CN101691020A - Sliding formwork control method used in motion control of virtual axis machine tool cutter - Google Patents

Abstract

The invention discloses a sliding mode control method for the motion control of a virtual axis machine tool tool. Firstly, according to the processing requirements, the spatial movement track of the tool in the virtual axis machine tool processing process is planned, and the expected motion of each active pair of the virtual axis machine tool is determined during the processing process. Then establish the mathematical model of the controlled object in each control branch of the virtual axis machine tool, detect and determine the actual motion state of each active pair of the virtual axis machine tool, calculate the switch surface function according to the sliding mode control theory, and determine each control branch of the virtual axis machine tool The motor drive control amount is sent to each motor driver, and finally each active pair is driven by the motor drive control amount of each control branch, thereby driving the virtual axis machine tool to realize the desired movement. The present invention does not need to establish an accurate model of the controlled object of each branch. The excellent characteristics of the sliding mode control technology are used to realize high-precision control of the tool movement; the sliding mode control amount is composed of continuous functions, and there is no tremor problem.

Description

A Sliding Mode Control Method for Tool Motion Control of Virtual Axis Machine Tool

technical field

The invention relates to a virtual axis machine tool, in particular to a motion control method of a tool driven by a motor.

Background technique

The key technology of the numerical control system of the virtual axis machine tool (also known as parallel machine tool) is to realize the linkage control of the virtual axis through the control of the real axis of the virtual axis machine tool, so as to obtain the required tool movement trajectory. However, since the virtual axis machine tool is composed of a multi-bar parallel kinematic mechanism, its dynamic model is a complex system with multiple degrees of freedom, multiple variables, high nonlinearity, and multi-parameter coupling. During the movement of the mechanism and the machining process of the machine tool, the parameters of the mechanism model and external disturbances vary greatly, which is uncertain. Compared with ordinary machine tools with a series structure, the accumulation of transmission errors is greatly reduced, but there are still other factors that affect the machining accuracy, such as: manufacturing and installation errors of the machine tool, the gap between the upper and lower spherical hinges of the drive rod, and the length deviation of the drive rod The impact on the position accuracy of the moving platform, the motion error of the actuator and the kinematic pair, the elastic deformation caused by gravity, the deformation caused by heat, the sensor accuracy, etc. Therefore, the precise control of virtual-axis machine tools is still a recognized problem in the control field, and it has become one of the biggest obstacles to the industrialization and practical application of virtual-axis machine tools in the field of high-precision machining, which seriously restricts its advantages and has become an urgent problem to be solved. key issues.

One of the key technologies to improve the positioning and machining accuracy of virtual axis machine tools is to improve the accuracy of the control of the solid-connected tools on the virtual axis machine tool parallel mechanism dynamic platform. For this reason, people have proposed different control methods. At present, there are mainly error compensation control methods, intelligent control methods, and model-based adaptive control methods. Among them, the error compensation control method is mostly aimed at specific virtual axis machine tools, and is carried out for specific error generating factors such as friction, vibration, gravity, etc. Therefore, it is not universal for different types of virtual axis machine tools; intelligent control methods It is usually based on the artificial neural network for the compensation or suppression of the coupling effect of the virtual axis machine tool or the load disturbance. This kind of control method is relatively complicated. At present, it is mostly implemented by simulation, and there are few practical applications; the adaptive control or robustness of the virtual axis machine tool is based on the model. The control method is not only difficult to implement, but also because its control accuracy depends on the accuracy of the model, it is necessary to establish an accurate mathematical model of the virtual axis machine tool in advance. Due to the complexity of the parallel mechanism of the virtual axis machine tool and the uncertainty of external interference during processing, it is not only very difficult to accurately establish its mathematical model, but also the built model is usually very complicated and difficult to be used for actual control. The existing domestic experimental prototypes mostly ignore the coupling effect between the branches of the virtual axis machine tool, treat each branch as a completely independent system, and implement traditional PID control. Usually, error compensation measures must be taken at the same time to meet the accuracy requirements of the virtual axis machine tool . In addition, reviewing the patent situation of virtual axis machine tools at home and abroad, it can be seen that the patents of virtual axis machine tools are all new mechanism designs of various virtual axis machine tools. So far, no relevant literature has proposed an ideal control method for virtual axis machine tools.

Variable structure control has developed into an important method for the control research of dynamical systems with uncertainties. The variable structure system is a discontinuous feedback control system. Its main feature is that it establishes a sliding model on a switch surface, which is called "sliding mode". The general form of the conventional sliding mode control law is

u＝u _eq +ηsgn(s)(1)

In formula (1), η is a normal constant; s is the switch surface function; u _eq is the equivalent control quantity to maintain the sliding mode motion; ηsgn(s) aims to control the unknown parts such as system uncertainty and disturbance.

When the conventional sliding mode control method is implemented by a numerical control system such as a computer, the sampling interval will cause small tremors in the control output, which will affect the accuracy of the sliding mode control method.

Contents of the invention

The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and provide a sliding mode control method for virtual axis machine tools driven by motors with the best dynamic quality for the motion control of virtual axis machine tools.

The technical scheme that the present invention adopts is to adopt following steps:

1) According to the processing requirements, plan the spatial movement trajectory of the tool during the machining process of the virtual axis machine tool, and determine the expected movement trajectory of each active pair of the virtual axis machine tool during the machining process;

2) Establish the mathematical model of the controlled object of each control branch of the virtual axis machine tool;

3) Detect and determine the actual motion state of each active pair of the virtual axis machine tool;

4) Calculate the switch surface function according to the sliding mode control theory;

5) Determine the motor drive control amount of each control branch of the virtual axis machine tool and send it to each motor driver;

6) Drive each active pair with the motor drive control amount of each control branch, so as to drive the virtual axis machine tool to achieve the desired movement.

The present invention applies the sliding mode control method to the motion control of the tool of the virtual axis machine tool for the first time, and its characteristics and beneficial effects are:

1. Compared with the model-based adaptive control method in the prior art, the sliding mode control method of the present invention is insensitive to system parameter changes and external disturbances, so the control system adopting the sliding mode control method does not need to establish accurate controlled object mathematics Its control accuracy does not need to depend on the accuracy of the model, and it does not need to consider the coupling problem between multiple branches and multiple variables of the controlled object. It only needs to use the excellent characteristics of the sliding mode control technology to achieve high-precision control of the tool movement of the virtual axis machine tool , can have excellent control quality.

2. The surface parameters of the sliding mode control switch are designed according to the second-order optimal dynamic quality system, which not only makes the virtual axis machine tool system have the best dynamic quality after forming the sliding mode movement, but also greatly reduces the workload of control parameter debugging.

3. The determined sliding mode control quantity with the best dynamic quality is composed of a continuous function, which has continuity, which solves the tremor problem existing in the conventional sliding mode control technology, and greatly enhances the practicability of the sliding mode control technology.

Description of drawings

The present invention will be described in further detail below in conjunction with the accompanying drawings and specific embodiments.

Figure 1 is a schematic diagram of the sliding mode control system of a virtual axis machine tool.

Fig. 2 is a diagram of expected motion and actual motion track of each branch of the virtual axis machine tool in Fig. 1, wherein: Fig. 2a is a curve diagram of the motion tracking of the active pair of branch 1, and Fig. 2b is a curve diagram of the motion tracking of the active pair of branch 2, Fig. 2c is the active and auxiliary motion tracking curve of branch 3, Fig. 2d is the active and auxiliary motion tracking curve of branch 4, Fig. 2e is the active and auxiliary motion tracking curve of branch 5, and Fig. 2f is the active and auxiliary motion tracking curve of branch 6 picture.

Fig. 3 is the motion error diagram of the active pair of each branch of the virtual axis machine tool, in which: Fig. 3a is the motion error diagram of the active pair of branch 1, Fig. 3b is the motion error diagram of the active pair of branch 2, and Fig. 3c is the motion error diagram of the active pair of branch 3 For the error graph, Fig. 3d is the motion error graph of the active pair of branch 4, Fig. 3e is the motion error graph of the active pair of branch 5, and Fig. 3f is the motion error graph of the active pair of branch 6.

Fig. 4 is the driving control quantity of each branch motor of the virtual axis machine tool, in which: Fig. 4a is the driving control quantity diagram of the branch 1 motor, Fig. 4b is the driving control quantity diagram of the branch 2 motor, and Fig. 4c is the driving control quantity diagram of the branch 3 motor Figure 4d is the drive control quantity diagram of the branch 4 motor, Figure 4e is the drive control quantity diagram of the branch 5 motor, and Figure 4f is the drive control quantity diagram of the branch 6 motor.

Detailed ways

As shown in Figure 1, after planning the spatial movement trajectory of the tool in the machining process according to the processing requirements, first determine the expected movement trajectory of each active pair of the virtual axis machine tool during the machining process and establish the mathematical model of the controlled object of each control branch of the virtual axis machine tool; Secondly, according to the motion state of each motor detected by the encoder of each branch, the actual motion state of each active pair is obtained; then, the driving command of each motor is calculated by using the pre-designed sliding mode control law with the best dynamic quality, and sent to each motor The driver (motor servo amplifier), finally drives the ball screw of the virtual axis machine tool to achieve the desired movement of the tool. The specific method is as follows:

1. Determine the expected movement of each active pair in advance according to the processing requirements of the virtual axis machine tool

(单位为mm/s)和期望运动加速度(单位为mm²/s)。After completing the tool machining trajectory planning according to the processing requirements of the virtual axis machine tool, according to the kinematic inverse solution of the parallel mechanism of the virtual axis machine tool, determine the expected displacement x _d (unit: mm ), the expected speed of motion

(unit: mm/s) and expected motion acceleration (The unit is mm ² /s).

2. Pre-establish the mathematical model of the controlled object in each control branch of the virtual axis machine tool

Because the present invention adopts sliding mode control, its design process is naturally decoupled, so the cutter motion control scheme that each branch can be independently controlled respectively, and the control scheme that has to consider the coupling effect between each branch (such as carrying out coupling compensation) Compared with the intelligent control scheme), this control scheme does not need to analyze the coupling effect and establish a complex coupling effect model, so the design and implementation are convenient; compared with the PID control scheme that also uses independent control of each branch, when the machine tool is processed, the system parameters Changes and load disturbances often make PID control unable to obtain satisfactory control results, but the performance of the sliding mode control system is not affected by system parameter changes and load disturbances.

When the sliding mode control scheme in which each branch is independently controlled is adopted, the mathematical model of the control object can be established independently for each motor control branch, and there is no need to consider the system parameter changes and load change interference on each branch. Since each branch of the parallel mechanism of the virtual axis machine tool generally uses the same motor and its driving components, for the virtual axis machine tool, when the system parameter changes and external interference are not considered, for each motor drive branch, the mathematical parameters of the controlled object The models have the same form, here set as a third-order model:

$\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; bu</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

(单位为mm²/s)是虚拟轴机床各主动副的实际运动加速度；

是虚拟轴机床各主动副实际位移的三阶导数；a₂、a₁和b分别是常系数，由电机伺服放大器的设置参数和电机参数确定。In the formula (2), u is the input of the control quantity, which is converted by the numerical control system and becomes an instruction sent to the motor servo amplifier (driver), which is generally the number of input pulses or the input quantity of analog voltage (unit is V). After the present invention adopts or; b is the control quantity coefficient; (unit: mm/s) is the actual movement speed of each active pair of the virtual axis machine tool;

(unit: mm ² /s) is the actual motion acceleration of each driving pair of the virtual axis machine tool;

is the third derivative of the actual displacement of each active pair of the virtual axis machine tool; a ₂ , a ₁ and b are constant coefficients respectively, which are determined by the setting parameters of the motor servo amplifier and the motor parameters.

If system parameter changes and external disturbances are considered, the mathematical model of the controlled object for each motor drive branch of the virtual axis machine tool should be

$\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; bu</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

In formula (3), d(t) is interference. Since the changes of system parameters a ₂ (t), a ₁ (t) and disturbance d(t) are uncertain during the machining process of the virtual axis machine tool, the model of formula (3) is actually not easy to establish accurately.

If the control scheme of independent control of each branch is not adopted, the dynamic mathematical model established will be a set of extremely long and highly coupled nonlinear time-varying differential equations, which generally cannot give analytical solutions and cannot be used for real-time control.

Based on the above analysis, since the present invention adopts the sliding mode control technology, when establishing the mathematical model of the controlled object, it is sufficient to establish a linear model such as formula (2).

The reason why the performance of the sliding mode control system does not depend on the accuracy of the mathematical model of the controlled object is that the performance of the sliding mode control system has nothing to do with the characteristics of the original system due to the formation of the sliding mode, but is determined by the characteristics of the switch surface equation . This is the essential property of the sliding mode control system.

3. Detect and determine the actual motion state of each active pair of the virtual axis machine tool

Use the encoder equipped with the virtual axis machine tool to detect the motion state of the motor, and determine the actual motion state of each active pair of the virtual axis machine tool according to the reduction ratio of the reduction mechanism or the pitch of the lead screw.

4. Calculate the switch surface function

According to the sliding mode control theory, the switch surface function is calculated, which corresponds to the third-order system formula (2) of the virtual axis machine tool, and its calculation formula is

$\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2e"\; label="k"\; filenames="H2009100360684E0000021.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

为虚拟轴机床各主动副运动的速度误差(单位为mm/s)；

为虚拟轴机床各主动副运动的加速度误差(单位为mm²/s)。In formula (4), e=x _d -x is the position error (in mm) of each active pair motion of the virtual axis machine tool; x (in mm) is the actual displacement of each active pair of the virtual axis machine tool,

is the speed error of each active pair motion of the virtual axis machine tool (unit is mm/s);

is the acceleration error of each active pair motion of the virtual axis machine tool (unit is mm ² /s).

In this switch surface function, the general determination method of two adjustable parameters _k1 and _k2 is as follows: firstly, in order to ensure the stability of the control system, these two parameters must be greater than 0 respectively, and then through computer simulation or the test before actual processing The adjustments were finalized and, obviously, it took a lot of time and effort.

In order to solve the above problems, the present invention proposes a method for designing switch surface parameters according to the second-order optimal dynamic quality system.

按此关系设计开关超平面参数，则参数调试工作量将大大降低，而且可使虚拟轴机床系统在产生滑模运动后具有最佳动态品质。依据本发明提出的开关曲面参数设计方法，本发明所提出和采用的开关曲面函数计算公式为According to the variable structure sliding mode control theory, once the sliding mode control system forms a sliding mode motion, its system characteristics are determined by the switch surface equation s=0 formed by the switch surface function. Since the second-order system has the best dynamic quality when the damping coefficient ξ=0.707, according to the switching hyperplane equation s=0, we have so

Designing switch hyperplane parameters according to this relationship will greatly reduce the workload of parameter debugging, and enable the virtual axis machine tool system to have the best dynamic quality after generating sliding mode motion. According to the switch surface parameter design method proposed by the present invention, the switch surface function calculation formula proposed and adopted by the present invention is

$\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1.414</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2e"\; label="k"\; filenames="H2009100360684E0000021.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}{<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2e"\; label="k"\; filenames="H2009100360684E0000021.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

5. Determine the motor drive control amount of each control branch of the virtual axis machine tool

For each control branch of the virtual axis machine tool, the calculation formula of the motor drive control amount is:

$\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; [</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1.414</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="k"\; filenames="H2009100360684E0000021.png,H2009100360684E0000022.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="k"\; filenames="H2009100360684E0000021.png,H2009100360684E0000022.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&eta;s</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

为维持滑模运动的等效控制量，ηs旨在控制系统不确定性和干扰等未知部分，η为正常数，其大小取决于系统不确定性和干扰。Equation (6) is the sliding mode control law with the best dynamic quality designed by the present invention, wherein

In order to maintain the equivalent control quantity of sliding mode motion, ηs aims to control the unknown parts such as system uncertainty and disturbance, and η is a normal constant, and its magnitude depends on system uncertainty and disturbance.

较大，因此虚拟轴机床控制系统形成滑模的条件

一定满足，依据滑模控制理论，此时虚拟轴机床的运动和加工不受负载变化等干扰或系统惯量等参数变化的影响，具有较高的控制精度；当系统未受干扰或系统参数稳定时，

较小，系统可能会不符合滑模条件，但此时虚拟轴机床的运动处于接近期望状态处，由控制律计算公式(6)及所设开关曲面函数s可见，此时的滑模控制律中的非等效控制量部分ηs相当于一个PID增量式控制器，对此时的虚拟轴机床系统运行状态来说，PID控制器完全能够产生较好的控制效果。It can be proved theoretically and verified by simulation. As long as the adjustable parameter η is not too small, when the system is disturbed or the system parameters change, due to the

Larger, so the condition of the virtual axis machine tool control system to form a sliding mode

It must be satisfied. According to the theory of sliding mode control, the movement and processing of the virtual axis machine tool are not affected by disturbances such as load changes or system inertia and other parameter changes, and have high control accuracy; when the system is not disturbed or the system parameters are stable ,

Smaller, the system may not meet the sliding mode conditions, but at this time the motion of the virtual axis machine tool is close to the desired state, it can be seen from the control law calculation formula (6) and the set switch surface function s, the sliding mode control law at this time The non-equivalent control quantity part ηs in is equivalent to a PID incremental controller. For the running state of the virtual axis machine tool system at this time, the PID controller can produce better control effect.

The present invention is based on the basic theory of sliding mode control. The calculation method of the motor drive control quantity of each branch is different from the conventional calculation method in that: the sliding switch surface function s is used instead of the conventional calculation symbolic function sgn(s) (see formula ( 1)), the change of its sign is actually the same as the original sign function, but its control law is composed of a continuous function, so the sliding mode controller will not have chattering problems when implemented by a numerical control system, which greatly improves the sliding mode control method practicality. The chatter-free sliding mode control method is applied to the motion control of the tool of the virtual axis machine tool for the first time by the present invention.

6. Drive each active pair with the motor drive control amount of each control branch

The motor drive control quantity of each branch determined in step 5, see the calculation formula (6), through the digital/analog conversion of the numerical control system, it becomes a voltage analog quantity of (-10V, 10V). The analog quantity is sent to each motor servo amplifier as a driving command, and each branch motor is controlled to drive each active pair of the virtual axis machine tool, thereby driving the virtual axis machine tool to complete the desired motion.

An embodiment of the invention is provided below:

Example

It is assumed that the virtual axis machine tool is composed of 6 branch parallel mechanisms, driven by AC servo motors, and adopts rolling screw drive (ball screw). The block diagram of its control system is shown in Figure 1. The specific implementation of this control method is as follows:

1. Determine the expected movement of each active pair of the virtual axis machine tool according to the processing requirements in advance

Assume that according to the processing requirements, the tool needs to move linearly from the (20mm, 20mm, 20mm) space point to the (30mm, 30mm, 30mm) space point. According to the inverse solution of the kinematics of the virtual axis machine tool, the expected motion trajectories of the active pairs of each branch of the virtual axis machine tool are obtained, as shown in the small circle trajectories of each sub-figure in Figure 2.

2. Pre-establish the transfer function of each branch control object

Each branch takes the motor driver and the motor as the controlled objects, and takes the parallel mechanism of the virtual axis machine tool and the tool as the load. Assuming that the AC servo motor driver is set to the speed control mode, its current feedback gain is K _i , and the power amplification gain is K _a . The speed loop gain is K _pre , the speed feedback coefficient is K _v ; the AC servo motor winding resistance is R _p (unit is Ω), the winding inductance is L _p (unit is H), and the torque constant is K _tp (unit is N m/A), the total moment of inertia on the AC servo motor shaft is J (unit is kg m ² ); if the pitch of the ball screw is h (unit is mm), then the transfer function of each branch control object of the virtual axis machine tool for

$\frac{{\mathrm{<span\; class="notranslate">\; 1.5</span>}\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; tp</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; pre</span>}}\mathrm{<span\; class="notranslate">\; h</span>}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="L\; p\; js"\; filenames="H2009100360684E0000032.png,H2009100360684E0000041.png"\; state="\{\{state\}\}">L</figure-callout></span><figure-callout\; id="3"\; label="L\; p\; js"\; filenames="H2009100360684E0000032.png,H2009100360684E0000041.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}{}^{}{\mathrm{<span\; class="notranslate">\; js</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; js</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 1.5</span>}\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; tp</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; tp</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; pre</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

In Equation (7), S is the differential operator, U(S) is the Laplace transformation value of the controller output u (corresponding to the analog value (-10V, 10V)), X(S) is the virtual axis machine tool parallel mechanism The Laplace transform value of active and auxiliary displacement x (unit: mm).

According to the driver setting and motor model, the parameters in formula (7) are: J＝0.39kg·m ² , L _p ＝0.03837H, R _p ＝5.09Ω, K _pre ＝88, K _v ＝0.54, K _i ＝ 2.2, K _a =6, K _tp =3.41N·m/A, screw pitch is 5mm. Substituting each parameter into formula (7), and transforming formula (7) into a differential equation has

$\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 475.533</span>}\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 98388.733</span>}\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 143.692</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

3. Detect the actual movement of the active pair of each branch of the virtual axis machine tool

The motion state of the corresponding branch motors is directly measured from the readings of the branch encoders. For a virtual axis machine tool with a lead screw pitch of 5 mm, every time the motor rotates one revolution, the active pair on the corresponding branch produces a displacement of 5 mm, which can be obtained The actual motion state of each active pair of the virtual axis machine tool.

4. Calculate the switch surface function s

The formula for calculating the switching surface function s of the parameter design according to the second-order optimal dynamic quality system proposed by the present invention is

$\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1.414</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2e"\; label="k"\; filenames="H2009100360684E0000021.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}{<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2e"\; label="k"\; filenames="H2009100360684E0000021.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; e</span>}$

5. Determine the motor drive control amount of each control branch

According to each branch motor drive control quantity calculation formula (6) proposed by the present invention, the calculation formula for determining each control branch motor drive control quantity is as follows:

$\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0.007</span>}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3.309</span>}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 684.720</span>}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0.010</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3.309</span>}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0.007</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 684.720</span>}<span\; class="notranslate">\; )</span>\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&eta;s</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

In formula (9), k ₂ and η are adjustable parameters. k ₂ has a great influence on system performance, which can be determined by computer simulation or test before actual processing. And as long as η is not too small, it can overcome the system uncertainty and interference and make the system achieve good control quality. Its possible value range is wide and does not need to be precise.

6. Drive each active pair with the motor drive control amount of each control branch

After the control quantity determined in step 5 is digital/analog converted by the numerical control system, it becomes an analog voltage command and sends it to the motor servo amplifier (driver), which drives the motors of each branch to move, thereby driving the parallel mechanism of the virtual axis machine tool and the tool to complete the desired movement. . The actual trajectory of the active pair of each branch of the virtual axis machine tool is shown by the solid lines in the sub-figures of Fig. 2. The motion errors of the active pair of each branch of the virtual axis machine tool are shown in the sub-figures of Fig. 3 respectively. The driving control quantity of each branch motor is shown in each sub-graph in Fig. 4 respectively.

Figure 4 shows that the designed sliding mode control method has the best dynamic quality, its control quantity is continuous, and there is no tremor problem of the conventional sliding mode control method, so it has strong practicability. Figure 2 and Figure 3 show that the control of each branch of the virtual axis machine tool is precise, and it has good dynamic and steady-state quality.

Claims (2)

1. A sliding mode control method for virtual shaft machine tool motion control, characterized in that the following steps are adopted: 1) According to the processing requirements, plan the spatial movement trajectory of the tool during the machining process of the virtual axis machine tool, and determine the expected movement trajectory of each active pair of the virtual axis machine tool during the machining process; 2) Establish the mathematical model of the controlled object of each control branch of the virtual axis machine tool; 3) Detect and determine the actual motion state of each active pair of the virtual axis machine tool; 4) Calculate the switch surface function according to the sliding mode control theory; 5) Determine the motor drive control amount of each control branch of the virtual axis machine tool and send it to each motor driver; 6) Drive each active pair with the motor drive control amount of each control branch, so as to drive the virtual axis machine tool to achieve the desired motion. 2. A kind of sliding mode control method for virtual axis machine tool tool motion control according to claim 1, is characterized in that: In step 1), determine the expected displacement x _d and expected movement speed of each active pair of the virtual axis machine tool

desired motion acceleration

In step 2), the mathematical model of each control branch controlled object is; $\stackrel{\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;}{x}=a_2\stackrel{\&Center\; Dot;\&Center\; Dot;}{x}+a_1\stackrel{\&Center\; Dot;}{x}+\mathrm{bu},$ In the formula: u is the number of input pulses or the input quantity of analog voltage; b is the control quantity coefficient;

is the actual movement speed of each active pair of the virtual axis machine tool;

is the actual motion acceleration of each active pair of the virtual axis machine tool;

is the third-order derivative of the actual displacement of each active pair of the virtual axis machine tool; a ₂ , a ₁ , and b are constant coefficients respectively, which are determined by the setting parameters of the motor driver and the motor parameters; Step 4), through the formula $\mathrm{the\; s}=\stackrel{\&Center\; Dot;\&Center\; Dot;}{e}+1.414\sqrt{k_2}\stackrel{\&CenterDot;}{e}+k_{2}e$ Calculate the switch surface function s; in the formula: e=x _d -x is the position error of each active pair motion of the virtual axis machine tool; x is the actual displacement of each active pair of the virtual axis machine tool;

is the velocity error of each active pair motion of the virtual axis machine tool;

is the acceleration error of each active pair motion of the virtual axis machine tool; Step 5), through the formula $u=\frac{1}{b}[{\stackrel{\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;}{x}}_d-a_2{\stackrel{\&Center\; Dot;\&Center\; Dot;}{x}}_d-a_1{\stackrel{\&CenterDot;}{x}}_d+(1.414\sqrt{k_2}+a_2)\stackrel{\&CenterDot;\&CenterDot;}{e}+(k_2+a_1)\stackrel{\&CenterDot;}{e}]+\mathrm{\&eta;s}$ Determine the motor drive control quantity of each control branch of the virtual axis machine tool; in the formula, the adjustable parameter _k should be greater than 0, and η is a normal number, and the size depends on the system uncertainty and interference; is the equivalent control quantity for maintaining the sliding mode motion.

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