyciycu.
uE3ycyceyce Oe yuE3 ) yc3ycyceyce = .
uE3 ycyceyce yca6 .
uE3ycyceyce Oe yuE3 ) yua1 = 0.
c1ycyceyce N yca7 ycIyciycu.
c1ycyceyce Oe yc1 ) yca8 .
c1ycyceyce Oe yc1 )) .
yua2 = 0.
c2ycyceyce N yca9 ycIyciycu.
c2ycyceyce Oe yc2 ) yca10 .
c2ycyceyce Oe yc2 )) 0.
c3ycyceyce yca11 ycIyciycu.
c3ycyceyce Oe yc3 ) yca12 .
c3ycyceyce Oe yc3 )) .
yua3 = 0.
c2ycyceyce N yca9 ycIyciycu.
c2ycyceyce Oe yc2 ) yca10 .
c2ycyceyce Oe yc2 )) 0.
c3ycyceyce yca11 ycIyciycu.
c3ycyceyce Oe yc3 ) yca12 .
c3ycyceyce Oe yc3 )) .
The constants .
caCA, yca3 , yca5 , yca7 , yca9 , yca11 ) in the derivation of the control laws in SMC correspond to the constant k in .
Fig.
The block diagram of robot system control using the sliding mode The two primary parts of a LADRC are an ESO and a proportional controller .
as shown in Fig.
To enable the controller to actively correct for these impacts, the ESO is in charge of calculating the generalized disturbance as well as the system states.
The tracking error is used by the proportional controller to drive the error to zero, guaranteeing precise and consistent tracking performance .
, .
To regulate the angular position for one joint of the arm using an ADRC, the state space is defined as follows:
= yce.
uE, ycc, y.
yca0 yc.
ycn = 1,2,3 yccyc Where yce.
uE, ycc, y.
is the dynamical model and any internal or external system disturbances, and b0 is the known parameter of the system.
is the control input which represents the reference angular velocity ycycyceyce .
Equation .
can be transformed into a state-space representation for better control and observer design as follows:
yccyc1 = yc2 yca0 yc.
yccyc yccyc2 yccyce yccyc yccyc Mohamed Abdelhakim Basal.
Advanced Sliding Mode Control with Disturbance Rejection Techniques for Multi-DOF Robotic Systems .
Journal of Robotics and Control (JRC) ISSN: 2715-5072 Where, yc1 is the Represents the system's output .
uE).
yc2 is the Represents the dynamics of any internal or external system disturbances like the effect of the angular velocity regulation loop using SMC which is the inner loop of the control system.
To estimate the system states yc1 and yc2 , the observer equations are given as follows:
= yc2 yca0 yc.
Oe yaA1 yce = OeyaA2 yce yce = yc1 Oe yuE Where .
aA1 yaA2 ] = .
yui0 yui02 ] is the observer gain vector.
yui0 denotes the observer's cut-off pulse.
The control input yc.
is formulated as:
ycycu Oe yc2 yc0 = ycoycy .
c Oe yc1 ) .
= Where ycycu is defined as:
The controller gain ycoycy is denoted yuiyca, which is the closed loop natural frequency and yc is the reference signal.
Fig.
shows the block diagram of the proposed control system.
to do this.
yuiCA is usually selected as yuiCA = .
Oe .
ycoCo .
, .
Fig.
5 shows the bode plot characteristics of the open loop control system of angular positions of the arm, for different values of yuiCA, where yca0 = 1 ycaycuycc ycoycy = 222.
It can be seen that with increasing the value of yuiCA, the system's response is faster, but it becomes less robust and stable, so an intermediate value can be taken that ensures the stability and robustness of the system while maintaining fasttracking of the reference signal.
IV.
SIMULATION RESULTS
The main goal of robot control is to adjust the operating torque in such a way that it follows the desired path as accurately as possible, and as quickly as possible.
To test the effectiveness of the proposed control system, a simulation was performed in a MATLAB/Simulink environment to track a circular path.
Fig.
Fig.
7, and Fig.
8 show the tracking response for the first, second, and third joints, respectively.
It is clear from Fig.
Fig.
Fig.
8 that the performance of the proposed ADRC-SMC control system is superior, as it achieves higher tracking accuracy and no vibration.
The Structure of the ADRC-SMC for one joint The Structure of the ADRC-SMC of the arm's angular positions Fig.
The Structure of the ADRC-SMC Observer and Dynamics of ADRC To account for all system uncertainties and disturbances, the observer estimates ycCA .
and yc .
eneralized Fast estimation is possible with a large observer gain .
uiCA), although noise amplification is more The proportional controller drives the tracking error to zero by ensuring that the system output ycCA tracks the reference signal.
To guarantee precise state estimates, the observer needs to be quicker than the controller.
The observer's poles .
uiCA) are positioned to the left of the controller poles .
Fig.
The bode plot characteristics of the open loop control system of the By examining Fig.
6, it is noted that the PID-based control system has the advantage of less vibration than the sliding mode control system, while the sliding mode control system is more effective in tracking speed when there is a change in the reference signal.
The same can be noted in Fig.
7 where it is noted that the joint deviates from the desired path at the moment of starting operation, then returns to the desired path, and the same can be noted at moment 6.
5 sec.
The proposed ADRC-SM control system combines the advantages of both control systems (PID and SM) as it is more effective in tracking accuracy and speed with a clear reduction in vibrations caused by the control system based only on the sliding mode.
This can be verified by examining Fig.
8 when tracking a fixed-value reference.
Mohamed Abdelhakim Basal.
Advanced Sliding Mode Control with Disturbance Rejection Techniques for Multi-DOF Robotic Systems Journal of Robotics and Control (JRC) ISSN: 2715-5072 starting moment, then return to it and maintains good tracking, and the same can be observed at the moment 6.
5 sec.
However, when using the proposed control system, both advantages can be obtained.
Examining Fig.
8 shows that the PID-based control system is superior compared to the sliding mode control system as no significant vibrations occur, but it has a longer settling time, while the proposed ADRC-SM control system combines the advantages of the two control systems (PIDC-SMC) as it is more effective in tracking accuracy and faster with a clear reduction in vibrations resulting from the sliding mode-based control system only.
Fig.
The tracking response for the first joint Fig.
The tracking response for the second joint Fig.
The tracking response for the third joint By examining Fig.
6, it is noted that the PID-based control system has the advantage of less vibration than the sliding mode control system, while the sliding mode control system is more effective in tracking when a change in the reference signal occurs.
The same can be observed in Fig.
7, where it is noted that the joint deviates from the desired path at the Fig.
9 shows a comparison between the error average values for tracking the reference signals of the joints using the three control systems presented in this research.
It is noted that the proposed control system achieves the lowest error The tracking error average value of the first joint is 0035 rad using ADRC-SMC, 0.
006 rad using PIDC, and 007 rad using SMC.
For the second joint, it is noted that the average tracking error value is 0.
0004 rad using ADRCSMC, 0.
00044 rad using SMC, and 0.
0033 rad using PIDC.
For the third joint, it is noted that the average tracking error value is 0.
0044 rad using ADRC-SMC, 0.
0077 rad using PIDC, and 0.
012 rad using SMC.
Fig.
A comparison between the error average values for tracking the reference signals of the joints The control signals applied to the three motors are shown in Fig.
Fig.
11 and Fig.
12, and it is clear that the proposed control system (ADRC-SMC) outperforms the SMC system in its effectiveness in generating a smooth and vibration-free control signal.
On the other hand, a difference is observed between the torque values required to rotate the three joints of the arm, which can be explained by referring to equation .
It is noted from Fig.
10 that the torque required for the first joint is low compared to the second and third joints, as the first joint is supported on the base and the first joint forms a right angle with the ground, which means that the gravitational force acting on it is zero.
It is noted from Fig.
11 that the torque required to rotate the second joint is greater compared to the first and second joints, as the second joint carries both the second and third joints, which means that the torque required to overcome the gravitational force is greater.
It is noted from Fig.
12 that the torque required to rotate the third joint is less compared to the torque of the second joint because the effect of the gravitational force is less, as shown in equation .
To test the time-responses characteristics of control systems, a test was conducted to track reference signals with a constant value .
tep response, ycyceyce = 0.
1 ycycayc.
Fig.
Mohamed Abdelhakim Basal.
Advanced Sliding Mode Control with Disturbance Rejection Techniques for Multi-DOF Robotic Systems Journal of Robotics and Control (JRC) ISSN: 2715-5072 shows the response of the first joint.
Fig.
14 shows the response of the second joint, and Fig.
15 shows the response of the third joint.
Fig.
The response of the first joint for step response, ycyceyce = 0.
1 ycycaycc Fig.
The control signal applied to the first actuator Fig.
The response of the second joint step response, ycyceyce = 0.
1 ycycaycc Fig.
The control signal applied to the second actuator Fig.
The response of the third joint step response, ycyceyce = 0.
1 ycycaycc Fig.
The control signal applied to the third actuator It is noted from the Fig.
13 that the proposed control system achieves better performance in terms of tracking fast and accuracy, the settling time is 0.
02 sec, while it is noted that the settling time using the SM controller is 1.
7 sec, followed by the PID control system where the settling time 2 secs.
The overshoot using the proposed controller Mohamed Abdelhakim Basal.
Advanced Sliding Mode Control with Disturbance Rejection Techniques for Multi-DOF Robotic Systems Journal of Robotics and Control (JRC) ISSN: 2715-5072 is zero, while it is 4% using the PID control system and 70% using the SM controller.
For the second joint, it is also noted from Fig.
14 that the proposed control system achieves better performance in terms of tracking fast and accuracy, the settling time is 0.
01 sec, while it is noted that the settling time using the SM controller is 0.
5 sec, followed by the PID control system where the settling time reaches 6.
2 secs.
The overshoot using the proposed controller is zero, while it is 10% using the PID control system and 40% using the SM As can be seen from Fig.
15, the proposed control system achieves the best performance in terms of tracking accuracy and achieving a lower static error.
monitor includes a proportional limit in addition to two complementary limits.
The reasons for the superiority of the ADRC-SMC control system can be summarized as follows:
Different scenarios were conducted in the simulation environment to track a circular path, as well as to track fixedvalue reference signals for the three joints.
Table II shows a summary of the simulation results including a comparison of the performance of control systems during circular trajectory tracking and when regulating angular positions at fixed .
The use of ADRC in the external control loop provides a proactive estimation and monitoring mechanism to compensate for disturbances and uncertainties in the system, making it able to generate a control signal for the internal loop faster without the need for a long damping This allows the internal SMC loop to respond faster, which significantly reduces the settling time.
Also, the presence of a disturbance monitor contributes to achieving more precise control of the system response, preventing large overshoots as in PID or even SMC.
Unlike PID, which can introduce overshoot due to its integral action.
ADRC-SMC dynamically adjusts the control effort, ensuring a smoother and more precise .
The use of SMC in the internal control loop contributes to achieving system robustness and increasing response SMC ensures high robustness against parameter variations and disturbances, while ADRC enhances adaptability, achieving optimal performance.
Regarding the limits of this system or its degree of complexity, by looking at Fig.
, we notice that the degree of complexity of the control system ADRC is not very large compared to traditional control systems, as it includes a proportional limit in the control law, while the disturbance CONCLUSION This study deals with the design and evaluation of a hybrid control system that combines sliding control (SMC) and active disturbance cancellation (ADRC) to improve the 3-DoF By utilising the robustness of classic SMC, the proposed sys tem sought to minimise its inherent vibrations while guarant eeing smooth, quick, and extremely dynamic responses with efficient disturbance rejection.
The results in Table II show that the classical SMC control methodology provides superior performance compared to the traditional PIDC from the low stability time, but suffers from a higher value of path tracking error as well as a higher value of target overshoot.
In contrast, the proposed control methodology contributes to improving the performance of the robotic arm, achieving faster response, lower value of target overshoot as well as lower value of path tracking error.
To provide a clear evaluation of the performance.
Table i compares the PIDC.
SMC and ADRC-SMC control methods based on the main performance criteria.
From the above comparison, it is clear that the ADRCSMC controller outperforms both PIDC and SMC by providing superior tracking accuracy, fast response, and significantly reduced vibration.
This makes it a promising solution for high-precision robotics applications, especially in industrial automation, medical robotics, etc.
Its ability to balance robustness, speed, and accuracy while mitigating vibrations makes it the ideal choice for controlling multidegree-of-freedom robotic systems.
TABLE II.
A SUMMARY OF THE SIMULATION RESULTS
Joint 1
Fixed reference signals circular reference path
Joint 2
Fixed reference signals circular reference path
Joint 3
Fixed reference signals circular reference path
Settling Time
Overshoot
tracking error average Settling Time
Overshoot
tracking error average Settling Time
Overshoot
tracking error average ADRC-SMC
PIDC
SMC
0035 rad 01 sec 0004 rad 7 sec 0044 rad 2 .
006 rad 0033 rad 5 sec 0077 rad 7 .
5 sec 00044 rad 5 sec 012 rad TABLE i.
COMPARING THE PERFORMANCE OF THE CONTROL METHODS
Performance Criterion Tracking Accuracy Settling Time Overshoot Vibration Reduction Implementation Complexity Overall Performance PIDC Good Low Low Easy Average SMC Moderate High High Moderate Good ADRC-SMC (Propose.
Excellent Very small Very low Nearly Eliminated Relatively Complex Excellent Mohamed Abdelhakim Basal.
Advanced Sliding Mode Control with Disturbance Rejection Techniques for Multi-DOF
Robotic Systems Journal of Robotics and Control (JRC) ISSN: 2715-5072
REFERENCES