CN107070336A - The two patterns paste fractional order System with Sliding Mode Controller and method of permanent magnet linear synchronous motor - Google Patents
The two patterns paste fractional order System with Sliding Mode Controller and method of permanent magnet linear synchronous motor Download PDFInfo
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Abstract
Description
技术领域technical field
本发明属于数控技术领域，特别涉及一种永磁直线同步电机的二型模糊分数阶滑模系统及方法。The invention belongs to the technical field of numerical control, and in particular relates to a type-two fuzzy fractional-order sliding mode system and method of a permanent magnet linear synchronous motor.
技术背景technical background
数控机床作为传统机器工业制造、重型加工产业的重要基础，随着社会的发展，对高速、高精度的数控加工技术提出了越来越高的要求。传统的数控机床的进给系统主要是“旋转电机+滚珠丝杠”的形式，这种形式中间环节间的正反间隙、摩擦及弹性变形使系统的非线性误差增大，限制其很难达到高速度、高精度技术生产的要求。As the important foundation of traditional machine manufacturing and heavy processing industry, CNC machine tools have put forward higher and higher requirements for high-speed and high-precision CNC machining technology with the development of society. The feed system of traditional CNC machine tools is mainly in the form of "rotary motor + ball screw". The positive and negative gaps, friction and elastic deformation between the intermediate links of this form increase the nonlinear error of the system, and it is difficult to limit it. High-speed, high-precision technical production requirements.
直线电动机传动取消了中间机械传动机构,克服了传统驱动方式的中间传动环节带来的缺点，显著提高了机床的动态灵敏度、加工精度和可靠性，在高精度、快响应的微进给伺服系统中具有非常明显的优势。但由于其直接驱动的特点，负载扰动、电机参数变化等不确定因素直接作用在直线电机动子上，对控制器的设计提出了新的更高的要求。The linear motor transmission cancels the intermediate mechanical transmission mechanism, overcomes the shortcomings brought about by the intermediate transmission link of the traditional drive method, and significantly improves the dynamic sensitivity, machining accuracy and reliability of the machine tool. In the high-precision, fast-response micro-feed servo system has very obvious advantages. However, due to its direct drive characteristics, uncertain factors such as load disturbance and motor parameter changes directly act on the linear motor mover, which puts forward new and higher requirements for the design of the controller.
为了实现高速度高精度直接驱动进给、定位系统，学者们提出了诸多控制策略，如采用自适应控制理论设计控制器，可以有效克服参数变化对系统的影响，但在参数变化较快、外部干扰频率高的情况下则效果不佳。采用滑模变结构控制理论设计控制器，具有鲁棒性强、实现简单的优点，然而由于其控制作用的不连续性会导致抖振现象。把分数阶微积分理论与滑模控制相结合，设计分数阶滑模趋近律，可以使系统状态平滑缓慢地收敛到原点，但同时增加了控制器参数选取的难度。采用模糊控制理论设计控制器，该方法不需对象数学模型、能充分运用控制专家的信息及具有相当鲁棒性的优点，特别在系统存在不确定性因素的情况下，往往优于常规控制的效果，但模糊控制仍面临模糊控制器参数须经反复试凑才能确定，缺少稳定性分析等系统化的分析和综合方法的问题。采用模糊滑模控制理论设计控制器，该方法对系统的模型依赖程度小，能充分运用控制专家的信息及具有相当鲁棒性的优点，减轻或避免了一般滑模控制的抖振现象，但是普通模糊滑模控制器的设计使用一型模糊系统，在实际应用中，因为系统结构的复杂不确定性边界可能不容易获得，一型模糊系统会显得力不从心，在于它使用了由精确隶属度函数表示的一型模糊集合，不能直接处理自身模糊规则的不确定性。In order to realize high-speed and high-precision direct-drive feeding and positioning systems, scholars have proposed many control strategies, such as designing controllers using adaptive control theory, which can effectively overcome the influence of parameter changes on the system, but in the case of rapid parameter changes and external In the case of high interference frequency, the effect is not good. Using the sliding mode variable structure control theory to design the controller has the advantages of strong robustness and simple implementation. However, the discontinuity of its control effect will lead to chattering. Combining fractional calculus theory with sliding mode control and designing fractional order sliding mode reaching law can make the system state converge to the origin smoothly and slowly, but at the same time it increases the difficulty of selecting controller parameters. The fuzzy control theory is used to design the controller. This method does not require the object mathematical model, can make full use of the information of control experts and has the advantages of considerable robustness. Especially when there are uncertain factors in the system, it is often better than conventional control. However, the fuzzy control still faces the problem that the parameters of the fuzzy controller must be determined through trial and error, and there is a lack of systematic analysis and synthesis methods such as stability analysis. The fuzzy sliding mode control theory is used to design the controller. This method has little dependence on the system model, can make full use of the information of control experts and has the advantages of considerable robustness, and reduces or avoids the chattering phenomenon of general sliding mode control, but The design of the ordinary fuzzy sliding mode controller uses a type-one fuzzy system. In practical applications, because the complex uncertainty boundary of the system structure may not be easy to obtain, the type-one fuzzy system will appear to be powerless, because it uses the exact membership function A type of fuzzy set represented by , cannot directly deal with the uncertainty of its own fuzzy rules.
发明内容Contents of the invention
发明目的purpose of invention
针对现有控制技术中存在的不足，本发明提供了一种永磁直线同步电机的二型模糊分数阶滑模控制系统及方法，将滑模控制与分数阶微积分理论、区间二型模糊系统相结合，可以有效地削弱滑模控制抖振现象，且对系统受到参数变化和外部扰动具有不变性，提高系统的鲁棒性，其目的是解决以往所存在的问题。Aiming at the deficiencies in the existing control technology, the present invention provides a type-two fuzzy fractional-order sliding mode control system and method for permanent magnet linear synchronous motors. The combination can effectively weaken the chattering phenomenon of the sliding mode control, and it is invariant to the parameter changes and external disturbances of the system, and the robustness of the system can be improved. The purpose is to solve the existing problems in the past.
技术方案：Technical solutions:
本发明所设计的控制系统包括速度控制器以及整个系统的硬件部分。其中，所述速度控制器使用区间二型模糊分数阶滑模控制设计。The control system designed by the present invention includes the speed controller and the hardware part of the whole system. Wherein, the speed controller is designed using interval-type fuzzy fractional-order sliding mode control.
区间二型模糊分数阶滑模控制器设计包括如下几部分：The design of interval type II fuzzy fractional order sliding mode controller includes the following parts:
1.建立分数阶滑模面。定义系统跟踪误差为：e＝v*-v，其中v*和v分别为系统速度的给定值和实际值，建立如(1)式分数阶PIαDα滑模面1. Establish a fractional sliding mode surface. Define the system tracking error as: e=v * -v, where v * and v are the given value and actual value of the system speed respectively, and establish the fractional order PI α D α sliding mode surface as in formula (1)
其中kp和ki为非零正数；表示分数阶微积分算子，当α(0＜α＜1)时表示分数阶微分，则表示分数阶积分。Where k p and k i are non-zero positive numbers; Represents fractional calculus operator, when α(0<α<1) represents fractional differential, then Represents a fractional order integral.
2.设计滑模控制律为2. Design the sliding mode control law as
u＝ueq+usw (2)u＝u eq +u sw (2)
其中，ueq为等效控制项，由确定，可求得表达式为：Among them, u eq is the equivalent control item, by OK, the expression that can be obtained is:
式中，M为直线电机动子的质量，kf为电磁推力系数，Bv为粘滞摩擦因数，e＝v*-v为系统速度跟踪误差，其中v*和v分别为系统速度的给定值和实际值。In the formula, M is the mass of the linear motor mover, k f is the electromagnetic thrust coefficient, B v is the viscous friction coefficient, e=v * -v is the system speed tracking error, where v * and v are the given speed of the system respectively Fixed value and actual value.
式(2)中usw为切换控制项，计算表达式如下：In formula (2), u sw is the switching control item, and the calculation expression is as follows:
其中，Ks为负的常值，s为滑模面。Among them, K s is a negative constant value, and s is the sliding surface.
将等效控制项ueq和切换控制项usw代入式(2)中，则有：Substituting the equivalent control item u eq and the switching control item u sw into formula (2), then:
由于滑模控制切换项影响着系统的控制性能，如果切换项中的Ks的绝对值取值过大，系统存在较大抖振；反之，系统的鲁棒性降低。由于永磁直线同步电机伺服系统易受不确定因素的扰动，且扰动不易测量，本发明采用区间二型模糊控制器替换(4)式中Kssgn(s)项，区间二型模糊控制器输入为式(1)定义的滑模面s，输出为Δu，则(4)式为Since the switching item of sliding mode control affects the control performance of the system, if the absolute value of K s in the switching item is too large, the system will have large chattering; otherwise, the robustness of the system will decrease. Since the permanent magnet linear synchronous motor servo system is easily disturbed by uncertain factors, and the disturbance is not easy to measure, the present invention replaces the K s sgn(s) item in (4) with an interval type two fuzzy controller, and the interval type two fuzzy controller The input is the sliding surface s defined by formula (1), and the output is Δu, then formula (4) is
将上述控制方法嵌入DSP控制电路中实现对永磁直线同步电机伺服系统的速度控制。The above control method is embedded in the DSP control circuit to realize the speed control of the permanent magnet linear synchronous motor servo system.
3.本发明所设计的二型模糊分数阶滑模控制系统的硬件实现包括主电路、控制电路和控制对象三部分；控制电路包括DSP、位置和速度检测电路、电流检测电路、光耦隔离电路、驱动电路及故障检测和保护电路；主电路包括调压电路、整流滤波单元和IPM逆变单元；控制对象为三相永磁直线同步电机，机身装有光栅尺。DSP的SCI端口连接上位机，DSP的SPI端口连接显示电路，DSP的GPIO端口连接I/O接口电路；故障检测和保护电路连接控制电源。DSP采用TMS320F28335处理器。3. The hardware realization of the designed two-type fuzzy fractional-order sliding mode control system of the present invention comprises main circuit, control circuit and control object three parts; Control circuit comprises DSP, position and speed detection circuit, current detection circuit, optocoupler isolation circuit , drive circuit and fault detection and protection circuit; the main circuit includes a voltage regulating circuit, a rectifier filter unit and an IPM inverter unit; the control object is a three-phase permanent magnet linear synchronous motor, and the body is equipped with a grating ruler. The SCI port of the DSP is connected to the upper computer, the SPI port of the DSP is connected to the display circuit, the GPIO port of the DSP is connected to the I/O interface circuit; the fault detection and protection circuit is connected to the control power supply. DSP adopts TMS320F28335 processor.
4.本发明方法最终由嵌入DSP处理器中的控制程序实现，具体步骤如下：4. the inventive method is finally realized by the control program embedded in the DSP processor, and concrete steps are as follows:
步骤1系统初始化；Step 1 system initialization;
步骤2 DSP系统初始化；Step 2 DSP system initialization;
步骤3初始化寄存器和变量；Step 3 initialize registers and variables;
步骤4初始化中断向量；Step 4 initializes the interrupt vector;
步骤5开中断；Step 5 enable interrupt;
步骤6是否结束运行？是则进行步骤9；Does step 6 end running? If yes, go to step 9;
步骤7是否有通用定时器下溢中断产生，否则进行步骤6；In step 7, whether there is a general-purpose timer underflow interrupt, otherwise proceed to step 6;
步骤8执行T1中断处理子控制程序；进行步骤6；Step 8 executes the T1 interrupt processing sub-control program; proceed to step 6;
步骤9保存数据；Step 9 save the data;
步骤10关中断；Step 10 turn off interrupt;
步骤11结束。Step 11 ends.
其中上述步骤8的T1中断处理子控制程序按以下步骤：Wherein the T1 interrupt processing sub-control program of above-mentioned step 8 follows the steps:
步骤1保护现场；Step 1 protect the site;
步骤2读取编码器值，得到电角度；Step 2 read the encoder value to get the electrical angle;
步骤3电流采样；Step 3 current sampling;
步骤3 CLARK变换；Step 3 CLARK transformation;
步骤5 PARK变换；Step 5 PARK transformation;
步骤6判断是否需要速度调节；否则进入步骤8；Step 6 judges whether speed adjustment is needed; otherwise, enter step 8;
步骤7调用速度调节处理子控制程序；Step 7 calls the speed regulation processing sub-control program;
步骤8 d q轴电流调节；Step 8 d q-axis current regulation;
步骤9 PARK逆变换；Step 9 PARK inverse transformation;
步骤10 SVPWM输出；Step 10 SVPWM output;
步骤11恢复现场；Step 11 restore the scene;
步骤12中断返回。Step 12 interrupts and returns.
其中上述步骤7的速度调节中断处理子控制程序按以下步骤：Wherein the speed adjustment interrupt processing sub-control program of above-mentioned step 7 follows the steps:
步骤1速度调节中断子控制程序开始；Step 1 The speed adjustment interrupt sub-control program starts;
步骤2读取编码器值；Step 2 read the encoder value;
步骤3角度计算；Step 3 angle calculation;
步骤4速度计算；Step 4 speed calculation;
步骤5计算速度反馈误差；Step 5 calculates the speed feedback error;
步骤6设定二型模糊分数阶滑模变结构初始工况参数；Step 6 sets the initial operating condition parameters of the type II fuzzy fractional-order sliding mode variable structure;
步骤7判断是否已经在预设滑模面上；是则进行步骤9；Step 7 judges whether it is already on the preset sliding surface; if so, proceed to step 9;
步骤8计算usw；Step 8 calculate u sw ;
步骤9计算ueq；Step 9 calculate u eq ;
步骤10计算电流命令并输出，即区间二型模糊分数阶滑模控制律u＝ueq+usw；Step 10 calculates and outputs the current command, that is, the interval type II fuzzy fractional-order sliding mode control law u=u eq +u sw ;
步骤11中断返回；Step 11 interrupt return;
本发明的优点在于：针对永磁直线同步电机(PMLSM)伺服系统，本发明提出一种永磁直线同步电机的二型模糊分数阶滑模控制系统及方法；设计中引入区间二型模糊控制器和分数阶滑模面，并采用基于分数阶微积分理论的切换项，可以有效降低抖振；同时解决了一型模糊系统模糊规则存在的不确定性问题，提高系统的鲁棒性，最终本发明方法实现了提高系统的鲁棒性，并削弱系统的抖振现象。The advantages of the present invention are: for the permanent magnet linear synchronous motor (PMLSM) servo system, the present invention proposes a type II fuzzy fractional-order sliding mode control system and method of a permanent magnet linear synchronous motor; the interval type II fuzzy controller is introduced into the design and fractional-order sliding mode surface, and adopting switching items based on fractional-order calculus theory can effectively reduce chattering; at the same time, it solves the uncertainty problem existing in the fuzzy rules of the first-type fuzzy system and improves the robustness of the system. The inventive method improves the robustness of the system and weakens the chattering phenomenon of the system.
附图说明Description of drawings
图1为本发明的二型模糊分数阶滑模控制永磁同步直线伺服系统框图。Fig. 1 is a block diagram of a permanent magnet synchronous linear servo system of type II fuzzy fractional order sliding mode control of the present invention.
图2为带有不确定中心值的区间二型模糊集。Figure 2 is an interval type II fuzzy set with an uncertain central value.
图3为区间二型模糊逻辑系统框图。Figure 3 is a block diagram of the interval type II fuzzy logic system.
图4为本实现发明的控制系统硬件原理图。Fig. 4 is a schematic diagram of the hardware of the control system of the present invention.
图5为二型模糊分数阶滑模控制软件实现主流程图。Figure 5 is the main flow chart for the implementation of Type II fuzzy fractional-order sliding mode control software.
图6为电流环实现程序流程图(即T1中断处理子控制程序流程图)。Fig. 6 is a flow chart of the implementation program of the current loop (that is, a flow chart of the T1 interrupt processing sub-control program).
图7为速度调节处理子控制程序流程图。Fig. 7 is a flow chart of the speed adjustment processing sub-control program.
图8(a)电机驱动系统主电路原理图。Figure 8(a) Schematic diagram of the main circuit of the motor drive system.
图8(b)A、B相电流采样电路原理图。Figure 8(b) Schematic diagram of A and B-phase current sampling circuits.
图8(c)光栅尺信号采样电路原理图。Fig. 8(c) Schematic diagram of grating ruler signal sampling circuit.
图9为区间二型模糊控制器输入s的隶属函数。Figure 9 shows the membership function of the input s of the interval type II fuzzy controller.
图10为区间二型模糊控制器输出Δu的隶属函数。Figure 10 is the membership function of the output Δu of the interval type II fuzzy controller.
图11为一型模糊滑模和二型模糊分数阶滑模控制系统的速度阶跃响应对比试验曲线。Fig. 11 is the speed step response comparative test curves of type-1 fuzzy sliding mode and type-2 fuzzy fractional-order sliding mode control systems.
图12为二型模糊分数阶滑模控制器的输出交轴电流iq试验曲线。Figure 12 is the experimental curve of the output quadrature axis current i q of the type II fuzzy fractional order sliding mode controller.
图13为使用二型模糊分数阶滑模控制器的系统参数变化前后速度阶跃响应曲线。Figure 13 is the speed step response curve before and after the system parameter changes using the type II fuzzy fractional-order sliding mode controller.
具体实施方式detailed description
下面结合附图对本发明做进一步的说明：Below in conjunction with accompanying drawing, the present invention will be further described:
图1为永磁直线同步电机的二型模糊分数阶滑模控制系统的原理框图，其中v*为系统速度的给定值，d是外加扰动，系统跟踪误差为e＝v*-v。Fig. 1 is the functional block diagram of the type II fuzzy fractional-order sliding mode control system of the permanent magnet linear synchronous motor, where v * is the given value of the system speed, d is the external disturbance, and the system tracking error is e = v * -v.
实现本发明的主要步骤如下：Realize that main steps of the present invention are as follows:
步骤一：建立永磁直线同步电机的数学模型Step 1: Establish the mathematical model of the permanent magnet linear synchronous motor
永磁直线同步电机的d-q轴模型如下The d-q axis model of the permanent magnet linear synchronous motor is as follows
式中In the formula
式中，ωr＝πv/τ，v为动子线速度；ud、uq、id、iq、Ld、Lq、ψd、ψq分别为d-q轴电压、电流、电感、磁链；Rs为动子电阻；ψf为永磁体在动子绕组直轴上的磁链分量；τ为极距。In the formula, ω r = πv/τ, v is the moving element linear velocity; u d , u q , i d , i q , L d , L q , ψ d , ψ q are dq axis voltage, current, inductance, Flux linkage; R s is the resistance of the mover; ψ f is the flux linkage component of the permanent magnet on the direct axis of the mover winding; τ is the pole pitch.
永磁直线同步电机的电磁推力表达式为The electromagnetic thrust expression of the permanent magnet linear synchronous motor is
由于面装式永磁直线同步电机中Ld＝Lq，则(9)可表示为Since L d = L q in the surface-mounted permanent magnet linear synchronous motor, (9) can be expressed as
式中：pn为极对数，kf为电磁推力系数。In the formula: p n is the number of pole pairs, and k f is the electromagnetic thrust coefficient.
永磁同步直线电机的机械运动方程为The mechanical motion equation of the permanent magnet synchronous linear motor is
式中：l为动子位移；M为动子和所带负载总质量；Bv为粘滞摩擦因数；d(t)为外部干扰，d(t)＝Ffric+Frip+Fl，Ffric为摩擦力，其表达式v为动子线速度；为端部效应产生的推力波动，Fripplem＝40为端部效应产生的推力波动的幅值，θ0为初始相位电角度，设为0。l为动子位移，τ为极距；Fl为负载阻力。In the formula: l is the displacement of the mover; M is the total mass of the mover and the load; Bv is the viscous friction coefficient; d(t) is the external disturbance, d(t)=F fric +F rip +F l , F fric is the friction force, its expression v is the linear velocity of the mover; is the thrust fluctuation generated by the end effect, F ripplem =40 is the amplitude of the thrust fluctuation generated by the end effect, θ 0 is the initial phase electrical angle, which is set to 0. l is the mover displacement, τ is the pole distance; F l is the load resistance.
令状态量x＝[xl x2]T＝[l v]T，u＝iq为输入控制量，由式(11)可得永磁同步直线电机状态方程为Let the state quantity x＝[x l x 2 ] T ＝[lv] T , u＝i q be the input control quantity, and the state equation of the permanent magnet synchronous linear motor can be obtained from formula (11):
步骤二：分数阶PIαDα滑模面的设计Step 2: Design of fractional order PI α D α sliding mode surface
定义：分数阶微积分算子表示为t0、t为算子的上下限；连续可积分函数f(t)的(RL型)Riemann-Liouville分数阶微积分定义为Definition: The fractional calculus operator is expressed as t 0 , t are the upper and lower limits of the operator; the (RL type) Riemann-Liouville fractional calculus of the continuous integrable function f(t) is defined as
式中：m为整数，且m-1<α<m，t>t0；τ表示函数f(t)在[t0，t]范围内的任意值；Gamma函数Γ(·)定义为其中z在复平面的右半平面取值，即Re(z)＞0。t表示函数Γ(·)在[0，∞]的任意值。。In the formula: m is an integer, and m-1<α<m, t>t 0 ; τ represents any value of the function f(t) in the range of [t 0 , t]; the Gamma function Γ( ) is defined as Where z takes a value in the right half plane of the complex plane, that is, Re(z)>0. t represents any value of the function Γ(·) in [0, ∞]. .
为解决不能直接精确计算出函数的分数阶微积分的值，本发明采用整数阶Oustaloup滤波器来逼近分数阶微分算子Dα。该滤波器的传递函数如下In order to solve the problem that the value of the fractional calculus of the function cannot be directly and accurately calculated, the present invention uses an integer-order Oustaloup filter to approximate the fractional-order differential operator D α . The transfer function of this filter is as follows
其中，G(s)为复变函数，k∈[-N,N],N为滤波器阶数, (ωb,ωh)为给定的滤波频率区间，α为分数阶微积分的阶次。Among them, G(s) is a complex variable function, k∈[-N,N], N is the filter order, (ω b ,ω h ) is a given filter frequency interval, and α is the order of fractional calculus.
设计如下式所示的分数阶PIαDα滑模面Design the fractional order PI α D α sliding mode surface shown in the following formula
其中，kp和ki是非零正常数；表示分数阶微积分算子，当α(0＜α＜1)时表示分数阶微分，则表示分数阶积分；e为系统速度跟踪误差。Among them, k p and k i are non-zero constants; Represents fractional calculus operator, when α(0<α<1) represents fractional differential, then Indicates the fractional order integral; e is the system velocity tracking error.
步骤三：设计滑模控制律为Step 3: Design the sliding mode control law as
u＝ueq+usw (16)u＝u eq +u sw (16)
其中，usw为滑模控制的切换项；ueq为滑模控制的等效控制部分，由滑模面s的导数确定，则Among them, u sw is the switching item of sliding mode control; u eq is the equivalent control part of sliding mode control, by the derivative of sliding mode surface s OK, then
其中，为系统跟踪误差的导数。in, is the derivative of the system tracking error.
由分别为动子给定速度v*和动子输出速度v的导数，结合式(12)和式(18)，可得Depend on are the derivatives of the given speed v * of the mover and the output speed v of the mover, respectively, combined with formula (12) and formula (18), we can get
其中，M为动子质量；kf为永磁同步直线电机的电磁推力系数；Bv为粘滞摩擦因数。Among them, M is the mass of the mover; k f is the electromagnetic thrust coefficient of the permanent magnet synchronous linear motor; B v is the viscous friction coefficient.
定义切换控制项s为式(15)的滑模面，Ks为负的常值。Define toggle controls s is the sliding mode surface of formula (15), and K s is a negative constant value.
则式(19)变为Then formula (19) becomes
步骤四：由于滑模控制切换项影响着系统的控制性能，如果切换项中的Ks的绝对值取值过大，系统存在较大抖振；反之，系统的鲁棒性降低。由于永磁直线同步电机伺服系统易受不确定因素的扰动，且扰动不易测量，本发明采用区间二型模糊控制器替换(20)式中Kssgn(s)项，区间二型模糊控制器输入为式(15)中的滑模面s，输出为Δu。Step 4: Since the switching item of sliding mode control affects the control performance of the system, if the absolute value of K s in the switching item is too large, the system has a large chattering; otherwise, the robustness of the system decreases. Since the permanent magnet linear synchronous motor servo system is easily disturbed by uncertain factors, and the disturbance is not easy to measure, the present invention replaces the K s sgn(s) term in (20) with an interval type two fuzzy controller, and the interval type two fuzzy controller The input is the sliding surface s in formula (15), and the output is Δu.
图2为本发明使用的带有不确定中心值的区间二型模糊集，区间二型模糊高斯隶属函数由一型模糊高斯隶属函数的可调整不确定中心值与标准偏差值构成，x为区间二型模糊系统的输入，则带有可调整不确定中心值[m1,m2]与可调整标准方差σ的区间二型高斯隶属函数如下式Fig. 2 is the interval type II fuzzy set with uncertain center value that the present invention uses, interval type II fuzzy Gaussian membership function is made up of the adjustable uncertain center value and standard deviation value of type one fuzzy Gaussian membership function, and x is interval The input of the type 2 fuzzy system is the interval type 2 Gaussian membership function with adjustable uncertain center value [m 1 ,m 2 ] and adjustable standard deviation σ as follows
从图2可以看出，区间二型模糊集是一个域，该域描述隶属度函数不确定性的一种模糊集合，且以传统的模糊隶属函数为约束界，域的上界用UMF表示，域的下界用LMF表示，此域称为不确定域(foot-print of uncertain，FOU)，如图2灰色部分。区间二型模糊隶属函数的UMF和LMF分别用表示，为图2中的μ2、μ1。It can be seen from Fig. 2 that the interval type II fuzzy set is a field, which describes a fuzzy set of uncertainty of the membership function, and the traditional fuzzy membership function is used as the constraint boundary, and the upper boundary of the field is represented by UMF, The lower bound of the domain is represented by LMF, and this domain is called the foot-print of uncertain (FOU), as shown in the gray part of Figure 2. The UMF and LMF of the interval type II fuzzy membership function are respectively used Expressed as μ 2 and μ 1 in Fig. 2 .
区间二型模糊逻辑系统如图3所示，与一型模糊逻辑系统相似，包括模糊器、规则库、推理机、降型器以及解模糊器五部分，但是模糊逻辑系统的前后件由区间二型模糊集来代替。本发明采用Mamdani型区间二型模糊系统，本发明使用的区间二型模糊系统由IF-THEN形式的模糊规则构成：Interval II type fuzzy logic system is shown in Figure 3, which is similar to Type I fuzzy logic system, including five parts: fuzzer, rule base, inference engine, de-former and defuzzifier, but the front and rear parts of the fuzzy logic system are composed of type fuzzy sets instead. The present invention adopts Mamdani type interval type two fuzzy system, and the interval type two fuzzy system used in the present invention is made of the fuzzy rules of IF-THEN form:
其中，s为式(15)中的滑模面，为区间二型模糊系统的输入；y为区间二型模糊系统的输出，是规则前件集合，是规则后件集合；i＝1，2，…，W是模糊规则数，W为正的常数。其模糊规则前、后件集合均是区间二型模糊集合。基于乘机推理机、单值模糊器，经过集合中心(Center-of-sets，COS)降型得到降阶集如下式Among them, s is the sliding mode surface in formula (15), which is the input of interval-type fuzzy system; y is the output of interval-type fuzzy system, is the set of antecedents of the rule, is the set of rule consequences; i=1, 2,..., W is the number of fuzzy rules, and W is a positive constant. The antecedent and consequent sets of the fuzzy rules are both interval-type fuzzy sets. Based on the opportunistic reasoning machine and single-valued fuzzer, the reduced-order set is obtained through the Center-of-sets (COS) reduction as follows:
其中，∫表示逻辑并，Ycos是由后件模糊集合的中心区间两个端点yl和yr决定的区间集合；表示后件模糊集合的中心区间集。Among them, ∫ represents logical union, and Y cos is a fuzzy set of consequents The set of intervals determined by the two endpoints y l and y r of the central interval of ; Represents the consequent fuzzy set The central interval set of .
利用重心法解模糊后的清晰输出为The clear output after using the center of gravity method to defuzzify is
其中，yl和yr为Among them, y l and y r are
其中， in,
把式(28)和式(29)代入式(27)，可得区间二型模糊器的输出为Substituting Equation (28) and Equation (29) into Equation (27), the output of interval type-2 fuzzer can be obtained as
令y＝Δu，其中本发明采用7条模糊规则，输入输出对应的模糊语言变量为：PB(正大)、PM(正中)、PS(正小)、ZO(零)、NS(负小)、NM(负中)、NB(负大)，模糊规则如下Make y=Δu, wherein the present invention adopts 7 fuzzy rules, and the fuzzy language variable corresponding to input and output is: PB (positive big), PM (positive center), PS (positive small), ZO (zero), NS (negative small), NM (negative medium), NB (negative large), the fuzzy rules are as follows
R1:IF s isPB,THEN Δu isNB；R 1 : IF s isPB, THEN Δu isNB;
R2:IF s isPM,THEN Δu isNM；R 2 : IF s isPM, THEN Δu isNM;
R3:IF s isPS,THEN Δu isNS；R 3 : IF s isPS, THEN Δu isNS;
R4:IF s isZO,THEN Δu isZO；R 4 : IF s isZO, THEN Δu isZO;
R5:IF s isNS,THEN Δu isPS；R 5 : IF s isNS, THEN Δu isPS;
R6:IF s isNM,THEN Δu isPM；R 6 : IF s isNM, THEN Δu isPM;
R7:IF s isNB,THEN Δu isPB；R 7 : IF s isNB, THEN Δu isPB;
采用乘机推理机、单值模糊器、集合中心(Center-of-sets，COS)降型以及重心解模糊，得到模糊控制器输出The output of the fuzzy controller is obtained by using the opportunistic reasoning machine, single-valued fuzzer, center-of-sets (COS) reduction and center-of-sets defuzzification
其中， in,
则式(20)变为Then formula (20) becomes
其中，M为动子质量；kf为永磁同步直线电机的电磁推力系数；Bv为粘滞摩擦因数；kp和ki是非零正常数；表示分数阶微积分算子，当α(0＜α＜1)时表示分数阶微分，则表示分数阶积分；e＝v*-v系统速度跟踪误差，其中v*为系统速度的给定值，v为动子输出速度，Δu为二型模糊系统的输出。Among them, M is the mass of the mover; k f is the electromagnetic thrust coefficient of the permanent magnet synchronous linear motor; B v is the viscous friction coefficient; k p and ki are non-zero normal constants; Represents fractional calculus operator, when α(0<α<1) represents fractional differential, then Indicates the fractional order integral; e=v * -v system speed tracking error, where v * is the given value of the system speed, v is the output speed of the mover, and Δu is the output of the type II fuzzy system.
步骤五：编写实现二型模糊分数阶滑模控制律实现的DSP程序部分。Step 5: Write the DSP program part that realizes the realization of Type II fuzzy fractional order sliding mode control law.
本发明控制算法由嵌入DSP程序实现。其主控程序流程图如图5所示，具体步骤如下：The control algorithm of the present invention is realized by embedding DSP program. The main control program flow chart is shown in Figure 5, and the specific steps are as follows:
第一步：开始；The first step: start;
第二步：DSP系统初始化；The second step: DSP system initialization;
第三步：程序数据初始化；The third step: program data initialization;
第四步：允许TN1、TN2中断；Step 4: Allow TN1 and TN2 interrupts;
第五步：启动T1下溢中断；Step 5: Start T1 underflow interrupt;
第六步：开总中断；Step 6: Open the general interrupt;
第七步：是否结束运行？是，执行第九步。否，执行第八步。Step 7: Do you want to end the operation? Yes, go to Step 9. If not, go to step eight.
第八步：是否有中断请求？是，调用T1中断处理子程序。否，执行第七步。Step 8: Is there an interrupt request? Yes, call the T1 interrupt processing subroutine. If no, go to step seven.
第九步：保存数据；Step 9: Save the data;
第十步：关中断；Step 10: Turn off the interrupt;
第十一步：结束。Step eleven: end.
TN1中断处理子程序流程图即电流环T1中断处理子程序流程图如图6，具体步骤如下：The flow chart of the TN1 interrupt processing subroutine, that is, the flow chart of the current loop T1 interrupt processing subroutine is shown in Figure 6, and the specific steps are as follows:
第一步：TN1中断子控制程序开始；The first step: the TN1 interrupt sub-control program starts;
第二步：保护现场；The second step: protect the site;
第三步：读取编码器信号；Step 3: Read the encoder signal;
第四步：电流采样，CLARK变换，PARK变换；The fourth step: current sampling, CLARK transformation, PARK transformation;
第五步：判断是否需要速度调节，否，进入步骤(7)；Step 5: Determine whether speed adjustment is needed, if not, go to step (7);
第六步：速度调节中断处理子控制程序；Step 6: Speed adjustment interrupt processing sub-control program;
第七步：d、q轴电流调节；The seventh step: d, q axis current regulation;
第八步：PARK逆变换；Step 8: PARK inverse transformation;
第九步：计算CMPPx及PWM输出；Step 9: Calculate CMPPx and PWM output;
第十步：恢复现场；Step 10: Restoring the scene;
第十一步：中断返回。Step 11: Interrupt return.
TN1中断程序中第六步速度调节中断处理子程序即二型模糊分数阶滑模控制律计算流程图如图7，按如下步骤执行：The sixth step in the TN1 interrupt program is the speed adjustment interrupt processing subroutine, that is, the calculation flow chart of the type II fuzzy fractional-order sliding mode control law is shown in Figure 7, and it is executed according to the following steps:
第一步：中断开始；The first step: interrupt start;
第二步：读取编码器信号；Step 2: Read the encoder signal;
第三步：电角度计算、速度计算；The third step: electrical angle calculation, speed calculation;
第四步：计算速度误差；Step 4: Calculate the speed error;
第五步：设定二型模糊分数阶滑模变结构初始工况参数；Step 5: Set the initial working condition parameters of the type II fuzzy fractional-order sliding mode variable structure;
第六步：判断是否已经在预设滑模面上；是则进行步骤9；Step 6: Determine whether it is already on the preset sliding surface; if yes, go to step 9;
第七步：计算usw；Step 7: Calculate u sw ;
第八步：计算ueq；Step 8: Calculate u eq ;
第九步：计算电流命令并输出，即二型模糊分数阶滑模控制律u＝ueq+usw；Step 9: Calculate and output the current command, that is, the type-2 fuzzy fractional-order sliding mode control law u=u eq +u sw ;
第十步：中断返回。Step 10: Interrupt return.
步骤六：本发明二型模糊分数阶滑模控制系统的硬件实现Step 6: The hardware realization of the present invention's Type II fuzzy fractional-order sliding mode control system
图8为实现本发明的硬件控制系统原理图。该系统包括主电路、控制电路和控制对象三部分；控制电路包括DSP、位置和速度检测电路、电流检测电路、光耦隔离电路、驱动电路及故障检测和保护电路；DSP采用TI公司的TMS320F28335芯片。DSP的QEP端口连接位置和速度检测电路，DSP的ADC端口连接电流检测电路，DSP的PWM端口和PDPINT端口连接光耦隔离电路，光耦隔离电路连接驱动电路和故障检测和保护电路，驱动电路连接IPM逆变单元；主电路包括调压电路、整流滤波单元和IPM逆变单元；控制对象为永磁直线同步电机，机身装有光栅尺；调压电路连接整流滤波单元，整流滤波单元连接IPM逆变单元，IPM逆变单元连接三相永磁直线同步电机。Fig. 8 is a schematic diagram of the hardware control system for realizing the present invention. The system includes three parts: main circuit, control circuit and control object; the control circuit includes DSP, position and speed detection circuit, current detection circuit, optocoupler isolation circuit, drive circuit and fault detection and protection circuit; DSP adopts TMS320F28335 chip of TI Company . The QEP port of the DSP is connected to the position and speed detection circuit, the ADC port of the DSP is connected to the current detection circuit, the PWM port and the PDPINT port of the DSP are connected to the optocoupler isolation circuit, the optocoupler isolation circuit is connected to the drive circuit and the fault detection and protection circuit, and the drive circuit is connected IPM inverter unit; the main circuit includes a voltage regulation circuit, a rectification filter unit and an IPM inverter unit; the control object is a permanent magnet linear synchronous motor, and the body is equipped with a grating scale; the voltage regulation circuit is connected to the rectifier filter unit, and the rectifier filter unit is connected to the IPM The inverter unit, the IPM inverter unit is connected with the three-phase permanent magnet linear synchronous motor.
DSP的SCI端口连接上位机，DSP的SPI端口连接显示电路，DSP的GPIO端口连接I/O接口电路；故障检测和保护电路连接控制电源。The SCI port of the DSP is connected to the upper computer, the SPI port of the DSP is connected to the display circuit, the GPIO port of the DSP is connected to the I/O interface circuit; the fault detection and protection circuit is connected to the control power supply.
实现本发明的控制系统主电路如图8(a)所示，调压电路采用反向调压模块EUV-25A-II，可实现0～220V隔离调压。整流滤波单元采用桥式不可控整流，大电容滤波，配合适当的阻容吸收电路，可以获得IPM工作所需的恒定直流电压。IPM采用富士公司6MBP50RA060智能功率模块，耐压600V，最大电流50A，最高工作频率20kHz。IPM用四组独立的15V驱动电源供电。主电源输入端子(P，N)，输出端子(U，V，W)，主端子用自带的螺钉固定，可实现电流传输。P、N为变频器的整流变换平滑滤波后的主电源输入端子，P为正端，N为负端，逆变器输出的三相交流电通过输出端子U、V、W接至电机。The main circuit of the control system realizing the present invention is shown in Fig. 8(a). The voltage regulation circuit adopts the reverse voltage regulation module EUV-25A-II, which can realize 0-220V isolation voltage regulation. The rectification filter unit adopts bridge type uncontrollable rectification, large capacitor filter, and appropriate resistance-capacity absorption circuit, which can obtain the constant DC voltage required for IPM work. The IPM uses Fuji 6MBP50RA060 intelligent power module, with a withstand voltage of 600V, a maximum current of 50A, and a maximum operating frequency of 20kHz. The IPM is powered by four independent 15V drive power supplies. The main power input terminals (P, N), output terminals (U, V, W), and the main terminals are fixed with their own screws, which can realize current transmission. P and N are the input terminals of the main power supply after rectification, transformation and smoothing of the inverter. P is the positive terminal and N is the negative terminal. The three-phase alternating current output by the inverter is connected to the motor through the output terminals U, V, and W.
本发明的控制电路的核心为TMS320F28335处理器，其配套的开发板包括目标只读存储器、模拟接口、eCAN接口、串行引导ROM、用户指示灯、复位电路、可配置为RS232/RS422/RS485的异步串口、SPI同步串口和片外256K*16位RAM。The core of the control circuit of the present invention is the TMS320F28335 processor, and its supporting development board includes target read-only memory, analog interface, eCAN interface, serial boot ROM, user indicator light, reset circuit, and can be configured as RS232/RS422/RS485 Asynchronous serial port, SPI synchronous serial port and off-chip 256K*16-bit RAM.
实际控制系统中电流采样采用LEM公司霍尔电流传感器LT58-S7。由两个霍尔电流传感器检测A、B相电流，得到电流信号，经过电流采样电路，转换成0～3.3V的电压信号，最后由TMS320LF28335的A/D转换模块转换成12位精度的二进制数，并保存在数值寄存器中。A、B相的电流采样电路如图8(b)所示。可调电阻VR2调节信号幅值，可调电阻VR1调节信号偏移量，通过对这两个电阻的调节，可以将信号调整到0～3.3V，再将其送入DSP的AD0、AD1管脚。图中的稳压管是为了防止送入DSP的信号超过3.3V，导致DSP被高压损坏。运算放大器采用OP27，电源接正负15V电压，在电压和地间接去耦电容。电路输入端接电容滤波，以去除高频信号干扰，提高采样精度。The current sampling in the actual control system adopts the Hall current sensor LT58-S7 of LEM Company. The A and B phase currents are detected by two Hall current sensors to obtain current signals, which are converted into 0-3.3V voltage signals through the current sampling circuit, and finally converted into binary numbers with 12-bit precision by the A/D conversion module of TMS320LF28335 , and stored in the value register. The current sampling circuit of A and B phases is shown in Fig. 8(b). The adjustable resistor VR2 adjusts the signal amplitude, and the adjustable resistor VR1 adjusts the signal offset. By adjusting these two resistors, the signal can be adjusted to 0~3.3V, and then sent to the AD0 and AD1 pins of the DSP. . The regulator tube in the figure is to prevent the signal sent to the DSP from exceeding 3.3V, causing the DSP to be damaged by high voltage. The operational amplifier adopts OP27, the power supply is connected to positive and negative 15V voltage, and the decoupling capacitor is indirect between the voltage and the ground. The input terminal of the circuit is connected with a capacitor filter to remove high-frequency signal interference and improve sampling accuracy.
光栅尺输出的A相和B相脉冲信号要通过快速光耦6N137对信号进行隔离，然后经过分压电路将信号电平由5V转换为3.3V，最后连接到DSP的两路正交编码脉冲接口QEP1和QEP2。电路原理如图8(c)所示。直线电机驱动电路主要包括一个智能功率模块，本发明选用的是IRAMS10UP60B，它适用于较大功率的电机中，它能驱动的电机功率范围是400W～750W；主要由6个IGBT构成的三相桥式电路，控制板上DSP芯片产生的PWM控制信号输入到功率模块，控制3个桥臂的关断，产生合适驱动电压，驱动直线电机运动图中的HIN1和LIN1分别是第一相的上下桥臂的控制信号，它们都是低电平有效。IRAMS10UP60B的工作电压VDD是15V，VSS为接地端，为了达到良好的去耦效果，在这两端加入两个并联的去耦电容。功率芯片自身有过温和过流保护，当电路出现异常时能起到自我保护的作用。The A-phase and B-phase pulse signals output by the grating ruler should be isolated by a fast optocoupler 6N137, and then the signal level will be converted from 5V to 3.3V by a voltage divider circuit, and finally connected to the two-way orthogonal encoding pulse interface of DSP QEP1 and QEP2. The circuit principle is shown in Fig. 8(c). The linear motor drive circuit mainly includes an intelligent power module. The present invention selects IRAMS10UP60B, which is suitable for relatively high-power motors. The power range of the motor it can drive is 400W to 750W; the three-phase bridge mainly composed of 6 IGBTs The PWM control signal generated by the DSP chip on the control board is input to the power module to control the shutdown of the three bridge arms and generate a suitable driving voltage to drive the linear motor. The HIN1 and LIN1 in the motion diagram of the linear motor are the upper and lower bridges of the first phase respectively. Arm control signals, they are all active low. The operating voltage VDD of IRAMS10UP60B is 15V, and VSS is the ground terminal. In order to achieve a good decoupling effect, two parallel decoupling capacitors are added at these two ends. The power chip itself has over-temperature and over-current protection, which can protect itself when the circuit is abnormal.
本发明的一个实例An example of the invention
永磁直线同步电机的参数为M＝8kg，kf＝50.7N/A，Bv＝12Ns/m。摩擦力端部效应产生的推力波动Frip＝40cos(392l)，v、l分别为动子的速度、位移。The parameters of the permanent magnet linear synchronous motor are M=8kg, k f =50.7N/A, B v =12Ns/m. friction Thrust fluctuation F rip =40cos(392l) generated by the tip effect, where v and l are the speed and displacement of the mover, respectively.
二型模糊分数阶滑模参数：kp＝354，ki＝0.001，α＝0.98，(ωb,ωh)取值为(10-3,103)，N＝2，区间二型模糊控制器输入s的隶属度函数如图9所示，输出Δu的隶属度函数如图10所示。Type II fuzzy fractional sliding mode parameters: k p =354, k i =0.001, α =0.98, (ω b ,ω h ) is (10 -3 ,10 3 ), N = 2, interval type II fuzzy The membership function of the controller input s is shown in Figure 9, and the membership function of the output Δu is shown in Figure 10.
基于以上参数，当给定v*＝1m/s电机空载启动，并在t＝0.5s时突加Fl＝200N负载干扰时，一型模糊滑模和二型模糊分数阶滑模控制系统的速度阶跃响应曲线分别如图11中虚线和实线所示。实验结果表明二型模糊分数阶滑模控制的系统响应时间较小，受到扰动后速度下降最大值为0.061m/s，恢复时间为0.06s；而一型模糊滑模控制的系统受到扰动后速度下降最大值为0.077m/s，恢复时间为0.12s，说明本发明的方法具有较强鲁棒性。图12为采用二型模糊分数阶滑模控制器时系统的iq输出曲线，可以看出系统几乎无抖振。图13为永磁直线同步电机启动后将动子质量M变为原来的2倍，二型模糊分数阶滑模控制的速度阶跃响应曲线，参数变化前后系统响应时间几乎不变，参数变化前，受到突加负载扰动后速度下降最大值为0.061m/s，参数变化后，受到突加负载扰动后速度下降最大值为0.041m/s，可知参数变化对系统性能影响较小。二型模糊分数阶滑模控制可以削弱抖振，提高系统的鲁棒性。Based on the above parameters, when the given v * = 1m/s motor starts with no load, and a load disturbance of F l = 200N is suddenly added at t = 0.5s, the type I fuzzy sliding mode and type II fuzzy fractional order sliding mode control systems The speed step response curves of are shown in dotted line and solid line in Fig. 11 respectively. The experimental results show that the response time of the type-2 fuzzy fractional-order sliding mode control system is relatively small, the maximum speed drop after being disturbed is 0.061m/s, and the recovery time is 0.06s; The maximum drop is 0.077m/s, and the recovery time is 0.12s, which shows that the method of the present invention has strong robustness. Figure 12 is the iq output curve of the system when the type II fuzzy fractional-order sliding mode controller is used. It can be seen that the system has almost no chattering. Figure 13 shows the speed step response curve of type II fuzzy fractional-order sliding mode control after the permanent magnet linear synchronous motor is started and the mass M of the mover is doubled. , the maximum speed drop after being disturbed by a sudden load is 0.061m/s, and after the parameter changes, the maximum speed drop after being disturbed by a sudden load is 0.041m/s, it can be seen that the parameter change has little influence on the system performance. Type II fuzzy fractional-order sliding mode control can weaken chattering and improve the robustness of the system.
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