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The SCARA robot, an industrial robot capable of replacing human workers in various operations, can also function as a machine tool for tasks like welding, handling, painting, assembling, automotive, electronics, and others It features two rotational joints on a horizontal plane and typically one translational joint on the vertical axis Due to its simple structure, SCARA robots are extensively used worldwide, particularly in automation lines and industrial settings, where they excel in pick-and-place operations The periodic motion of SCARA robots has been the subject of numerous studies, including a dynamic modeling and linearization technique introduced in [2] Another study proposed a new energy-saving approach for SCARA robots [3] to effectively reduce energy consumption by liberalizing the nonlinear robot dynamics Model-based methods offer efficient solutions for robot learning tasks due to their prediction capabilities, as discussed in [4], despite their complexity and specific structural requirements Residual vibrations in wafer handling applications were analyzed in [5] using polynomial chaos theory to investigate the dynamic performance of a SCARA robot manipulator under uncertainty Advantages of sliding mode control, such as fast response, good transient performance, and robustness to parameter variations, were highlighted in [6,7], although these methods may exhibit chattering phenomenon, which can be mitigated using saturation functions The concept of model-free control, sometimes referred to as control-based observer or state estimation, is explored in [8, 9], emphasizing its reliance on the model structure for building estimators or observers A model-free filtered backstepping control for marine power systems was proposed in [10], demonstrating slow convergence of the estimated dynamic model to its actual value In [11], a terminal sliding mode controller combined with a nonlinear disturbance observer is introduced, showing suboptimal control performance due to the model-based observer Various control strategies, including linear and nonlinear approaches such as PD Control, PID Control, CTC, Adaptive Control, and Fuzzy Control,
6 are employed to address the nonlinearity, uncertainty, external disturbances, strong coupling, and time-varying nature of robotic systems [12-16] Nevertheless, existing methods have struggled to handle both time-varying model uncertainties and disturbances,often relying on complex model-based design processes Therefore, this study proposes a model-free sliding mode control for regulating systems with time-varying model uncertainties and unknown disturbances, aiming to achieve accurate tracking performance and stable convergence for nonlinear systems.
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The initial SCARA robot emerged as an innovative prototype in 1978, within ProfessorHiroshi Makino's laboratory at Yamanashi University in Japan [1] The 2-axis SCARA was conceived unlike any other robotic arm of that era, showcasing remarkable simplicity that enabled enhanced functionality through reduced motion, coupled with high speed and precision The acronym SCARA denotes Selective Compliance Assembly Robot Arm.While the physical attributes of these robots may differ in dimensions and configurations,all SCARA arms share a consistent 2-axis motion characteristic SCARA excels particularly in "pick and place" operations, showcasing a distinctive capability to retrieve industrial components from one location and accurately relocate them elsewhere with precision, speed, and fluid motion The behavior of the SCARA arm some what resembles that of the human arm, featuring joints that facilitate both vertical and horizontal movement Nonetheless, the SCARA arm exhibits constrained motion at the wrist,allowing rotation but not tilting This limited wrist motion proves advantageous in various assembly tasks, including pick-and-place maneuvers, assembly processes, and packaging applications In 1981, SCARA robots made their debut on commercial assembly lines and continue to offer the most favorable price/performance ratio for high-speed assembly tasks.The introduction of the Japanese flexible assembly system, centered around the SCARA robot, sparked a global surge in small electronics manufacturing, leading to the development of products that not only propelled the economy but also left an enduring e Structure and application e SCARA robot:
SCARA consists of three parallel rotary joints and a prismatic joint The rotary joints can move along the horizontal plane and the prismatic joint moves along the vertical plane The special characteristic of SCARA is that the robot is smooth while operating on x and y- axis but very strong versus the z-axis Figure 1 shows the schematic diagram of SCARA se Application of SCARA:
The Selective Compliance Assembly Robot Arm (SCARA) robots were initially devised for the purpose of executing assembly and disassembly tasks The incorporation of both flexible and rigid axes in their design simplifies the process of automating fundamental assemblies without necessitating intricate programming SCARA robots demonstrate a high level of proficiency in swiftly assembling parts for automated assembly tasks, consequently reducing cycle times and enhancing precision The selection of SCARA robots for pick and place automation is often attributed to their cost-effectiveness and speed Despite the potential theoretical superiority of delta robots in terms of speed, the straightforward configuration of SCARA robots grants them a competitive advantage in
8 this aspect Particularly in tasks involving simple vertical movements, SCARA robots are well-suited for automating dispensing operations, aligning effectively with their automation capabilities The precise distribution of materials during dispensing tasks is ensured by the selective compliance feature of SCARA robots Owing to their rapid printing capabilities, SCARA robots are suitable for automating small-scale 3D printing tasks, facilitating swift printing processes The increasing prevalence of utilizing SCARA robots for 3D printing applications is noteworthy The introduction of laser-equipped engraving tools for robotic End-of-Arm Tools (EOATs) has facilitated the automation of engraving procedures Equipped with precision, accuracy, and a compact form, SCARA robots are suitable for efficiently carrying out engraving tasks SCARA robots are suitable for automating material handling tasks with light payloads, such as packaging processes. Commonly automated tasks like palletizing, bin picking, and labeling can be effectively performed using SCARA robots The compact dimensions and tabletop mounting option of SCARA robots make them well-suited for automating machine tending operations Their compact arm design enables easy access to machinery and operation within confined spaces, allowing them to tend to tasks like injection molds and CNC machines.
1.3 Research method and report layout
The research is based on an advanced method in control and automation, mechatronics, and mathematics apply The system model will be obtained by using some transform (Laplace), differential equations, and mechatronic knowledge The controller will be developed based on advanced stability conditions and mathematic techniques The system performance will be observed by simulation on Matlab/Simulink.
Main contribution of this work can be summarized as follows:
Inspired from aforementioned works, in this paper, a collaborative between model-free and sliding control In addition, a low-pass filter is taken on a consideration to eliminated a high frequency and achieve the efficient performance of robot Scara e Propose a novel continuous-time input disturbance estimator for multiple-input multiple-output double integrator systems using filters Then, a model-free sliding
9 mode controller was proposed for the input-disturbed double integrator system for tracking control Indeed, this disturbance estimator does not use any information of the robot manipulator except its state variables and model order e Practical stability of the tracking control system, involving the linear state feedback controller, the disturbance estimator and the robot Scara, was rigorously analyzed and proved An attractive set of the tracking error has been determined and its radius can be reduced by changing the poles of the closed-loop system and the filter.
The research endeavor comprises four chapters In Chapter 1, we provided an overview of the study's history, research objectives, mechanical structure, research methods, and conclusions The goals, study questions, and techniques employed to accomplish these goals are also described in this chapter the literature on the SCARA system and its relevant control We examine the concepts and elements of the SCARA system and its behavior. This chapter also evaluates the literature on linear and nonlinear control methods, optimal and robust factors related to the control design.
The system modeling research technique and dynamic equation of SCARA is fully described in Chapter 2
In this chapter 3, an overview of sliding mode control method and model - free approach will be presented Subsequently, we will combine these two controllers, and develop and demonstrate a model - free sliding mode control scheme to achieve accurate tracking performance for SCARA systems and guarantee tracking convergence stability This chapter will also provide the stability condition to ensure the system's performance and to obtain the required controller parameter.
In Chapter 4, We present simulations and evaluations of the results and provide necessary adjustments for the controller In addition, the results of the data analysis and discussion of the findings align with our research questions and hypotheses.
Conclusions, suggestions for future work, and applications to real-life of the research are described in in Chapter 5.
DYNAMICS MODEL 008
CONTROLLER DESIGN FOR SCARA ROBOIT Ác Sen 13 3.1 Sliding mode Control 0.0.0.0 ccc ec cceceec
Model-free sliding mode CONtIO] ccceccescesceeseeseeeeeeseeseeseceseesecseceseeseceeeeseseseeeeaeseeeeseseseneaes 15
In this section, a model-free sliding mode controller is derived for SCARA systems As shown in the previous section, the sliding mode controller can compensate for system disturbances and uncertainties While system disturbances are caused by external factors, system uncertainties are caused by system modelling imprecision Thus, system modelling is vital when designing a control system, as it can drastically affect the overall performance
15 of the controller In addition, if the system model is considerably complex, the derivation of the sliding mode control law can become cumbersome.
This article introduces a novel model-free sliding mode control strategy, requiring only knowledge of the system's order Notably, the proposed method estimates system stability under model uncertainty and disturbances The controller's operation relies solely on previous control inputs and state measurements, eliminating the need for a system model.
3.2.1 Control diagram for SCARA system
The control scheme of SCARA robot is presented in Figure
In this scheme, we will initialize a desired trajectory r =[r r]ẽ for the SCARA robot's operation The control error of closed-loop system, x=col[e ¿] is used as the input value for the low pass filter, which is used to filter out high-frequency noise from the signal, and the output is denoted with z Then the block estimation component called the ‘disturbance estimator’ will be used to calculate used to calculate and approximate the lumped matched disturbance 7 by 77 after a period time delay 7(s) Then, the control signal of the model- free controller is calculated using the formula w,, =2 Simultaneously, the system's feedback signal will be transmitted to the sliding mode controller to calculate the control signal u,,, The formula w =u,, + u,,, will calculate the control signal for the entire system. Under the influence of control signals, time-varying disturbances, and uncertain
16 components The proposed controller will demonstrate the system's stability through the robot's movement, and these motions will be described by the output state variables qt)=[q_ q]' This value is then fed back to update the control signal to maintain the stability of the system.
Substituting the sliding mode function s=0 and derivative of function s=0 to the equation (3.11) in the previous section, we can obtain the equivalent control input “,, as below
The purpose of control problems is to determine a state feedback controller
Mu [uo › Ugo] in order to force g to track a desired trajectory 7 under the influence of disturbances # and make the tracking error đ=7— approach to zero in finite time.
But in reality, it is difficult to determine the disturbance d and the accuracy of n-DOF SCARA model Consequently, rather than dealing with an uncertain M , we will define arbitrarily an invertible matrix M The discrepancy between TM and the actual inertia matrix of the robot is denoted by M =M-M Therefore, from (3.12) we derive the following.
This study focuses on designing control laws for robots to achieve desired objectives without explicitly knowing system parameters The controller must enable effective control despite disturbances, parameter variations, and external forces All system states, their derivatives, and input disturbances are assumed to be bounded, considering that robot motion is inherently constrained in practical applications This assumption ensures the controller's robustness and efficiency.
17 structure of the hardware, and the control input from the actuator cannot be excessively large to induce infinite velocities in the system states.
Since M is symmetric and positive defined, the matrix M M are also symmetric and positive defined Therefore, M is invertible and multiplying Mˆ' both size of equation
Subtracting 7 into both size of equation (1.19) we obtain:
Expending the expression A,e + A,€ in the right side of (3.15), this is equivalent to: j—Ƒ= Ae+ Aje+M Tu +11 '(Mọ+u+d—C— f)-F-Ae-Aộ (3.16)
With A, is the matrix of error system, A, is the matrix of derivative error system The parameter matric A, and A, will be determined in the next section.
Rewrite (3.16) in tracking errors space: é=—Ae-Ae-M'u,, +#+Ae+Ae-M"(MgG+d-C-f) — G17)
In the above equation, we define that 7 =7+Aje+A,é -M" (Mg + Ug +d-C-f) (3.18) With the compensator to be designed 7 = Mu, „: We have: é=-Ae-A,e-n+n
Let x =col[e,é], then the model of tracking error above is expressed as: x= Ax+ B(-7 +7) (3.19)
Where 0, is the zero matrix of nxn dimension and J, denotes the identity matrix
And we denote that dimension of nxn It is obviously that if the control signal u,, = M 7 , the system (3.19) will follow a linear reference stable model:
Since A, and A, are arbitrary, we can choose them which ensures the matrix A becomes
The stability of the reference model (3.19) is dependent on the precision of the estimation of 77 When 77 is accurately estimated, the tracking errors x will converge to zero This demonstrates that the closer 77 is to its reference value 77, the more precise x will be To improve the accuracy of 77 and its estimation to match 77 as closely as possible, the estimation problem of 77 will be addressed in the following subsection.
Denote