CN106067747B - A kind of design method of sliding formwork disturbance observer for servo system control - Google Patents

A kind of design method of sliding formwork disturbance observer for servo system control Download PDF

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CN106067747B
CN106067747B CN201610382613.5A CN201610382613A CN106067747B CN 106067747 B CN106067747 B CN 106067747B CN 201610382613 A CN201610382613 A CN 201610382613A CN 106067747 B CN106067747 B CN 106067747B
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disturbance observer
sliding mode
servo system
friction torque
coefficient
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CN106067747A (en
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王毅
柳佳男
何朕
万树同
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Harbin Institute of Technology Shenzhen
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P7/00Arrangements for regulating or controlling the speed or torque of electric DC motors

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Abstract

本发明提供一种用于伺服系统控制的滑模扰动观测器的设计方法,针对伺服系统低速时的摩擦干扰问题并且考虑系统建模的误差和不确定性问题。使用普通直流电机模型,将扰动观测器与滑模变结构控制相结合,设计滑模扰动观测器。首先利用扰动观测器去观测摩擦力矩的大小,然后根据得到的摩擦力矩设计滑模控制器。对摩擦力矩的观测可以减少滑模控制器的切换项增益,减少抖振现象。通过滑模扰动观测器实现低速伺服系统对死区、爬行、自振荡等非线性现象的抑制,减弱了对建模精度的要求,且具有良好的鲁棒性。

The invention provides a design method of a sliding mode disturbance observer used for servo system control, aiming at the problem of friction disturbance at low speed of the servo system and considering the error and uncertainty of system modeling. Using the ordinary DC motor model, combining the disturbance observer with the sliding mode variable structure control, a sliding mode disturbance observer is designed. Firstly, the disturbance observer is used to observe the magnitude of the friction torque, and then the sliding mode controller is designed according to the obtained friction torque. The observation of the friction torque can reduce the gain of the switching term of the sliding mode controller and reduce the chattering phenomenon. The low-speed servo system suppresses nonlinear phenomena such as dead zone, crawling, and self-oscillation through the sliding mode disturbance observer, which weakens the requirement for modeling accuracy and has good robustness.

Description

一种用于伺服系统控制的滑模扰动观测器的设计方法A Design Method of Sliding Mode Disturbance Observer for Servo System Control

技术领域technical field

本发明涉及一种用于伺服系统控制的滑模扰动观测器的设计方法。The invention relates to a design method of a sliding mode disturbance observer used for servo system control.

背景技术Background technique

在低速伺服系统中,摩擦力矩对伺服系统的动态性能造成了严重影响。并且导致了一些非线性现象,比如转速过零点死区、低速爬行现象、滞滑自振荡等。为了能够消除这些非线性现象,需要对摩擦力矩进行补偿。目前总体来说有两种补偿方式,一种是基于摩擦模型的补偿方法,如Stribeck模型、LuGre模型。过程是首先利用获得的速度、位置信息来估计模型参数,得到实时的摩擦力矩大小,然后在控制器中加入相应的补偿值。这种方法由于事先需要通过测试或者在线辨识的方法确定模型参数,导致控制律比较复杂。另一种是基于非模型的摩擦补偿方式,将摩擦视为扰动信号进行消除。扰动观测器是一种常见的非模型的摩擦补偿方式,它在力矩电机上被广泛使用来观测并补偿摩擦力,但是在模型相对较复杂的直流电机上没有应用说明。另外,扰动观测器补偿方式对系统建模的精度要求很高,如果存在未建模动态或者建模有误差的情况下补偿效果会变坏。In low-speed servo systems, the friction torque has a serious impact on the dynamic performance of the servo system. And it leads to some non-linear phenomena, such as the zero-crossing dead zone of the speed, low-speed crawling phenomenon, stagnation and self-oscillation, etc. In order to eliminate these non-linear phenomena, it is necessary to compensate the friction torque. Generally speaking, there are currently two compensation methods, one is the compensation method based on the friction model, such as the Stribeck model and the LuGre model. The process is to first use the obtained speed and position information to estimate the model parameters, get the real-time friction torque, and then add the corresponding compensation value in the controller. Because this method needs to determine the model parameters through testing or online identification in advance, the control law is more complicated. The other is a non-model-based friction compensation method, which treats friction as a disturbance signal for elimination. Disturbance observer is a common non-model friction compensation method. It is widely used in torque motors to observe and compensate friction force, but there is no application description for DC motors with relatively complex models. In addition, the disturbance observer compensation method has high requirements on the accuracy of system modeling. If there are unmodeled dynamics or modeling errors, the compensation effect will deteriorate.

滑模变结构控制具有对系统的参数和扰动变化不敏感的特点,鲁棒性较强。但是如果用滑模变结构控制摩擦较大的伺服系统,会使其中的符号函数具有较高的增益而导致较大的抖振现象,因此在设计滑模控制器的时候必须要考虑摩擦因素。Sliding mode variable structure control has the characteristics of insensitivity to system parameters and disturbance changes, and has strong robustness. However, if the sliding mode variable structure is used to control the servo system with high friction, the sign function will have a high gain and cause a large chattering phenomenon. Therefore, the friction factor must be considered when designing the sliding mode controller.

发明内容Contents of the invention

本发明针对伺服系统低速时的摩擦干扰问题并且考虑系统建模的误差和不确定性问题,提供一种用于伺服系统控制的滑模扰动观测器的设计方法。The invention provides a design method of a sliding mode disturbance observer for servo system control aiming at the problem of frictional disturbance at low speed of the servo system and considering the error and uncertainty of system modeling.

本发明采用如下技术方案:一种用于伺服系统控制的滑模扰动观测器的设计方法,步骤如下:The present invention adopts following technical scheme: a kind of design method for the sliding mode disturbance observer of servo system control, the steps are as follows:

(1)首先建立伺服系统的状态方程如下:(1) First establish the state equation of the servo system as follows:

其中,状态变量x1表示转角,x2表示转速,Ce是电机的反电动势系数,u是控制输入,Ku是PWM驱动器的放大系数,Km是力矩系数,J是转动惯量,R是电枢电阻,Tf表示摩擦干扰力矩;Among them, the state variable x1 represents the rotation angle, x2 represents the rotational speed, C e is the back electromotive force coefficient of the motor, u is the control input, K u is the amplification factor of the PWM driver, K m is the torque coefficient, J is the moment of inertia, and R is Armature resistance, T f represents the frictional disturbance torque;

(2)设计滑模控制率(2) Design sliding mode control rate

r表示给定信号,角位置和角速度的跟踪误差分别是r represents the given signal, the tracking errors of angular position and angular velocity are respectively

e=r-x1(2)e=rx 1 (2)

设计切换函数sDesign switching function s

其中c表示切换面的参数,c越大,使系统的响应速度越快,但稳定性会受到影响;Where c represents the parameter of the switching surface, the larger c is, the faster the response speed of the system will be, but the stability will be affected;

采用指数趋近律Exponential reaching law

其中ε>0,k>0,ε是等速趋近项系数,k是指数趋近项系数,都需要人为适当选取,结合式(1)和(4)得Among them, ε>0, k>0, ε is the coefficient of the constant velocity approach term, and k is the coefficient of the exponential approach term, both of which need to be selected manually. Combining formulas (1) and (4), we get

根据式(5)(6)得到控制率u的表达式According to the formula (5) (6), the expression of the control rate u is obtained

上式中除了摩擦力矩Tf外,其余物理量都是已知的,下面采用扰动观测器的方式来观测摩擦力矩;In the above formula, except for the friction torque T f , other physical quantities are known, and the disturbance observer is used to observe the friction torque below;

(3)根据直流电机的模型设计扰动观测器,扰动观测器的输出值是等效到伺服系统输入端的等效摩擦力矩的估计值下面的式子表示了它与其他物理量的关系,(3) Design the disturbance observer according to the model of the DC motor, and the output value of the disturbance observer is the estimated value of the equivalent friction torque equivalent to the input end of the servo system The following formula expresses its relationship with other physical quantities,

其中是电机转速,Gn-1(s)是被控对象名义传递函数的逆,U(s)是控制器的输出,Q(s)表示一个低通滤波器,其表达式选择为in is the motor speed, Gn -1 (s) is the inverse of the nominal transfer function of the controlled object, U(s) is the output of the controller, Q(s) represents a low-pass filter, and its expression is chosen as

其中时间常数τ根据系统的带宽适当选取;The time constant τ is properly selected according to the bandwidth of the system;

将式(8)乘以系数之后得到真实摩擦力矩的估计值,Multiply equation (8) by the coefficient Then an estimate of the true friction torque is obtained,

最终结合式(7)和式(10)得到的控制率完成滑模扰动观测器的设计。Finally, the control rate obtained by combining formula (7) and formula (10) is used to complete the design of the sliding mode disturbance observer.

本发明的优点:通过结构变换使扰动观测器能够观测普通直流电机的摩擦干扰,而不仅仅是力矩电机。扰动观测器对摩擦力矩的观测能够减少滑模控制的抖动问题,而滑模控制器的使用能够有效改善扰动观测器的缺点,减弱了对建模精度的要求,提高了系统的鲁棒性和抗干扰能力,二者相得益彰。The invention has the advantages that the disturbance observer can observe the friction disturbance of the common DC motor, not just the torque motor, through the structure transformation. The observation of the friction torque by the disturbance observer can reduce the jitter problem of the sliding mode control, and the use of the sliding mode controller can effectively improve the shortcomings of the disturbance observer, weaken the requirements for modeling accuracy, and improve the robustness and stability of the system. Anti-interference ability, the two complement each other.

附图说明Description of drawings

图1为含摩擦伺服系统的滑模控制图;Figure 1 is a sliding mode control diagram of a friction servo system;

图2为扰动观测器的原理图;Fig. 2 is the schematic diagram of disturbance observer;

图3为滑模扰动观测器的结构图;Fig. 3 is the structural diagram of sliding mode disturbance observer;

图4为正弦输入下PID控制的转速曲线图;Fig. 4 is the speed curve diagram of PID control under sinusoidal input;

图5为正弦输入下滑模扰动观测器控制的转速曲线图;Fig. 5 is the rotating speed curve figure that sine input sliding mode disturbance observer controls;

图6为阶跃位置输入下两种控制策略的位置误差曲线图;Fig. 6 is the position error graph of two kinds of control strategies under step position input;

图7为低速斜坡输入下两种控制策略的响应曲线图。Figure 7 shows the response curves of the two control strategies under low-speed ramp input.

具体实施方式Detailed ways

下面根据说明书附图举例对本发明做进一步解释:The present invention will be further explained below by way of example according to the accompanying drawings of the description:

实施例1Example 1

一种用于伺服系统控制的滑模扰动观测器的设计方法,步骤如下:A method for designing a sliding mode disturbance observer for servo system control, the steps are as follows:

1.滑模控制器的设计1. Design of sliding mode controller

如图1表示使用滑模控制器控制一个受到摩擦影响的伺服系统,首先建立伺服系统的状态方程如式(1)所示:As shown in Figure 1, a sliding mode controller is used to control a servo system affected by friction. First, the state equation of the servo system is established as shown in equation (1):

其中r(t)是指令信号,u是控制输入,Ce是电机的反电动势系数,Ku是PWM驱动器的放大系数,R是电枢电阻,Km是力矩系数,J是转动惯量,Tf表示摩擦干扰力矩。状态变量x1表示转角,x2表示转速。where r(t) is the command signal, u is the control input, C e is the back EMF coefficient of the motor, K u is the amplification factor of the PWM driver, R is the armature resistance, K m is the torque coefficient, J is the moment of inertia, T f represents the frictional disturbance torque. The state variable x1 represents the angle of rotation, and x2 represents the rotational speed.

角位置和角速度的跟踪误差分别是The tracking errors of angular position and angular velocity are respectively

e=r-x1 (2)e=rx 1 (2)

设计切换函数Design switching function

采用指数趋近律Exponential reaching law

其中ε>0,k>0。结合式(1)和(4)可得Where ε>0, k>0. Combining formulas (1) and (4) can get

根据式(5)(6)可以得到控制率u的表达式According to the formula (5) (6), the expression of the control rate u can be obtained

上式中除了摩擦力矩Tf外,其余物理量都是已知的。下面采用扰动观测器的方式来观测摩擦力矩。In the above formula, except the friction torque Tf , other physical quantities are known. Next, we use the disturbance observer method to observe the friction torque.

2.扰动观测器的原理2. The principle of the disturbance observer

扰动观测器的原理图如图2所示,图中n表示干扰信号,表示干扰的观测值,Gp(s)表示被控对象传递函数,Gn -1(s)表示被控对象名义模型的逆,ξ表示输出端噪声,Q(s)是一个低通滤波器。通常Q(s)可以选择The schematic diagram of the disturbance observer is shown in Figure 2, where n in the figure represents the disturbance signal, Represents the observed value of the disturbance, G p (s) represents the transfer function of the controlled object, G n -1 (s) represents the inverse of the nominal model of the controlled object, ξ represents the noise at the output end, Q(s) is a low-pass filter . Usually Q(s) can be chosen

对于图1所示的直流电机,由于其受到的摩擦干扰位于被控对象的内部,需要进行一定的数学处理。如果仍然按照图2的结构设计扰动观测器,那么扰动观测器的输出值并不是真实的摩擦力矩,而是它在伺服系统输入端的等效值Teq。等效摩擦力矩Teq和原有摩擦力矩Tf的关系是For the DC motor shown in Figure 1, since the frictional disturbance it receives is located inside the controlled object, certain mathematical processing is required. If the disturbance observer is still designed according to the structure in Figure 2, then the output value of the disturbance observer is not the real friction torque, but its equivalent value T eq at the input end of the servo system. The relationship between the equivalent friction torque T eq and the original friction torque T f is

忽略电感的影响,近似有Neglecting the effect of inductance, approximately

3.滑模扰动观测器的设计3. Design of the sliding mode disturbance observer

结合滑模变结构控制和扰动观测器的方法,得到伺服系统的控制框图如图3所示。首先通过扰动观测器得到摩擦力矩的估计值由于干扰观测器的输出值是等效摩擦力矩的估计值根据式(10),乘以系数之后得到真实摩擦力矩的估计值 Combining the method of sliding mode variable structure control and disturbance observer, the control block diagram of the servo system is shown in Figure 3. First, the estimated value of the friction torque is obtained by the disturbance observer Since the output value of the disturbance observer is an estimate of the equivalent friction torque According to formula (10), multiply by the coefficient Then get an estimate of the true friction torque

最后根据式(7)设计出控制器的滑模控制率。Finally, the sliding mode control rate of the controller is designed according to formula (7).

实施例2Example 2

已知被控电机伺服系统的参数:R=14.7Ω,Km=1.134N·m/A,Ce=0.119V/(r/min),J=1.79*10-6kg*m2,Ku=12。The parameters of the servo system of the controlled motor are known: R=14.7Ω, K m =1.134N·m/A, C e =0.119V/(r/min), J=1.79*10 -6 kg*m 2 , K u =12.

电机的传递函数是The transfer function of the motor is

选择低通滤波器Q(s)的参数τ=0.001ms,则Select the parameter τ=0.001ms of the low-pass filter Q(s), then

然后根据Q(s)和Gp(s),构建扰动观测器得到摩擦力矩的估计值选择c=30,k=1,ε=1作为控制参数设计控制率u。Then according to Q(s) and G p (s), build a disturbance observer to get the estimated value of friction torque Choose c=30, k=1, ε=1 as the control parameter design control rate u.

通过计算机simulink仿真,比较PID控制和滑模干扰观测器控制的好坏。Through computer simulink simulation, compare the quality of PID control and sliding mode disturbance observer control.

首先使用速度环和位置环的双闭环PID控制,PID参数选取的规则是:首先不考虑电机的非线性摩擦部分,采用临界比例度法依次确定速度环和位置环的PID系数,然后再对系数进行微调,获得接近于最佳的跟踪性能。最终确定速度环的比例系数是0.021,积分系数是1.6,由于摩擦干扰的作用使输出端有较大噪声,微分项为零;位置环比例系数是6,积分系数是1.8,微分项为零。Firstly, double-closed-loop PID control of speed loop and position loop is used. The rules for selecting PID parameters are as follows: Firstly, regardless of the nonlinear friction part of the motor, the PID coefficients of the speed loop and position loop are determined sequentially by the critical proportionality method, and then the coefficients Fine-tune for near-optimal tracking performance. Finally, the proportional coefficient of the speed loop is 0.021, and the integral coefficient is 1.6. Due to the frictional interference, the output end has a large noise, and the differential term is zero; the proportional coefficient of the position loop is 6, the integral coefficient is 1.8, and the differential term is zero.

给定幅值为6°频率为2rad/s的正弦位置输入信号θ=6sin2t(o),理论上其速度表达式是ω=2cos2t(r/min)。图4表示了PID控制下的角速度变化曲线,转速曲线在过零点表现出死区现象,死区时间约为0.15s,占一个周期的4.8%,这主要是由于摩擦非线性导致的。图5表示了采用滑模干扰观测器后转速的变化曲线,死区时间约为0.02s,占周期的0.64%,说明采用滑模扰动观测器能够有效抑制死区现象。Given a sinusoidal position input signal θ=6sin2t( o ) whose amplitude is 6° and frequency is 2rad/s, its velocity expression is theoretically ω=2cos2t(r/min). Figure 4 shows the angular velocity change curve under PID control. The speed curve shows a dead zone phenomenon at the zero crossing point. The dead zone time is about 0.15s, accounting for 4.8% of a cycle, which is mainly caused by friction nonlinearity. Figure 5 shows the change curve of the speed after using the sliding mode disturbance observer. The dead time is about 0.02s, accounting for 0.64% of the cycle, which shows that the use of the sliding mode disturbance observer can effectively suppress the dead zone phenomenon.

给定6°的阶跃位置输入信号,图6表示当达到稳态时两种控制策略的位置误差曲线。PID控制的位置误差曲线,在位置跟踪达到稳态时出现了滞滑自振荡的现象,位置偏差最大值是0.012°。采用滑模扰动观测器(SMDOB)的位置误差曲线,振荡值明显减少,位置偏差最大值是0.001°,振荡幅值是PID控制的8%。Given a step position input signal of 6°, Fig. 6 shows the position error curves of the two control strategies when the steady state is reached. The position error curve of PID control shows the phenomenon of stagnation and self-oscillation when the position tracking reaches a steady state, and the maximum position deviation is 0.012°. Using the position error curve of the sliding mode disturbance observer (SMDOB), the oscillation value is significantly reduced, the maximum position deviation is 0.001°, and the oscillation amplitude is 8% of the PID control.

给定斜率为0.01°的低速斜坡位置输入,图7中的虚线表示了采用PID控制下输出位置随时间变化的曲线,表现出了明显的爬行现象;实线是采用滑模扰动观测器(SMDOB)控制的位置响应曲线,爬行现象基本上得到了消除。说明了SMDOB控制方案能够很好的抑制电机低速运行时发生的爬行现象。Given a low-speed ramp position input with a slope of 0.01°, the dotted line in Figure 7 shows the curve of the output position changing with time under PID control, showing an obvious creeping phenomenon; the solid line is the sliding mode disturbance observer (SMDOB ) controlled position response curve, the crawling phenomenon is basically eliminated. It shows that the SMDOB control scheme can well suppress the creeping phenomenon that occurs when the motor is running at low speed.

Claims (1)

1.一种用于伺服系统控制的滑模扰动观测器的设计方法,其特征在于,步骤如下:1. a method for designing a sliding mode disturbance observer for servo system control, characterized in that, the steps are as follows: (1)首先建立伺服系统的状态方程如下:(1) First establish the state equation of the servo system as follows: 其中,状态变量x1表示转角,x2表示转速,Ce是电机的反电动势系数,u是控制输入,Ku是PWM驱动器的放大系数,Km是力矩系数,J是转动惯量,R是电枢电阻,Tf表示摩擦干扰力矩;Among them, the state variable x1 represents the rotation angle, x2 represents the rotational speed, C e is the back electromotive force coefficient of the motor, u is the control input, K u is the amplification factor of the PWM driver, K m is the torque coefficient, J is the moment of inertia, and R is Armature resistance, T f represents the frictional disturbance torque; (2)设计滑模控制率(2) Design sliding mode control rate r表示给定信号,角位置和角速度的跟踪误差分别是r represents the given signal, the tracking errors of angular position and angular velocity are respectively e=r-x1 (2)e=rx 1 (2) 设计切换函数sDesign switching function s 其中c表示切换面的参数,c越大,使系统的响应速度越快,但稳定性会受到影响;Where c represents the parameter of the switching surface, the larger c is, the faster the response speed of the system will be, but the stability will be affected; 采用指数趋近律Exponential reaching law 其中ε>0,k>0,ε是等速趋近项系数,k是指数趋近项系数,都需要人为适当选取,结合式(1)和(4)得Among them, ε>0, k>0, ε is the coefficient of the constant velocity approach term, and k is the coefficient of the exponential approach term, both of which need to be selected manually. Combining formulas (1) and (4), we get 根据式(5)(6)得到控制率u的表达式According to the formula (5) (6), the expression of the control rate u is obtained 上式中除了摩擦力矩Tf外,其余物理量都是已知的,下面采用扰动观测器的方式来观测摩擦力矩;In the above formula, except for the friction torque T f , other physical quantities are known, and the disturbance observer is used to observe the friction torque below; (3)根据直流电机的模型设计扰动观测器,扰动观测器的输出值是等效到伺服系统输入端的等效摩擦力矩的估计值下面的式子表示了它与其他物理量的关系,(3) Design the disturbance observer according to the model of the DC motor, and the output value of the disturbance observer is the estimated value of the equivalent friction torque equivalent to the input end of the servo system The following formula expresses its relationship with other physical quantities, 其中是电机转速,Gn-1(s)是被控对象名义传递函数的逆,U(s)是控制器的输出,Q(s)表示一个低通滤波器,其表达式选择为in is the motor speed, Gn -1 (s) is the inverse of the nominal transfer function of the controlled object, U(s) is the output of the controller, Q(s) represents a low-pass filter, and its expression is chosen as 其中时间常数τ根据系统的带宽适当选取;The time constant τ is properly selected according to the bandwidth of the system; 将式(8)乘以系数之后得到真实摩擦力矩的估计值,Multiply equation (8) by the coefficient Then an estimate of the true friction torque is obtained, 最终结合式(7)和式(10)得到的控制率完成滑模扰动观测器的设计。Finally, the control rate obtained by combining formula (7) and formula (10) is used to complete the design of the sliding mode disturbance observer.
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