CN111007716A - Alternating current servo motor variable discourse domain fuzzy PI control method based on prediction function - Google Patents
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Abstract
Description
技术领域technical field
本发明涉及伺服电机控制技术领域,具体涉及一种基于预测函数的交流伺服电机变论域模糊PI控制方法。The invention relates to the technical field of servo motor control, in particular to a variable universe fuzzy PI control method of an AC servo motor based on a prediction function.
背景技术Background technique
交流伺服电机是把电能转变为机械能的一种机器,由一个用以产生磁场的电磁铁绕组或分布的定子绕组和一个旋转电枢或转子组成。交流伺服电机具有运行稳定、速度可控性好、响应速度快等优势,目前已广泛应用于数控机床、工业机器人、医疗器械等设备。随着工业生产的不断发展,对交流伺服电机控制也提出了越来越高的要求,研究高性能的伺服控制系统已成为提高装备制造业水平的关键问题之一。An AC servo motor is a machine that converts electrical energy into mechanical energy, consisting of an electromagnet winding or distributed stator winding for generating a magnetic field and a rotating armature or rotor. AC servo motors have the advantages of stable operation, good speed controllability and fast response speed, and have been widely used in CNC machine tools, industrial robots, medical equipment and other equipment. With the continuous development of industrial production, higher and higher requirements are also put forward for the control of AC servo motors, and the study of high-performance servo control systems has become one of the key issues to improve the level of equipment manufacturing.
现有技术中存在的主要问题和不足包括:The main problems and deficiencies in the prior art include:
PI控制器具有结构简单、鲁棒性强和易于实现等特点,目前仍是交流伺服电机最常用的控制策略。但是,固定增益的PI控制参数处理时变工作状态的能力较弱,无法有效应对伺服电机运转过程中的传感器延时、关键参数时变、未知的负载扰动等各类非线性问题。因此,为进一步提升控制性能,PI控制器需要与其他控制策略结合形成复合控制策略,从而实现控制参数在线自适应。PI controller has the characteristics of simple structure, strong robustness and easy implementation, and is still the most commonly used control strategy for AC servo motors. However, the fixed-gain PI control parameters have a weak ability to deal with time-varying working states, and cannot effectively deal with various nonlinear problems such as sensor delays, time-varying key parameters, and unknown load disturbances during the operation of the servo motor. Therefore, in order to further improve the control performance, the PI controller needs to be combined with other control strategies to form a composite control strategy, so as to realize online self-adaptation of control parameters.
模糊PI控制策略结合了模糊控制的非线性控制能力和PI控制良好的适应性,已在交流伺服系统的控制中得到了应用。它能够利用专家知识构建模糊规则库,基于模糊推理在线调整PI控制增益,避免了复杂耗时的系统模型辨识过程。其局限性在于模糊PI控制器的自适应能力严重依赖于模糊规则的数量,同时模糊规则缺乏理论的设计方法。若要进一步提升模糊控制的调节精度,则需要丰富的电机控制经验来设计复杂详细的模糊规则。当交流伺服电机的应用工况比较复杂时,高性能的模糊PI控制器设计比较困难,这限制了模糊PI控制在电机控制领域的进一步推广。因此,需要探索简单有效的控制策略,进一步提升模糊PI控制的自抗扰能力和动态响应性能。The fuzzy PI control strategy combines the nonlinear control ability of fuzzy control and the good adaptability of PI control, and has been applied in the control of AC servo system. It can use expert knowledge to build a fuzzy rule base, and adjust the PI control gain online based on fuzzy reasoning, avoiding the complex and time-consuming system model identification process. Its limitation is that the adaptive ability of the fuzzy PI controller depends heavily on the number of fuzzy rules, and the fuzzy rules lack theoretical design methods. To further improve the regulation accuracy of fuzzy control, rich experience in motor control is required to design complex and detailed fuzzy rules. When the application conditions of AC servo motors are complex, it is difficult to design a high-performance fuzzy PI controller, which limits the further promotion of fuzzy PI control in the field of motor control. Therefore, it is necessary to explore simple and effective control strategies to further improve the active disturbance rejection capability and dynamic response performance of fuzzy PI control.
发明内容SUMMARY OF THE INVENTION
针对现有技术中存在的上述问题和不足,本发明提供了一种基于预测函数的交流伺服电机变论域模糊PI控制方法,该方法采用变论域策略动态调整模糊规则的控制范围,改变在当前模糊控制器输入附近的规则数量,克服模糊控制规则设计困难导致控制性能不足的问题;同时,利用预测函数控制预测交流伺服电机控制系统未来的状态,为变论域模糊控制器提供输入信息,使得模糊控制器及PI控制器的参数能够得到快速调整。In view of the above problems and deficiencies existing in the prior art, the present invention provides a variable universe fuzzy PI control method for an AC servo motor based on a prediction function, which adopts the variable universe strategy to dynamically adjust the control range of the fuzzy rules, and changes the The number of rules near the input of the current fuzzy controller overcomes the problem of insufficient control performance caused by the difficulty of fuzzy control rule design; at the same time, the prediction function control is used to predict the future state of the AC servo motor control system, providing input information for the variable universe fuzzy controller, The parameters of fuzzy controller and PI controller can be adjusted quickly.
为此,本发明采用了以下技术方案:For this reason, the present invention adopts the following technical solutions:
一种基于预测函数的交流伺服电机变论域模糊PI控制方法,包括PI控制器、变论域模糊控制器和预测函数控制模块,所述PI控制器作为主控器,用于调节交流伺服电机转速;所述预测函数控制模块根据系统当前的输入指令、控制信号和反馈输出预测系统的未来状态;所述变论域模糊控制器以预测信息作为输入在线调整PI控制器的增益;设计变论域伸缩因子,利用预测信息超前在线调节变论域模糊控制器的论域,间接增加用于调整PI控制器增益的模糊规则。A variable universe fuzzy PI control method for an AC servo motor based on a prediction function, comprising a PI controller, a variable universe fuzzy controller and a prediction function control module. The PI controller acts as a main controller and is used to adjust the AC servo motor rotation speed; the prediction function control module predicts the future state of the system according to the current input command, control signal and feedback output of the system; the variable universe fuzzy controller uses the prediction information as input to adjust the gain of the PI controller online; design variable theory The domain scaling factor uses the prediction information to adjust the universe of variable universe fuzzy controller ahead of time, and indirectly increases the fuzzy rules used to adjust the gain of the PI controller.
进一步地,包括以下步骤:Further, the following steps are included:
步骤一,针对交流伺服电机控制系统的特性,对预测函数控制方程进行改进,用于预测系统未来的反馈速度ωp(t+p)、反馈误差e(t+p)及反馈误差变化率Δe(t+p);Step 1: According to the characteristics of the AC servo motor control system, the prediction function control equation is improved to predict the future feedback speed ω p (t+p), feedback error e(t+p) and feedback error change rate Δe of the system (t+p);
步骤二,选择p步后的预测反馈误差e(t+p)和预测反馈误差变化率Δe(t+p)作为变论域模糊控制器的输入变量,其对应的模糊变量为E和ΔE;Step 2: Select the prediction feedback error e(t+p) and the prediction feedback error change rate Δe(t+p) after p steps as the input variables of the variable universe fuzzy controller, and the corresponding fuzzy variables are E and ΔE;
步骤三,分析交流伺服电机的控制过程,基于PI控制参数在不同控制阶段的变化规律设计模糊规则;同时确定模糊控制器的隶属度函数和解模糊化策略,从而设计Mamdani型模糊控制器;
步骤四,设计伸缩因子,在线调整模糊输入论域;Step 4: Design the scaling factor and adjust the fuzzy input universe online;
步骤五,根据Mamdani型模糊推理法则进行模糊推理获得模糊输出量;Step 5, perform fuzzy inference according to the Mamdani fuzzy inference rule to obtain the fuzzy output;
步骤六,对模糊输出量进行清晰化操作,将模糊输出转换为清晰值;Step 6, perform a clearing operation on the fuzzy output, and convert the fuzzy output into a clear value;
步骤七,修改PI控制参数,输出到被控对象,从而根据当前和未来的系统状态调节电机转速。Step 7: Modify the PI control parameters and output them to the controlled object, so as to adjust the motor speed according to the current and future system states.
优选地,步骤一的具体过程如下:Preferably, the specific process of
预测函数控制以一阶自回归模型作为交流伺服电机控制系统的预测模型:ω(t)=aω(t-1)+biq(t-1),式中,a和b是模型待辨识的参数,iq(t-1)和ω(t-1)分别是交流伺服电机在t-1时刻的q轴输入电流和反馈输出转速,ω(t)是交流伺服电机在t时刻的输出转速;在交流伺服电机控制系统中,当预测时长不超过伺服系统的闭环响应时间时,q轴输入电流会保持不变,即iq(t+i)=iq(t),i=1,2,3......,p,式中,p为预测步长;The prediction function control uses the first-order autoregressive model as the prediction model of the AC servo motor control system: ω(t)=aω(t-1)+bi q (t-1), where a and b are the models to be identified Parameters, i q (t-1) and ω(t-1) are the q-axis input current and feedback output speed of the AC servo motor at time t-1, respectively, and ω(t) is the output speed of the AC servo motor at time t ; In the AC servo motor control system, when the prediction time does not exceed the closed-loop response time of the servo system, the input current of the q-axis will remain unchanged, that is, i q (t+i)=i q (t), i=1, 2,3...,p, where p is the prediction step size;
根据预测模型可得p步后交流伺服伺服电机的输出为:According to the prediction model, the output of the AC servo motor after p steps can be obtained as:
利用t时刻之前的偏差信息,预测t+p时刻预测模型输出存在的偏差:Using the deviation information before time t, predict the deviation of the output of the prediction model at time t+p:
式中,H={h(t-j)=ω(t-j)-ωm(t-j)|j=1,2,......,p},h(t-j)是t-j时刻的偏差信息;W=[w0,w1,...wj...wp-1]T是偏差权重向量;In the formula, H={h(tj)=ω(tj) -ωm (tj)|j=1,2,...,p}, h(tj) is the deviation information at time tj; W =[w 0 , w 1 ,...w j ...w p-1 ] T is the bias weight vector;
基于以上预测偏差,p步后交流伺服电机的预测输出被修正为:Based on the above prediction deviation, the predicted output of the AC servo motor after p steps is corrected as:
ωp(t+p)=ωm(t+p)+h(t+p);ω p (t+p)=ω m (t+p)+h(t+p);
p步后交流伺服电机的反馈转速误差和误差变化率被预测为:The feedback speed error and error rate of change of the AC servo motor after p steps are predicted as:
e(t+p)=ωr(t+p)-ωp(t+p),e(t+p)= ωr (t+ p )-ωp(t+p),
Δe(t+p)=e(t+p)-e(t+p-1)。Δe(t+p)=e(t+p)−e(t+p−1).
优选地,步骤二的具体过程如下:Preferably, the specific process of
将输入变量从自然论域映射到模糊论域其量化因子为ηe和ηΔe,相应的计算公式为:remove input variables from the natural universe Mapping to Fuzzy Universe Its quantization factors are η e and η Δe , and the corresponding calculation formulas are:
式中,和分别为自然论域和模糊论域的最大值,xi代表输入变量e(t+p)或Δe(t+p),ui代表模糊变量E或ΔE,k代表输入量化因子ηe或ηΔe且可以通过公式来确定。In the formula, and are the maximum values of the natural universe and the fuzzy universe, respectively, x i represents the input variable e(t+p) or Δe(t+p), ui represents the fuzzy variable E or ΔE, and k represents the input quantization factor η e or η Δe and can be obtained by the formula to make sure.
优选地,步骤三中使用的模糊语言变量为{N,Z,P},分别表示{负,零,正};在模糊推理之前,模糊数值变量通过隶属度函数进行模糊化处理,转换为模糊语言变量;在模糊论域的零点附近和两侧分别为三角型和高斯型隶属度函数。Preferably, the fuzzy linguistic variables used in
优选地,步骤四中伸缩因子的计算公式为:Preferably, the calculation formula of the scaling factor in step 4 is:
式中,ui是模糊化后的输入变量,是对称型模糊论域的最大值,ε是任意的非零最小正值且τ∈[0.5,1)。where ui is the input variable after fuzzification, is the maximum value of the symmetric fuzzy universe, ε is any non-zero minimum positive value and τ∈[0.5,1).
优选地,步骤五中模糊输出量为yΔk(e(t+p),Δe(t+p)),其中yΔk代表PI调整值的模糊量和 Preferably, the fuzzy output in step 5 is y Δk (e(t+p), Δe(t+p)), where y Δk represents the blurring of the PI adjustment value and
进一步地,根据Mamdani型模糊推理准则和公式,变论域模糊控制器的每条规则的开火度可计算为:Further, according to the Mamdani-type fuzzy inference criterion and formula, the firing rate of each rule of the variable universe fuzzy controller can be calculated as:
式中,η(·)是模糊变量Ei和ΔEi的隶属度,∧是取大算子,角标Δk代表Δkp或Δki;In the formula, η( ) is the membership degree of fuzzy variables E i and ΔE i , ∧ is the operator that takes the larger value, and the index Δk represents Δk p or Δk i ;
根据重心法去模糊化策略,模糊控制器的模糊输出为According to the defuzzification strategy of the center of gravity method, the fuzzy output of the fuzzy controller is
式中,yΔk代表和Cj代表模糊输出论域的离散值。In the formula, y Δk represents and C j represents the discrete value of the fuzzy output universe.
优选地,步骤六的具体过程如下:Preferably, the specific process of step 6 is as follows:
根据输出量化因子α0和β0对模糊输出量进行清晰化操作,将模糊输出转换为清晰值(Δkp,Δki);设计优化系数ζk对输出量化因子进行在线调整,其计算公式为:According to the output quantization factors α 0 and β 0 , the fuzzy output is sharpened, and the fuzzy output is converted into sharp values (Δk p , Δk i ); the output quantization factor is adjusted online by designing the optimization coefficient ζ k , and the calculation formula is: :
ζΔk=γ+yΔk(e(t+p),Δe(t+p)),ζ Δk =γ+y Δk (e(t+p),Δe(t+p)),
式中,γ是中点为0的模糊论域的最大值,角标Δk代表用于生成Δkp的参数或者用于生成Δki的参数;In the formula, γ is the maximum value of the fuzzy universe whose midpoint is 0, and the index Δk represents the parameter used to generate Δk p or the parameter used to generate Δki;
输出量化因子在线更新公式为:The online update formula of the output quantization factor is:
PI控制参数调整量(Δkp,Δki)根据如下公式更新:The PI control parameter adjustment amount (Δk p , Δk i ) is updated according to the following formula:
优选地,步骤七中控制参数的计算公式如下:Preferably, the calculation formula of the control parameter in step 7 is as follows:
其中,kp0、ki0分别表示PI控制器的初始参数。Among them, k p0 and k i0 respectively represent the initial parameters of the PI controller.
本发明中,首先基于预测函数控制理论,设计交流伺服电机控制的预测模型,预测p步后的电机转速和反馈转速误差;然后,构建变论域模糊控制器,模糊控制器的输入模糊论域通过伸缩因子实现自适应,输出量化因子依靠根据模糊输出设计的优化系数在线调整;最后,以预测信息作为变论域模糊控制器的输入变量,进行模糊推理在线修正PI控制参数。In the present invention, firstly, based on the prediction function control theory, a prediction model for AC servo motor control is designed to predict the motor speed and feedback speed error after p steps; then, a variable universe fuzzy controller is constructed, and the input fuzzy universe of the fuzzy controller is Self-adaptation is realized by scaling factor, and the output quantization factor is adjusted online by the optimization coefficient designed according to the fuzzy output.
与现有技术相比,本发明的有益效果是:Compared with the prior art, the beneficial effects of the present invention are:
(1)本发明针对交流伺服电机的运动特性对预测函数控制策略进行了改进,所设计的预测模型在保持良好预测精度的基础上,具有在线计算量小的优势。(1) The present invention improves the prediction function control strategy according to the motion characteristics of the AC servo motor, and the designed prediction model has the advantage of small online calculation amount on the basis of maintaining good prediction accuracy.
(2)本发明设计变论域模糊控制器能够通过输入模糊论域的自适应调整增加当前输入下的模糊规则数量,保证模糊规则不足的情况下仍具有实用的控制精度;同时,输出量化因子通过优化系数在线调整,强化了模糊控制的效果。(2) The variable universe fuzzy controller designed in the present invention can increase the number of fuzzy rules under the current input through self-adaptive adjustment of the input fuzzy universe, so as to ensure that the fuzzy rules still have practical control accuracy; at the same time, the output quantization factor Through the online adjustment of the optimization coefficient, the effect of fuzzy control is strengthened.
(3)本发明以预测信息作为优化模糊控制参数和PI控制参数的输入,有效提高了系统的动态响应性能,特别是在系统受到扰动时,能够及时调整控制输入使系统回归稳定状态。(3) The present invention uses prediction information as the input to optimize the fuzzy control parameters and PI control parameters, which effectively improves the dynamic response performance of the system, especially when the system is disturbed, the control input can be adjusted in time to make the system return to a stable state.
(4)本发明继承了变论域模糊控制精度较高的优势,并提高了动态响应性能和抗扰动能力,对于具有不确定扰动和非线性较大的应用场合,其优势更加突出。(4) The present invention inherits the advantages of high precision of variable universe fuzzy control, and improves dynamic response performance and anti-disturbance capability, and has more prominent advantages for applications with uncertain disturbance and large nonlinearity.
附图说明Description of drawings
图1是本发明所提供的一种基于预测函数的交流伺服电机变论域模糊PI控制方法的控制结构示意图。FIG. 1 is a schematic diagram of the control structure of a variable universe fuzzy PI control method for an AC servo motor based on a prediction function provided by the present invention.
图2是本发明实施例所提供的一种基于预测函数的交流伺服电机变论域模糊PI控制方法中交流伺服电机调速系统的结构组成示意图。2 is a schematic structural composition diagram of an AC servo motor speed regulation system in a variable universe fuzzy PI control method for an AC servo motor based on a prediction function provided by an embodiment of the present invention.
图3是本发明实施例所提供的一种基于预测函数的交流伺服电机变论域模糊PI控制方法的控制结构示意图。3 is a schematic diagram of a control structure of a variable universe fuzzy PI control method for an AC servo motor based on a prediction function provided by an embodiment of the present invention.
图4是本发明实施例所提供的模糊规则组成示意图。FIG. 4 is a schematic diagram of the composition of fuzzy rules provided by an embodiment of the present invention.
图5是本发明实施例所提供的隶属度函数示意图。FIG. 5 is a schematic diagram of a membership function provided by an embodiment of the present invention.
具体实施方式Detailed ways
下面结合附图以及具体实施例来详细说明本发明,其中的具体实施例以及说明仅用来解释本发明,但并不作为对本发明的限定。The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments, wherein the specific embodiments and descriptions are only used to explain the present invention, but are not intended to limit the present invention.
如图1所示,本发明公开了一种基于预测函数的交流伺服电机变论域模糊PI控制方法,包括PI控制器、变论域模糊控制器和预测函数控制模块,所述PI控制器作为主控器,用于调节交流伺服电机转速;所述预测函数控制模块根据系统当前的输入指令、控制信号和反馈输出预测系统的未来状态;所述变论域模糊控制器以预测信息作为输入在线调整PI控制器的增益;设计变论域伸缩因子,利用预测信息超前在线调节变论域模糊控制器的论域,间接增加用于调整PI控制器增益的模糊规则。As shown in FIG. 1 , the present invention discloses a variable universe fuzzy PI control method for an AC servo motor based on a prediction function, including a PI controller, a variable universe fuzzy controller and a prediction function control module. The PI controller acts as a The main controller is used to adjust the rotational speed of the AC servo motor; the prediction function control module predicts the future state of the system according to the current input command, control signal and feedback output of the system; the variable universe fuzzy controller takes the prediction information as input online Adjust the gain of the PI controller; design the variable universe scaling factor, use the prediction information to adjust the universe of the variable universe fuzzy controller ahead of time, and indirectly increase the fuzzy rules for adjusting the gain of the PI controller.
具体包括以下步骤:Specifically include the following steps:
(1)针对交流伺服电机控制系统的特性,对预测函数控制方程进行改进,以便更好预测系统未来的反馈速度ωp(t+p)、反馈误差e(t+p)及反馈误差变化率Δe(t+p)。(1) According to the characteristics of the AC servo motor control system, the prediction function control equation is improved to better predict the future feedback speed ω p (t+p), feedback error e(t+p) and feedback error rate of change of the system Δe(t+p).
(2)选择p步后的预测反馈误差e(t+p)和预测反馈误差变化率Δe(t+p)作为模糊控制器的输入变量,其对应的模糊变量为E和ΔE。因为自然论域中的输入量为清晰值而模糊论域中的输入量为模糊值,因此需要将输入变量从自然论域映射到模糊论域其量化因子为ηe和ηΔe,相应的计算公式为:(2) Select the prediction feedback error e(t+p) after p steps and the prediction feedback error change rate Δe(t+p) as the input variables of the fuzzy controller, and the corresponding fuzzy variables are E and ΔE. Because the input quantities in the natural universe are clear values and the input quantities in the fuzzy universe are fuzzy values, it is necessary to change the input variables from the natural universe Mapping to Fuzzy Universe Its quantization factors are η e and η Δe , and the corresponding calculation formulas are:
式(1)中,和分别为自然论域和模糊论域的最大值,xi代表输入变量e(t+p)或Δe(t+p),ui代表模糊变量E或ΔE,k代表输入量化因子ηe或ηΔe且可以通过公式来确定。In formula (1), and are the maximum values of the natural universe and the fuzzy universe, respectively, x i represents the input variable e(t+p) or Δe(t+p), ui represents the fuzzy variable E or ΔE, and k represents the input quantization factor η e or η Δe and can be obtained by the formula to make sure.
(3)分析交流伺服电机的控制过程,基于PI控制参数在不同控制阶段的变化规律设计模糊规则;同时确定模糊控制器的隶属度函数和解模糊化策略,从而设计Mamdani型模糊控制器。(3) Analyze the control process of AC servo motor, and design fuzzy rules based on the variation law of PI control parameters in different control stages; at the same time, determine the membership function and defuzzification strategy of the fuzzy controller, so as to design the Mamdani fuzzy controller.
(4)设计伸缩因子,在线调整模糊输入论域,计算公式为(4) Design the scaling factor and adjust the fuzzy input universe online. The calculation formula is:
式(2)中,ui是模糊化后的输入变量,是对称型模糊论域的最大值,ε是任意的非零最小正值且τ∈[0.5,1)。In formula (2), ui is the input variable after fuzzification, is the maximum value of the symmetric fuzzy universe, ε is any non-zero minimum positive value and τ∈[0.5,1).
(5)根据Mamdani型模糊推理法则进行模糊推理获得模糊输出量yΔk(e(t+p),Δe(t+p)),其中yΔk代表PI调整值的模糊量和 (5) Perform fuzzy inference according to the Mamdani fuzzy inference rule to obtain the fuzzy output y Δk (e(t+p), Δe(t+p)), where y Δk represents the fuzzy quantity of the PI adjustment value and
(6)根据输出量化因子α0和β0对模糊输出量进行清晰化操作,将模糊输出转换为清晰值(Δkp,Δki)。本发明设计优化系数ζk对输出量化因子进行在线调整,其计算公式为:(6) Perform a sharpening operation on the fuzzy output according to the output quantization factors α 0 and β 0 , and convert the fuzzy output into sharp values (Δk p , Δki ). The invention designs the optimization coefficient ζ k to adjust the output quantization factor online, and its calculation formula is:
ζΔk=γ+yΔk(e(t+p),Δe(t+p)) (3)ζ Δk =γ+y Δk (e(t+p),Δe(t+p)) (3)
式(3)中,γ是中点为0的模糊论域的最大值,角标Δk代表用于生成Δkp的参数或者用于生成Δki的参数。In formula (3), γ is the maximum value of the fuzzy universe whose midpoint is 0, and the index Δk represents the parameter used to generate Δk p or the parameter used to generate Δki.
因此,本发明的输出量化因子在线更新公式为:Therefore, the online update formula of the output quantization factor of the present invention is:
本发明的PI控制参数调整量(Δkp,Δki)根据如下公式更新:The PI control parameter adjustment amount (Δk p , Δk i ) of the present invention is updated according to the following formula:
(7)修改PI控制参数,输出到被控对象,从而根据当前和未来的系统状态调节电机转速。(7) Modify the PI control parameters and output to the controlled object, so as to adjust the motor speed according to the current and future system states.
此外,作为本发明的进一步改进,步骤(1)的具体如下:In addition, as a further improvement of the present invention, the details of step (1) are as follows:
本发明的预测函数控制以一阶自回归模型作为交流伺服电机控制系统的预测模型:ω(t)=aω(t-1)+biq(t-1),式中,a和b是模型待辨识的参数,iq(t-1)和ω(t-1)分别是交流伺服电机在t-1时刻的q轴输入电流和反馈输出转速。在交流伺服电机控制系统中,当预测时长不超过伺服系统的闭环响应时间时,q轴输入电流会保持不变,即iq(t+i)=iq(t),i=1,2,3......,p,式中,p为预测步长。The prediction function control of the present invention uses the first-order autoregressive model as the prediction model of the AC servo motor control system: ω(t)=aω(t-1)+bi q (t-1), where a and b are the models The parameters to be identified, i q (t-1) and ω (t-1) are the q-axis input current and feedback output speed of the AC servo motor at time t-1, respectively. In the AC servo motor control system, when the prediction time does not exceed the closed-loop response time of the servo system, the input current of the q-axis will remain unchanged, that is, i q (t+i)=i q (t), i=1,2 ,3...,p, where p is the prediction step size.
因此,本发明中,根据预测模型可得p步后交流伺服伺服电机的输出为:Therefore, in the present invention, according to the prediction model, the output of the AC servo motor after p steps can be obtained as:
因为模型辨识误差的存在及外界干扰的影响,以上预测输出不可避免的与实际控制输出存在偏差。因此,可以利用t时刻之前的偏差信息,预测t+p时刻预测模型输出存在的偏差:Due to the existence of model identification errors and the influence of external disturbances, the above predicted output inevitably deviates from the actual control output. Therefore, the deviation information before time t can be used to predict the deviation of the output of the prediction model at time t+p:
式(8)中,H={h(t-j)=ω(t-j)-ωm(t-j)|j=1,2,......,p},h(t-j)是t-j时刻的偏差信息;W=[w0,w1,...wj...wp-1]T是偏差权重向量。In formula (8), H={h(tj)=ω(tj) -ωm (tj)|j=1,2,...,p}, h(tj) is the deviation at time tj Information; W = [w 0 , w 1 , ... w j ... w p-1 ] T is the bias weight vector.
基于以上预测偏差,p步后交流伺服电机的预测输出被修正为Based on the above prediction deviation, the predicted output of the AC servo motor after p steps is corrected as
ωp(t+p)=ωm(t+p)+h(t+p) (9)ω p (t+p)=ω m (t+p)+h(t+p) (9)
同时,p步后交流伺服电机的反馈转速误差和误差变化率可被预测为:At the same time, the feedback speed error and error change rate of the AC servo motor after p steps can be predicted as:
e(t+p)=ωr(t+p)-ωp(t+p) (10)e(t+p)=ω r (t+p)-ω p (t+p) (10)
Δe(t+p)=e(t+p)-e(t+p-1) (11)Δe(t+p)=e(t+p)-e(t+p-1) (11)
实施例Example
一种基于预测函数的交流伺服电机变论域模糊PI控制方法,其中,基于PI控制策略的交流伺服电机调速系统采用如图2所示的控制结构,电机等效为一阶传递函数图中ωr是输入指令速度,ω是反馈速度,iq是q轴指令电流,Kf是力矩系数,J是电机转动惯量,B是粘性摩擦系数,Tl是包括负载力矩、摩擦转矩以及齿槽转矩等的负载扰动。虽然交流伺服电机调速系统是典型的非线性复杂系统,但是在不影响控制效果的前提下可以进行线性化处理。本实施例中,交流伺服电机调速系统采用一阶自回归模型(ARX)来描述:A variable universe fuzzy PI control method of AC servo motor based on prediction function, in which, the AC servo motor speed regulation system based on PI control strategy adopts the control structure shown in Figure 2, and the motor is equivalent to a first-order transfer function In the figure, ω r is the input command speed, ω is the feedback speed, i q is the q-axis command current, K f is the torque coefficient, J is the motor moment of inertia, B is the viscous friction coefficient, and T l is the load torque and friction torque. and load disturbances such as cogging torque. Although the AC servo motor speed control system is a typical nonlinear complex system, it can be linearized without affecting the control effect. In this embodiment, the AC servo motor speed control system adopts a first-order autoregressive model (ARX) to describe:
ω(t)=aω(t-1)+biq(t-1) (12)ω(t)=aω(t-1)+bi q (t-1) (12)
式(12)中,a和b是待辨识的模型参数。各类扰动对系统的影响可等效为模型参数的变化。In formula (12), a and b are the model parameters to be identified. The influence of various disturbances on the system can be equivalent to the change of model parameters.
本实施例的基于预测函数控制的变论域模糊PI控制策略如图3所示,在传统PI控制策略的基础上引入了预测函数控制模块和变论域模糊控制模块。反馈转速ω(t)与输入转速指令ωr(t)进行对比获得误差e(t),此误差经过PI控制模块转换为控制电机转速的q轴电流。为提高这一控制过程的响应速度和精度,需要根据系统的状态在线调整PI控制参数。具体步骤如下:The variable universe fuzzy PI control strategy based on predictive function control in this embodiment is shown in FIG. 3 , and a predictive function control module and a variable universe fuzzy control module are introduced on the basis of the traditional PI control strategy. The feedback speed ω(t) is compared with the input speed command ω r (t) to obtain the error e(t), which is converted into the q-axis current that controls the motor speed through the PI control module. In order to improve the response speed and accuracy of this control process, it is necessary to adjust the PI control parameters online according to the state of the system. Specific steps are as follows:
步骤1:首先利用预测函数控制模块预测系统未来的状态,以此为变论域模糊控制提供输入参考信息。在交流伺服电机控制系统中,闭环响应时间内的输入电流指令iq会保持不变。预测步长p在闭环响应时间内,则Step 1: First, use the prediction function control module to predict the future state of the system, so as to provide input reference information for the variable universe fuzzy control. In the AC servo motor control system, the input current command i q within the closed-loop response time will remain unchanged. The prediction step p is within the closed-loop response time, then
iq(t+i)=iq(t),i=1,2,3......,p (13)i q (t+i)=i q (t),i=1,2,3...,p (13)
根据式(12)和(13),利用数学归纳法,可得交流伺服电机的预测转速为According to equations (12) and (13), using mathematical induction, the predicted speed of the AC servo motor can be obtained as
式(14)中,ap+1代表a的p+1次方。In formula (14), a p+1 represents a raised to the p+1 power.
以上基于模型预测的电机转速不可避免的会与实际转速存在误差,为进一步提高预测精度,可利用之前预测值与实际值之间的偏差信息H预测ωm与未来的实际输出ω(t+p)存在的偏差h(t+p),从而基于此偏差对ωm(t+p)进行修正,其公式为:The motor speed predicted based on the above model will inevitably have errors with the actual speed. In order to further improve the prediction accuracy, the deviation information H between the previous predicted value and the actual value can be used to predict ω m and the future actual output ω(t+p ) existing deviation h(t+p), so as to correct ω m (t+p) based on this deviation, the formula is:
ωp(t+p)=ωm(t+p)+h(t+p) (15)ω p (t+p)=ω m (t+p)+h(t+p) (15)
其中,in,
式(16)中,H={h(t-j)=ω(t-j)-ωm(t-j)|j=1,2,......,p},W是权重系数wj的集合,W=[w1,w2,...wj...wp]T。In formula (16), H={h(tj)=ω(tj) -ωm (tj)|j=1,2,...,p}, W is the set of weight coefficients w j , W=[w 1 , w 2 , ... w j ... w p ] T .
同时,根据输入指令轨迹可预测p步后的输入指令ωr(t+p)。因此,p步后电机实际转速与指令转速的差值可通过如下公式预测:At the same time, the input command ω r (t+p) after p steps can be predicted according to the input command trajectory. Therefore, the difference between the actual speed of the motor and the commanded speed after p steps can be predicted by the following formula:
e(t+p)=ωr(t+p)-ωp(t+p) (17)e(t+p)= ωr (t+ p )-ωp(t+p) (17)
相应的误差变化率为:The corresponding error rate of change is:
Δe(t+p)=e(t+p)-e(t+p-1) (18)Δe(t+p)=e(t+p)-e(t+p-1) (18)
步骤2:设计变论域模糊控制器,以e(t+p)和Δe(t+p)作为控制器输入进行模糊推理在线调整PI控制参数。因为e(t+p)和Δe(t+p)都是自然论域内的清晰值,而模糊推理使用的是模糊值,因此需要使用输入量化因子ηe或ηΔe将其从自然论域映射到模糊论域计算公式为:Step 2: Design a variable universe fuzzy controller, and use e(t+p) and Δe(t+p) as controller inputs to perform fuzzy reasoning to adjust PI control parameters online. Because both e(t+p) and Δe(t+p) are clear values in the natural universe, and fuzzy inference uses fuzzy values, it needs to be converted from the natural universe using the input quantization factor η e or η Δe Mapping to Fuzzy Universe The calculation formula is:
式(19)中,和分别为自然论域和模糊论域的最大值,xi代表输入变量e(t+p)或Δe(t+p),ui代表模糊变量E或ΔE,k代表输入量化因子ηe或ηΔe且可以通过公式来确定。In formula (19), and are the maximum values of the natural universe and the fuzzy universe, respectively, x i represents the input variable e(t+p) or Δe(t+p), ui represents the fuzzy variable E or ΔE, and k represents the input quantization factor η e or η Δe and can be obtained by the formula to make sure.
本实施例中模糊控制器使用的模糊规则如图4所示,只包含9条规则。根据Mamdani型模糊推理原理,这些规则的基本结构为:“如果误差E为A,误差变化率ΔE为B,则PI控制器比例增益调整量为C,积分增益调整量为D”,其中,A、B、C和D代表模糊语言变量。本实施例中使用的模糊语言变量为{N,Z,P},分别表示{负,零,正}。The fuzzy rules used by the fuzzy controller in this embodiment are shown in FIG. 4 , and only include 9 rules. According to the Mamdani-type fuzzy reasoning principle, the basic structure of these rules is: "If the error E is A and the error rate of change ΔE is B, then the proportional gain adjustment of the PI controller is C, and the integral gain adjustment is D", where A , B, C, and D represent fuzzy linguistic variables. The fuzzy linguistic variables used in this embodiment are {N, Z, P}, which represent {negative, zero, positive} respectively.
在模糊推理之前,模糊数值变量需要通过隶属度函数进行模糊化处理,转换为模糊语言变量。本实施例使用的隶属度函数如图5所示,在模糊论域的零点附近和两侧分别为三角型和高斯型隶属度函数。可以看出,在零点附近参与控制的模糊规则较少。为动态增加模糊规则数量,可通过伸缩因子调整模糊论域来实现:Before fuzzy inference, fuzzy numerical variables need to be fuzzified by membership function and converted into fuzzy linguistic variables. The membership functions used in this embodiment are shown in FIG. 5 , which are triangular and Gaussian membership functions near and on both sides of the zero point of the fuzzy universe. It can be seen that there are fewer fuzzy rules involved in control near the zero point. In order to dynamically increase the number of fuzzy rules, the fuzzy domain of discourse can be adjusted by the scaling factor:
式(20)中,ε为任意的非零最小正值且τ∈[0.5,1).In formula (20), ε is any non-zero minimum positive value and τ∈[0.5,1).
定义关于输入xi的伸缩函数g(xi),以用来计算变论域后的模糊变量:Define a scaling function g(x i ) with respect to the input x i to calculate the fuzzy variable after the variable universe:
根据Mamdani型模糊推理准则和公式,变论域模糊控制器的每条规则的开火度可计算为:According to the Mamdani-type fuzzy inference criterion and formula, the firing rate of each rule of the variable universe fuzzy controller can be calculated as:
式(22)中,η(·)是模糊变量Ei和ΔEi的隶属度,∧是取大算子,角标Δk代表Δkp或Δki。In formula (22), η(·) is the membership degree of the fuzzy variables E i and ΔE i , ∧ is the operator that takes the larger value, and the superscript Δk represents Δk p or Δk i .
根据重心法去模糊化策略,模糊控制器的模糊输出为According to the defuzzification strategy of the center of gravity method, the fuzzy output of the fuzzy controller is
式(23)中,yΔk代表和Cj代表模糊输出论域的离散值。In formula (23), y Δk represents and C j represents the discrete value of the fuzzy output universe.
通过输出量化因子α0和β0对模糊输出量进行清晰化操作,将其转为优化PI控制器的清晰值(Δkp,Δki)。为强化模糊控制器的输出效果,本实施例设计了自适应输出量化因子:Through the output quantization factor α 0 and β 0 to the fuzzy output A sharpening operation is performed to convert it into sharpening values (Δk p , Δki ) for the optimized PI controller. In order to strengthen the output effect of the fuzzy controller, this embodiment designs an adaptive output quantization factor:
其中,in,
式(25)中,γ是中点为0的模糊论域的最大值。In formula (25), γ is the maximum value of the fuzzy universe whose midpoint is 0.
根据自适应输出量化因子,可得PI参数的调整值:According to the adaptive output quantization factor, the adjustment value of the PI parameter can be obtained:
通过预测函数控制模块和变论域模糊控制器,PI控制器的参数得到了在线自适应调整:Through the predictive function control module and the variable universe fuzzy controller, the parameters of the PI controller are adaptively adjusted online:
式(27)中,kp0和ki0是PI控制器的初始参数。In formula (27), k p0 and k i0 are the initial parameters of the PI controller.
针对交流伺服电机调速系统中的时滞、不确定性扰动或参数时变等非线性因素,本发明提供了基于预测函数控制的变论域模糊PI控制策略,弥补了传统PI控制器缺乏自适应性的缺陷。相对传统的模糊PI控制策略,本发明具有更好的响应性能、精度以及实用性。Aiming at nonlinear factors such as time delay, uncertain disturbance or time-varying parameters in the AC servo motor speed regulation system, the present invention provides a variable universe fuzzy PI control strategy based on predictive function control, which makes up for the lack of automatic control of traditional PI controllers. Adaptive deficiencies. Compared with the traditional fuzzy PI control strategy, the present invention has better response performance, precision and practicability.
以上所述仅为本发明的较佳实施例,并不用于限制本发明,凡在本发明的精神和原则范围之内所作的任何修改、等同替换以及改进等,均应包含在本发明的保护范围之内。The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and scope of the present invention shall be included in the protection of the present invention. within the range.
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CN112081913A (en) * | 2020-09-14 | 2020-12-15 | 中国一拖集团有限公司 | AMT transmission variable parameter gear shifting process control method |
CN112350316A (en) * | 2020-11-03 | 2021-02-09 | 河北工业大学 | Variable-discourse-domain cloud PI load frequency control method based on cloud scaling factor |
CN112350316B (en) * | 2020-11-03 | 2022-12-23 | 河北工业大学 | Variable domain cloud PI load frequency control method based on cloud scaling factor |
CN112486100A (en) * | 2020-12-11 | 2021-03-12 | 华中科技大学 | Method for solving control parameter stability domain of alternating current servo system |
CN112486100B (en) * | 2020-12-11 | 2022-02-22 | 华中科技大学 | Method for solving control parameter stability domain of alternating current servo system |
CN112596376A (en) * | 2020-12-14 | 2021-04-02 | 河海大学 | Synchronous phase modulator excitation system optimization control method based on variable-discourse-domain fuzzy self-adaptive PID control |
CN113219821A (en) * | 2021-04-26 | 2021-08-06 | 江苏博尚工业装备有限公司 | Proportional-integral sliding mode surface fuzzy sliding mode position control method for numerical control machine tool |
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CN114355842B (en) * | 2021-12-28 | 2024-03-15 | 中国航空工业集团公司北京长城航空测控技术研究所 | Position and force control switching method and system of electrohydraulic servo loading system |
CN115373267A (en) * | 2022-08-19 | 2022-11-22 | 南阳煜众精密机械有限公司 | A CNC vertical lathe servo system and its tracking precision self-healing control method and application |
CN115373267B (en) * | 2022-08-19 | 2024-09-10 | 南阳煜众精密机械有限公司 | Numerical control vertical lathe servo system, tracking precision self-healing regulation and control method and application thereof |
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