[Abstract]: This paper studies the system characteristics and required control strategies for the motion control of parallel robots , analyzes the characteristics of the Model-Free Adaptive Control (MFAC) algorithm, and compares it with PID control and neural network control. It proposes to apply MFAC to the control system of parallel robots. Theoretical analysis proves its rationality and shows that the system control performance will be improved.
Keywords : MFAC; PID control; neural network control; parallel robot;
Theory Study on Parallel Robots with Model-free Adaptive Control Dong Xin College of Electronic and Information Engineering jiangsu University jiangsu zhenjiang 212013
[Abstract]: This paper studies on the system specialty of parallel robots' movement control and control strategy of needing, and takes analysis on model-free adaptive control (MFAC). With comparing to PID control, neural network control, the author bring MFAC on the control system of parallel system. The analysis on theory proves that this plan is reasonable and the control capabilities of system are improved.
Key Word: MFAC; PID control; neural network control; parallel robot;
1. Introduction
The development of control theory has enabled increasingly precise control of complex nonlinear systems. Taking the control of a six-free parallel robot as an example, from the initial use of PID control and adaptive control to the use of fuzzy control, neural network and other intelligent control, and then to the application of sliding mode variable structure control theory to the control of parallel robots, the motion control performance of the parallel robot system has been significantly improved. In his doctoral dissertation in 1993-1994, Dr. Hou Zhongsheng first proposed the model-free adaptive control theory. After more than ten years of research and development, this control theory has its own unique control law. The basic idea is: using a newly introduced pseudo gradient vector (pseudo Jacobi matrix) and pseudo order concept, a series of dynamic linear time-varying models are used to replace the general discrete-time nonlinear system near the trajectory of the controlled system, and the pseudo gradient vector of the system is estimated online using only the I/O data of the controlled system, thereby realizing the MFAC of the nonlinear system. [1] This paper will analyze and study the system characteristics of the parallel robot and the function of the model-free adaptive control theory, and proposes for the first time to apply the model-free adaptive control theory to the control of the parallel robot. Theoretical analysis shows its rationality.
2 System characteristics of motion control for parallel robots
Parallel robots represent a new type of robot in terms of both structure and function. Compared to serial robots, they feature higher precision, greater stiffness, lower inertia, higher load-bearing capacity, simpler inverse kinematics model, higher operating speed, and easier control. From a dynamics perspective, a six-DOF parallel robot is a highly nonlinear, strongly coupled, and variable-parameter multivariable system. During motion, although the total mass of the motion platform is constant, the load acting on each branch will vary nonlinearly within a range of tens of times when it is in different poses or moves at different speeds, making it a typical variable-load system. Furthermore, due to the connection of the load system, the outputs and controls of each channel influence each other, leading to load coupling, affecting the dynamic and static characteristics of the system, and even causing instability. Meanwhile, due to the influence of uncertain factors in its power mechanism (such as model structure perturbation, parameter time variation and unpredictable external disturbances, etc.), it is difficult to meet the requirements of the six-degree-of-freedom motion control system of CNC machining by applying traditional PID control, neural network control and other control system design methods. Therefore, studying control strategies to solve strong load disturbances and cross-linking coupling disturbances is a key issue in the development of high-precision six-degree-of-freedom parallel robots. Among them, the highly robust control method is one of the effective ways to solve such problems, which is also the focus of research needed for the development of six-degree-of-freedom parallel robots in my country. [2]
3. Functional Analysis of Parallel Robot Controller
Based on the system characteristics of a six-degree-of-freedom parallel robot, the designed controller should have the following functions:
(1) Control function for multi-input multi-output nonlinear systems. A six-degree-of-freedom parallel robot is a complex multi-input multi-output nonlinear system, requiring the designed controller to possess model-free adaptive control law for multi-input multi-output nonlinear systems.
(2) Decoupling function. A six-degree-of-freedom parallel robot is a nonlinear multi-input multi-output system. There is strong coupling between the motion outputs of each degree of freedom. In order to obtain good control performance, decoupling control must be performed.
(3) Anti-interference function. A six-degree-of-freedom parallel robot is a typical system with variable load, time-varying parameters, and unpredictable interference requirements.
(4) High-precision trajectory tracking function. The end effector of the moving platform of a six-degree-of-freedom parallel robot will definitely be used to realize a certain specific function, such as CNC machining, so the designed control should have high trajectory tracking accuracy.
4 Design of Model-Free Adaptive Controllers [3][4][5][6]
Model-free adaptive control theory refers to control theory where the controller design utilizes only the I/O data of the controlled system, and the controller does not contain any information about the mathematical model of the controlled process. However, model-free control theory is not model-free; rather, it does not require building a model but relies on a "generalized model."
(1)In the formula, is the characteristic parameter for achieving adaptation. When the system is stable at the setpoint, is the gradient of y(k) with respect to u(k-1). The model-free adaptive control law consists of two parts: one is the basic model-free adaptive law; the other is the function combination algorithm.
(1) The basic model-free control algorithm is:
(2)In the formula, is a characteristic parameter, and is a certain estimate of ; α is a small positive constant; λk is a control parameter; y0 is a set value; and and λk are important parameters in the basic form.
(2) The basic model-free control law of the function combination algorithm can only achieve good control effect for some simple systems. Therefore, the basic model-free control law has shortcomings and must be improved. The method to improve the basic control law is to add a function combination part to it. The improved model-free control law is:
(3)In the formula, A and θ are the configuration parameters of the control law, and m and n are positive constants. D(·) is an appropriate function that represents the functional combination part of the control law, and:
Its constituent principles are as follows:
(1) Guided by the functional requirements of the controlled object for the control method, seek out all possible functions and decompose them into the simplest functions as much as possible, which are called original functions or functional elements.
(2) Represent all original functions that can be represented by algorithms using algorithms. And practice has shown that the vast majority of functional elements can be represented by algorithms.
(3) The set of all functional elements is called E, and it is called the functional space, which is the appropriate function defined on E, and θ is the parameter vector of the function.
5. Functional Analysis of MFAC Applied to Parallel Robots
Analysis suggests that MFAC should possess the functionality of three parallel robot controllers.
(1) By introducing the concept of quasi-dominant control variables, a gradient matrix (called a pseudo-matrix) is obtained to realize the input-output relationship of the system, thereby realizing the control function of a multi-input multi-output nonlinear system. Reference [7]
(2) The model-free adaptive controller has a "self-decoupling function". This decoupling function is inherent in the model-free adaptive controller algorithm itself and does not require complex decoupling processing. Reference [8]
(3) The anti-interference capability of the controller depends on its ability to overcome deviations, and the ability to overcome deviations depends on the convergence speed of the control law of the controller. The faster the convergence speed, the stronger the ability to overcome deviations, and thus the stronger the anti-interference capability. For the model-free adaptive control law (3), it can be proven that the convergence speed of the model-free adaptive controller is much faster than that of the PID controller and other intelligent controllers, that is, the model-free adaptive controller has a strong anti-interference capability. Obviously, it can also overcome the interference of variable load. We can regard the mutual coupling in the system as mutual interference between them. By designing a controller with a sufficiently fast convergence speed, we can overcome the interference caused by coupling, so that the decoupling function of the controller is stronger. References [5][8]
(4) According to references [9][10], simulations show that the model-free adaptive controller has a trajectory tracking function similar to that of the neural network controller and has high trajectory tracking performance. Moreover, the model-free adaptive control has all the control performance of the PID control. The simulation diagram of the tracking performance is as follows:
(a) Neural network control (b) MFAC (c) PID control
Based on the idea of functional combination, we can combine the four functions into functional modules to construct appropriate functions and design a perfect model-free adaptive law. The control law designed by combining the idea of functional combination has strong adaptability. When applied to the control of a six-degree-of-freedom parallel robot, it will surely produce good control results.
6. Conclusion
This paper theoretically analyzes the characteristics of the motion control system of a six-degree-of-freedom parallel robot and the control functions that the required control theory should possess. Furthermore, it analyzes the functions of model-free adaptive control theory in relation to the control requirements of the parallel robot, demonstrating that the idea of applying model-free adaptive control to the control of parallel robots is reasonable and correct. In the two years since the author began working with model-free adaptive control, numerous literature reviews have been conducted, all focusing on its application in industrial process control. The main contribution of this paper lies in theoretically applying model-free adaptive control theory to the control of parallel robots. The author will continue researching the construction and design of combined function functions, and hopes that experts and scholars will investigate how to concretely implement this approach.
References:
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Author Biography: Dong Xin (1983-), male, from Shandong Province, is a Master's student at the School of Electrical and Information Engineering, Jiangsu University, majoring in Control Theory and Control Engineering. His research interests include control strategies for parallel robots. E-mail: [email protected]. Address: Room 1106, Building 1, Area 6, Student Dormitory, Jiangsu University, Zhenjiang City, Jiangsu Province, 212013, China. Tel: 15952818559.
