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CN110597066B - Integral fuzzy sliding mode control method and equipment for thrust active magnetic suspension bearing - Google Patents

Integral fuzzy sliding mode control method and equipment for thrust active magnetic suspension bearing Download PDF

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CN110597066B
CN110597066B CN201910916619.XA CN201910916619A CN110597066B CN 110597066 B CN110597066 B CN 110597066B CN 201910916619 A CN201910916619 A CN 201910916619A CN 110597066 B CN110597066 B CN 110597066B
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禄盛
史军辉
赵洋
朴昌浩
陈翔
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Chongqing University of Post and Telecommunications
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Abstract

The invention discloses an integral fuzzy sliding mode control method and equipment of a thrust active magnetic suspension bearing, wherein the method comprises the following steps: according to the displacement of the thrust active magnetic suspension bearing rotor in the X direction, obtaining a transfer function through Laplace transformation, converting the transfer function into a state equation, and calculating a first output of an integral fuzzy sliding mode controller; the method can ensure that the thrust active magnetic suspension bearing system can operate stably from start to run within a certain time without oscillation, improve the control precision of the magnetic suspension bearing, effectively reduce and eliminate sliding mode buffeting, and have strong robust anti-interference capability.

Description

一种推力主动磁悬浮轴承的积分模糊滑模控制方法及设备Integral fuzzy sliding mode control method and equipment for thrust active magnetic suspension bearing

技术领域technical field

本发明涉及磁悬浮轴承控制领域，特别涉及一种推力主动磁悬浮轴承的积分模糊滑模控制方法及设备。The invention relates to the field of magnetic suspension bearing control, in particular to an integral fuzzy sliding mode control method and device for a thrust active magnetic suspension bearing.

背景技术Background technique

主动磁悬浮轴承(active magnetic bearing，AMB)具有无磨损、寿命长、无润滑油污染等一系列优点，因而已被运用于数百种不同的旋转或往复式运动机械上。由于磁悬浮轴承控制器性能的好坏直接决定了磁悬浮能否实现，所以高性能控制器的设计成为磁悬浮轴承研究的热点。Active magnetic bearing (AMB) has a series of advantages such as no wear, long life and no lubricating oil pollution, so it has been used in hundreds of different rotating or reciprocating machinery. Since the performance of the magnetic suspension bearing controller directly determines whether the magnetic suspension can be realized, the design of the high-performance controller has become a hot spot in the magnetic suspension bearing research.

目前比例-积分-微分PID控制器被广泛的应用于磁悬浮轴承实际控制当中，其中包括推力主动磁悬浮轴承。但是由于推力主动磁悬浮轴承是一个典型的强烈非线性系统，很难建立它的精确数学模型，所以PID控制器在工程实际中往往难以得到较好的动态性能。At present, proportional-integral-derivative PID controllers are widely used in the actual control of magnetic bearings, including thrust active magnetic bearings. However, because the thrust active magnetic bearing is a typical strong nonlinear system, it is difficult to establish its accurate mathematical model, so the PID controller is often difficult to obtain better dynamic performance in engineering practice.

滑模变结构控制由于具有强抗干扰能力，特别适合非线性系统的状态辨识与控制，从而得到广泛的研究。然而，滑模变结构控制存在滑模抖振这个固有缺点，随着系统非线性的增强，会严重影响控制器的控制性能，因此需要进行改善和消除滑模抖振。Because of its strong anti-interference ability, sliding mode variable structure control is especially suitable for state identification and control of nonlinear systems, so it has been widely studied. However, sliding mode variable structure control has the inherent disadvantage of sliding mode chattering. With the increase of system nonlinearity, it will seriously affect the control performance of the controller. Therefore, it is necessary to improve and eliminate sliding mode chattering.

发明内容SUMMARY OF THE INVENTION

本发明为解决上述问题，提出了一种推力主动磁悬浮轴承的积分模糊滑模控制方法及设备，利用模糊控制具有不需要被控对象精确数学模型的优点，将其与积分滑模控制结合起来组成积分模糊滑模控制，发挥两者优势以实现减轻与消除滑模抖振。In order to solve the above problems, the present invention proposes an integral fuzzy sliding mode control method and equipment for a thrust active magnetic suspension bearing. The fuzzy control has the advantage of not requiring an accurate mathematical model of the controlled object, and is combined with the integral sliding mode control to form a Integral fuzzy sliding mode control takes advantage of both to reduce and eliminate sliding mode chattering.

根据本发明的一个方面，提供一种推力主动磁悬浮轴承的积分模糊滑模控制方法，包括以下步骤：According to an aspect of the present invention, there is provided an integral fuzzy sliding mode control method for a thrust active magnetic suspension bearing, comprising the following steps:

步骤1，根据推力主动磁悬浮轴承转子在X方向上的位移，计算转子X方向上的力学方程，通过拉氏变换得到推力主动磁悬浮轴承的传递函数；Step 1, according to the displacement of the thrust active magnetic suspension bearing rotor in the X direction, calculate the mechanical equation of the rotor in the X direction, and obtain the transfer function of the thrust active magnetic suspension bearing through Laplace transformation;

步骤2，将推力主动磁悬浮轴承的传递函数转换成状态方程；Step 2, converting the transfer function of the thrust active magnetic bearing into a state equation;

步骤3，根据状态方程，计算积分模糊滑模控制器的第一输出；Step 3, according to the state equation, calculate the first output of the integral fuzzy sliding mode controller;

步骤4，根据积分滑模面的参数和所述第一输出，通过模糊规则调节等效控制和切换控制权重，计算积分模糊滑模控制器的第二输出，利用所述第二输出来控制推力主动磁悬浮轴承转子的位置。Step 4, according to the parameters of the integral sliding mode surface and the first output, adjust the equivalent control and switching control weights through fuzzy rules, calculate the second output of the integral fuzzy sliding mode controller, and use the second output to control the thrust The position of the active magnetic bearing rotor.

根据本发明的另一个方面，提供一种推力主动磁悬浮轴承的积分模糊滑模控制设备，包括：According to another aspect of the present invention, there is provided an integral fuzzy sliding mode control device for a thrust active magnetic suspension bearing, comprising:

一种推力主动磁悬浮轴承的积分模糊滑模控制设备，与推力主动磁悬浮轴承相连接，包括以下模块：An integral fuzzy sliding mode control device for a thrust active magnetic suspension bearing, which is connected with the thrust active magnetic suspension bearing, and includes the following modules:

磁悬浮轴承转子的力学转换模块，用于计算X方向上推力主动磁悬浮轴承转子的力学方程，通过拉氏变换得到推力主动磁悬浮轴承的传递函数；将传递函数转换成状态方程；The mechanical conversion module of the magnetic suspension bearing rotor is used to calculate the mechanical equation of the thrust active magnetic suspension bearing rotor in the X direction, and obtain the transfer function of the thrust active magnetic suspension bearing through Laplace transformation; convert the transfer function into the state equation;

积分模糊滑模控制器，包括等效控制器、切换控制器和模糊控制器，用于根据状态方程，计算积分模糊滑模控制器的第一输出；根据积分滑模面的参数和所述第一输出，通过模糊规则得到模糊控制器的输出，使用模糊控制器的输出调节等效控制器和切换控制器的权重，计算积分模糊滑模控制器的第二输出；利用所述第二输出来控制推力主动磁悬浮轴承转子的位置。The integral fuzzy sliding mode controller, including an equivalent controller, a switching controller and a fuzzy controller, is used to calculate the first output of the integral fuzzy sliding mode controller according to the state equation; according to the parameters of the integral sliding mode surface and the first output One output, obtain the output of the fuzzy controller through fuzzy rules, use the output of the fuzzy controller to adjust the weights of the equivalent controller and the switching controller, and calculate the second output of the integral fuzzy sliding mode controller; use the second output to Control the position of the thrust active magnetic bearing rotor.

本发明提供的一种推力主动磁悬浮轴承的积分模糊滑模控制方法及设备，其能够使系统在一定时间内从启动到稳定运行并且不会发生振荡现象，提高推力主动磁悬浮轴承的控制精度并有效减轻与消除滑模抖振，具有较强的鲁棒干扰能力。The invention provides an integral fuzzy sliding mode control method and device for a thrust active magnetic suspension bearing, which can make the system start to run stably within a certain period of time without oscillation, improve the control accuracy of the thrust active magnetic suspension bearing and effectively Reduce and eliminate sliding mode chattering, with strong robust interference capability.

附图说明Description of drawings

图1是本发明实施例提供的一种推力主动磁悬浮轴承的积分模糊滑模控制方法流程图；1 is a flowchart of an integral fuzzy sliding mode control method for a thrust active magnetic bearing provided by an embodiment of the present invention;

图2是本发明实施例提供的模糊控制器输入变量隶属度函数图；Fig. 2 is a fuzzy controller input variable membership function diagram provided by an embodiment of the present invention;

图3是本发明实施例提供的模糊控制器输出变量隶属度函数图；Fig. 3 is a fuzzy controller output variable membership function diagram provided by an embodiment of the present invention;

图4是本发明实施例提供的一种推力主动磁悬浮轴承的积分模糊滑模控制设备结构图；4 is a structural diagram of an integral fuzzy sliding mode control device for a thrust active magnetic suspension bearing provided by an embodiment of the present invention;

图5是本发明实施例提供的控制方法应用于控制对象之后的效果图；5 is an effect diagram after the control method provided by an embodiment of the present invention is applied to a control object;

图6是本发明实施例提供的控制方法和现有的传统等效滑模控制效果对比图。FIG. 6 is a comparison diagram of the control method provided by the embodiment of the present invention and the existing traditional equivalent sliding mode control effect.

具体实施方式Detailed ways

下面本发明具体的实施方式进行阐述，来进一步说明本发明的出发点以及相应的技术方案。The specific embodiments of the present invention are described below to further illustrate the starting point of the present invention and the corresponding technical solutions.

图1是本发明实施例提供的一种推力主动磁悬浮轴承的积分模糊滑模控制方法流程图，所述方法包括：1 is a flowchart of an integral fuzzy sliding mode control method for a thrust active magnetic bearing provided by an embodiment of the present invention, and the method includes:

步骤101，根据推力主动磁悬浮轴承转子在X方向上的位移，计算转子X方向上的力学方程，通过拉氏变换得到推力主动磁悬浮轴承的传递函数。Step 101 , according to the displacement of the thrust active magnetic suspension bearing rotor in the X direction, calculate the mechanical equation of the rotor in the X direction, and obtain the transfer function of the thrust active magnetic suspension bearing through Laplace transformation.

在不考虑作用在转子上的其他力时，根据牛顿力学方程，得到X方向上推力主动磁悬浮轴承转子的力学方程，通过拉氏变换得到其传递函数。Without considering other forces acting on the rotor, according to Newton's mechanical equation, the mechanical equation of the thrust active magnetic bearing rotor in the X direction is obtained, and its transfer function is obtained by Laplace transform.

推力主动磁悬浮轴承系统一般由电磁铁、转子、位移传感器、控制器、功率放大器等组成。传感器检测到转子相对于参考位置的偏移，作为控制器微处理器就此给出一个控制信号，通过功率放大器后转变为控制电流，控制电流在电磁铁执行器中形成相应的电磁场，最终所形成的磁场力始终维持着转子悬浮在设定的位置上。传感器检测的是转子相对于参考位置的偏移，转子的偏移是因为受到了力的作用，根据牛顿力学方程得到磁悬浮轴承转子的力学方程，通过拉氏变换得到其传递函数。Thrust active magnetic bearing system is generally composed of electromagnet, rotor, displacement sensor, controller, power amplifier and so on. The sensor detects the deviation of the rotor relative to the reference position, and the microprocessor as the controller gives a control signal, which is converted into a control current after passing through the power amplifier, and the control current forms a corresponding electromagnetic field in the electromagnet actuator, and finally forms a control current. The magnetic field force keeps the rotor suspended in the set position all the time. The sensor detects the offset of the rotor relative to the reference position. The offset of the rotor is due to the action of force. According to the Newtonian mechanical equation, the mechanical equation of the magnetic bearing rotor is obtained, and its transfer function is obtained through Laplace transformation.

步骤101，根据推力主动磁悬浮轴承转子在X方向上的位移，计算转子X方向上的力学方程，通过拉氏变换得到推力主动磁悬浮轴承的传递函数，具体包括：Step 101, according to the displacement of the thrust active magnetic suspension bearing rotor in the X direction, calculate the mechanical equation of the rotor in the X direction, and obtain the transfer function of the thrust active magnetic suspension bearing through Laplace transformation, which specifically includes:

根据推力主动磁悬浮轴承转子在X方向上的位移x，计算转子X方向上的力学方程：According to the displacement x of the thrust active magnetic bearing rotor in the X direction, calculate the mechanical equation of the rotor in the X direction:

Figure BDA0002216334910000041
Figure BDA0002216334910000041

通过拉氏变换得到拉氏变换式：The Laplace transform is obtained by Laplace transform:

ms2X(s)＝KxX(s)+KiI(s)；ms 2 X(s)=K x X(s)+K i I(s);

进而得到推力主动磁悬浮轴承的传递函数G(s)：Then the transfer function G(s) of the thrust active magnetic bearing is obtained:

Figure BDA0002216334910000051
Figure BDA0002216334910000051

其中，x表示的是转子在X方向上的位移，m是转子质量，

Figure BDA0002216334910000052
为转子位移的二阶导数，i是X方向上的控制电流，Kx为力位移刚度系数，Ki为力电流刚度系数，s是推力主动磁悬浮轴承转子的传递函数的变量，X(s)表示传递函数的输出量，I(s)表示传递函数的输入量。对推力主动磁悬浮轴承而言，输入的是电流，输出的是位移，这个位移是为了让转子稳定在参考位置。Among them, x represents the displacement of the rotor in the X direction, m is the mass of the rotor,
Figure BDA0002216334910000052
is the second derivative of the rotor displacement, i is the control current in the X direction, K x is the force-displacement stiffness coefficient, K i is the force-current stiffness coefficient, s is the variable of the transfer function of the thrust active magnetic bearing rotor, X(s) represents the output of the transfer function, and I(s) represents the input of the transfer function. For the thrust active magnetic bearing, the input is current, and the output is displacement. This displacement is to stabilize the rotor at the reference position.

步骤102，将推力主动磁悬浮轴承的传递函数转换成状态方程，所述的状态方程的表达式为：In step 102, the transfer function of the thrust active magnetic suspension bearing is converted into a state equation, and the expression of the state equation is:

Figure BDA0002216334910000053
Figure BDA0002216334910000053

其中，转子位移x的矩阵

Figure BDA0002216334910000054
Figure BDA0002216334910000055
是转子位移x的一阶导数，矩阵
Figure BDA0002216334910000056
为矩阵X的一阶导数，矩阵
Figure BDA0002216334910000057
矩阵
Figure BDA0002216334910000058
矩阵U′为积分模糊滑模控制器的第二输出u′的矩阵，m是转子质量，Kx为力位移刚度系数，Ki为力电流刚度系数。where, the matrix of rotor displacement x
Figure BDA0002216334910000054
Figure BDA0002216334910000055
is the first derivative of the rotor displacement x, matrix
Figure BDA0002216334910000056
is the first derivative of the matrix X, the matrix
Figure BDA0002216334910000057
matrix
Figure BDA0002216334910000058
The matrix U' is the matrix of the second output u' of the integral fuzzy sliding mode controller, m is the rotor mass, K x is the force-displacement stiffness coefficient, and K i is the force-current stiffness coefficient.

步骤103，根据状态方程，计算积分模糊滑模控制器的第一输出。具体包括：Step 103: Calculate the first output of the integral fuzzy sliding mode controller according to the state equation. Specifically include:

步骤103-1，根据状态方程计算参考位置指令

Figure BDA0002216334910000059
和位置误差
Figure BDA00022163349100000510
其中Xr为参考位置指令xr的矩阵形式，
Figure BDA00022163349100000511
为参考位置指令xr的一阶导数，X为转子位移x的矩阵形式，E为位置误差e的矩阵形式，
Figure BDA00022163349100000512
为位置误差e的一阶导数；Step 103-1, calculate the reference position command according to the state equation
Figure BDA0002216334910000059
and position error
Figure BDA00022163349100000510
where X r is the matrix form of the reference position instruction x r ,
Figure BDA00022163349100000511
is the first derivative of the reference position command x r , X is the matrix form of the rotor displacement x, E is the matrix form of the position error e,
Figure BDA00022163349100000512
is the first derivative of the position error e;

步骤103-2，定义积分滑模面为

Figure BDA00022163349100000513
其中，积分滑模面的参数k1和k2为非零正常数，t是代表转子运行的时间，0代表转子开始运行，
Figure BDA00022163349100000514
为参考位置指令xr的二阶导数；Step 103-2, define the integral sliding mode surface as
Figure BDA00022163349100000513
Among them, the parameters k 1 and k 2 of the integral sliding mode surface are non-zero positive constants, t is the running time of the rotor, 0 means the rotor starts running,
Figure BDA00022163349100000514
is the second derivative of the reference position command x r ;

计算积分滑模面w的一阶导数：Compute the first derivative of the integral sliding surface w:

Figure BDA0002216334910000061
Figure BDA0002216334910000061

其中x表示的是转子在X方向上的位移，m是转子质量，

Figure BDA0002216334910000066
为转子位移的一阶导数，Kx为力位移刚度系数，Ki为力电流刚度系数，u为积分模糊滑模控制器的第一输出；where x represents the displacement of the rotor in the X direction, m is the mass of the rotor,
Figure BDA0002216334910000066
is the first derivative of the rotor displacement, K x is the force-displacement stiffness coefficient, K i is the force-current stiffness coefficient, and u is the first output of the integral fuzzy sliding mode controller;

优选的，确定k1和k2，其中k1＝150，k2＝200，k1和k2是积分控制的增益常数，其作用是对于克服扰动有很大的帮助，可以有效提升系统性能。Preferably, k 1 and k 2 are determined, wherein k 1 =150, k 2 =200, and k 1 and k 2 are gain constants of integral control, which are of great help in overcoming disturbance and can effectively improve system performance .

令积分滑模面w的一阶导数

Figure BDA0002216334910000062
计算等效控制器的输出为：Let the first derivative of the integral sliding mode surface w
Figure BDA0002216334910000062
Calculate the output of the equivalent controller as:

Figure BDA0002216334910000063
Figure BDA0002216334910000063

步骤103-3，计算切换控制器的输出：Step 103-3, calculate the output of the switching controller:

us＝mηsgn(w)/(Kik2)，u s =mηsgn(w)/(K i k 2 ),

其中，m是转子质量，η为大于零的常数，sgn(·)为符号函数；where m is the rotor mass, η is a constant greater than zero, and sgn( ) is a sign function;

步骤103-4，计算积分模糊滑模控制器的第一输出u为：Step 103-4, calculate the first output u of the integral fuzzy sliding mode controller as:

u＝ueq+us，u=u eq +u s ,

其中，ueq为等效控制器的输出，us为切换控制器的输出；由于滑动模态存在的条件是

Figure BDA0002216334910000064
这样才能保证系统的稳定性，所以所述第一输出u的稳定性判定公式为：Among them, u eq is the output of the equivalent controller, and u s is the output of the switching controller; the condition for the existence of the sliding mode is
Figure BDA0002216334910000064
Only in this way can the stability of the system be guaranteed, so the stability determination formula of the first output u is:

Figure BDA0002216334910000065
Figure BDA0002216334910000065

相对于传统的二输入模糊控制器而言，可以采用积分滑模面w作为模糊控制器的输入，控制输入u作为模糊系统的输出，构成一个单输入/单输出模糊系统，根据经验构造模糊规则库，从而大大减小了模糊规则的数量。Compared with the traditional two-input fuzzy controller, the integral sliding mode surface w can be used as the input of the fuzzy controller, and the control input u can be used as the output of the fuzzy system to form a single-input/single-output fuzzy system, and the fuzzy rules are constructed according to experience. library, thereby greatly reducing the number of fuzzy rules.

步骤104，根据积分滑模面的参数和所述第一输出，通过模糊规则调节等效控制和切换控制权重，计算积分模糊滑模控制器的第二输出，利用所述第二输出来控制推力主动磁悬浮轴承转子的位置。具体包括：Step 104, according to the parameters of the integral sliding mode surface and the first output, adjust the equivalent control and switching control weights through fuzzy rules, calculate the second output of the integral fuzzy sliding mode controller, and use the second output to control the thrust The position of the active magnetic bearing rotor. Specifically include:

步骤104-1，根据积分滑模面w的参数k1和k2，以及积分模糊滑模控制器的第一输出u，确定模糊控制器的模糊规则Rule n为Step 104-1, according to the parameters k 1 and k 2 of the integral sliding mode surface w and the first output u of the integral fuzzy sliding mode controller, determine the fuzzy rule Rule n of the fuzzy controller as:

Figure BDA0002216334910000071
Figure BDA0002216334910000071

其中，

Figure BDA0002216334910000072
和αn分别为输入和输出的模糊集合，n表示N个模糊规则中的第n个；in,
Figure BDA0002216334910000072
and α n are the fuzzy sets of input and output, respectively, and n represents the nth of the N fuzzy rules;

优选的模糊规则Rule n包括以下5条模糊规则为：The preferred fuzzy rule Rule n includes the following five fuzzy rules:

(1)If(w is NB)then(u is PB)(1)If(w is NB)then(u is PB)

(2)If(w is NS)then(u is PS)(2)If(w is NS)then(u is PS)

(3)If(w is Z)then(u is Z)(3)If(w is Z)then(u is Z)

(4)If(w is PS)then(u is NS)(4)If(w is PS)then(u is NS)

(5)If(w is PB)then(u is NB)(5)If(w is PB)then(u is NB)

积分滑模面w和积分模糊滑模控制器的第一输出u的隶属函数采用“负大”(NB)、“负小”(NS)、“零”(Z)、“正小”(PS)、“正大”(PB)，用于在下一步骤中采用重心法进行反模糊化。The membership functions of the integral sliding mode surface w and the first output u of the integral fuzzy sliding mode controller adopt "negative large" (NB), "negative small" (NS), "zero" (Z), "positive small" (PS) ), "Zhengda" (PB) for de-blurring in the next step using the barycentric method.

步骤104-2，采用重心法进行反模糊化，得到模糊控制器的输出：Step 104-2, using the center of gravity method to de-fuzzify to obtain the output of the fuzzy controller:

Figure BDA0002216334910000073
Figure BDA0002216334910000073

其中，ωn和αn分别为第n条规则中前提隶属度和结论的隶属度；Among them, ω n and α n are the premise membership degree and the conclusion membership degree respectively in the nth rule;

若对论域研究的范围Ω中的任一元素δ，都有一个数H(δ)∈[0，1]与之对应，则称H为Ω上的模糊集，H(δ)称为δ对H的隶属度，表示某一元素和论域的关联程度。If there is a number H(δ)∈[0,1] corresponding to any element δ in the range Ω of the universe of discourse research, then H is called a fuzzy set on Ω, and H(δ) is called δ The degree of membership to H indicates the degree of association between an element and the domain of discourse.

采用矩阵实验室MATLAB的S函数程序建立模糊系统，并通过命令persistent将规则库一直保持在运行过程中。取flag＝1时，可给出隶属函数图。The fuzzy system is established by using the S-function program of MATLAB in the matrix laboratory, and the rule base is kept in the running process through the command persistent. When flag=1, the membership function graph can be given.

参见图2和图3，图2是模糊控制器输入变量隶属度函数图，图2的横坐标表示的是论域值，纵坐标表示的是模糊控制器的输入值，图2中的“负大”NB、“负小”NS、“零”Z、“正小”PS和“正大”PB为语言变量值，不同的论域值对应着不同的语言变量值；图3是模糊控制器输出变量隶属度函数图，图3的横坐标表示的是论域值，纵坐标表示的是模糊控制器的输出值，图3中的NB、NS、Z、PS和PB为语言变量值，不同的论域值对应着不同的语言变量值。图2和图3是由模糊输入变量w得到模糊输出变量ufz，模糊输出量ufz相当于切换控制器的系数，ufz和切换控制器相乘，由于ufz是变量，二者的乘积也随之变化，这样就更能适应系统的变化，就达到了提高控制精度的目的。Referring to Figure 2 and Figure 3, Figure 2 is a diagram of the membership function of the input variable of the fuzzy controller. The abscissa of Figure 2 represents the universe value, and the ordinate represents the input value of the fuzzy controller. "Big" NB, "negative small" NS, "zero" Z, "positive small" PS and "positive big" PB are linguistic variable values, and different domain values correspond to different linguistic variable values; Figure 3 is the output of the fuzzy controller The variable membership function diagram, the abscissa in Figure 3 represents the universe of discourse value, and the ordinate represents the output value of the fuzzy controller. In Figure 3, NB, NS, Z, PS and PB are linguistic variable values. Domain values correspond to different linguistic variable values. Figures 2 and 3 show the fuzzy output variable u fz obtained from the fuzzy input variable w. The fuzzy output u fz is equivalent to the coefficient of the switching controller, and u fz is multiplied by the switching controller. Since u fz is a variable, the product of the two It also changes accordingly, so that it can better adapt to the changes of the system and achieve the purpose of improving the control accuracy.

步骤104-3，计算积分模糊滑模控制器的第二输出：Step 104-3, calculate the second output of the integral fuzzy sliding mode controller:

u′＝ueq+ufzus，u′=u eq +u fz u s ,

其中ueq为等效控制器的输出，us为切换控制器的输出，ufz为模糊控制器的输出；积分模糊滑模控制器的第二输出u′是控制电流形式的输出。Among them, ue eq is the output of the equivalent controller, u s is the output of the switching controller, and u fz is the output of the fuzzy controller; the second output u' of the integral fuzzy sliding mode controller is the output in the form of control current.

步骤104-4，将积分模糊滑模控制器的第二输出u′作为控制信号，作用到推力主动磁悬浮轴承系统中来改变转子位置。Step 104-4, the second output u' of the integral fuzzy sliding mode controller is used as a control signal to act on the thrust active magnetic suspension bearing system to change the rotor position.

图4为本发明实施例提供的一种推力主动磁悬浮轴承的积分模糊滑模控制设备的结构图。所述设备与推力主动磁悬浮轴承相连接，包括以下模块：FIG. 4 is a structural diagram of an integral fuzzy sliding mode control device for a thrust active magnetic suspension bearing according to an embodiment of the present invention. The equipment is connected with the thrust active magnetic suspension bearing and includes the following modules:

磁悬浮轴承转子的力学转换模块410，用于计算X方向上推力主动磁悬浮轴承转子的力学方程，通过拉氏变换得到推力主动磁悬浮轴承的传递函数；将传递函数转换成状态方程；The mechanical conversion module 410 of the magnetic suspension bearing rotor is used to calculate the mechanical equation of the thrust active magnetic suspension bearing rotor in the X direction, obtain the transfer function of the thrust active magnetic suspension bearing through Laplace transformation; convert the transfer function into a state equation;

积分模糊滑模控制器420，包括等效控制器421、切换控制器422和模糊控制器423，用于根据状态方程，计算积分模糊滑模控制器420的第一输出；根据积分滑模面的参数和所述第一输出，通过模糊规则得到模糊控制器423的输出，使用模糊控制器423的输出调节等效控制器421和切换控制器422的权重，计算积分模糊滑模控制器420的第二输出；利用所述第二输出来控制推力主动磁悬浮轴承转子的位置。The integral fuzzy sliding mode controller 420 includes an equivalent controller 421, a switching controller 422 and a fuzzy controller 423, and is used to calculate the first output of the integral fuzzy sliding mode controller 420 according to the state equation; parameters and the first output, obtain the output of the fuzzy controller 423 through fuzzy rules, use the output of the fuzzy controller 423 to adjust the weights of the equivalent controller 421 and the switching controller 422, and calculate the first output of the integral fuzzy sliding mode controller 420. Two outputs; the second output is used to control the position of the thrust active magnetic bearing rotor.

优选的，所述磁悬浮轴承转子的力学转换模块410，具体用于：Preferably, the mechanical conversion module 410 of the magnetic suspension bearing rotor is specifically used for:

根据推力主动磁悬浮轴承转子在X方向上的位移x，计算转子X方向上的力学方程：According to the displacement x of the thrust active magnetic bearing rotor in the X direction, calculate the mechanical equation of the rotor in the X direction:

Figure BDA0002216334910000091
Figure BDA0002216334910000091

通过拉氏变换得到拉氏变换式：The Laplace transform is obtained by Laplace transform:

ms2X(s)＝KxX(s)+KiI(s)；ms 2 X(s)=K x X(s)+K i I(s);

进而得到推力主动磁悬浮轴承的传递函数G(s)：Then the transfer function G(s) of the thrust active magnetic bearing is obtained:

Figure BDA0002216334910000092
Figure BDA0002216334910000092

其中，x表示的是转子在X方向上的位移，m是转子质量，

Figure BDA0002216334910000093
为转子位移的二阶导数，i是X方向上的控制电流，Kx为力位移刚度系数，Ki为力电流刚度系数，s是推力主动磁悬浮轴承转子的传递函数的变量，X(s)表示传递函数的输出量，I(s)表示传递函数的输入量；Among them, x represents the displacement of the rotor in the X direction, m is the mass of the rotor,
Figure BDA0002216334910000093
is the second derivative of the rotor displacement, i is the control current in the X direction, K x is the force-displacement stiffness coefficient, K i is the force-current stiffness coefficient, s is the variable of the transfer function of the thrust active magnetic bearing rotor, X(s) Represents the output of the transfer function, and I(s) represents the input of the transfer function;

将传递函数转换成状态方程为：Converting the transfer function to the equation of state is:

Figure BDA0002216334910000094
Figure BDA0002216334910000094

其中，转子位移x的矩阵

Figure BDA0002216334910000095
Figure BDA0002216334910000096
是转子位移x的一阶导数，矩阵
Figure BDA0002216334910000097
为矩阵X的一阶导数，矩阵
Figure BDA0002216334910000101
矩阵
Figure BDA0002216334910000102
矩阵U′为积分模糊滑模控制器的第二输出u′的矩阵，m是转子质量，Kx为力位移刚度系数，Ki为力电流刚度系数。where, the matrix of rotor displacement x
Figure BDA0002216334910000095
Figure BDA0002216334910000096
is the first derivative of the rotor displacement x, matrix
Figure BDA0002216334910000097
is the first derivative of the matrix X, the matrix
Figure BDA0002216334910000101
matrix
Figure BDA0002216334910000102
The matrix U' is the matrix of the second output u' of the integral fuzzy sliding mode controller, m is the rotor mass, K x is the force-displacement stiffness coefficient, and K i is the force-current stiffness coefficient.

优选的，所述积分模糊滑模控制器420根据状态方程，计算积分模糊滑模控制器420的第一输出包括：Preferably, the integral fuzzy sliding mode controller 420 calculates the first output of the integral fuzzy sliding mode controller 420 according to the state equation, including:

根据状态方程计算参考位置指令

Figure BDA0002216334910000103
和位置误差
Figure BDA0002216334910000104
其中Xr为参考位置指令xr的矩阵形式，
Figure BDA0002216334910000105
为参考位置指令xr的一阶导数，X为转子位移x的矩阵形式，E为位置误差e的矩阵形式，
Figure BDA0002216334910000106
为位置误差e的一阶导数；Calculate the reference position command from the equation of state
Figure BDA0002216334910000103
and position error
Figure BDA0002216334910000104
where X r is the matrix form of the reference position instruction x r ,
Figure BDA0002216334910000105
is the first derivative of the reference position command x r , X is the matrix form of the rotor displacement x, E is the matrix form of the position error e,
Figure BDA0002216334910000106
is the first derivative of the position error e;

定义积分滑模面为

Figure BDA0002216334910000107
其中，k1和k2为非零正常数，t是代表转子运行的时间，0代表转子开始运行，
Figure BDA0002216334910000108
为参考位置指令xr的二阶导数；The integral sliding mode surface is defined as
Figure BDA0002216334910000107
Among them, k 1 and k 2 are non-zero positive constants, t is the running time of the rotor, 0 means the rotor starts running,
Figure BDA0002216334910000108
is the second derivative of the reference position command x r ;

计算积分滑模面w的一阶导数：Compute the first derivative of the integral sliding surface w:

Figure BDA0002216334910000109
Figure BDA0002216334910000109

其中，x表示的是转子在X方向上的位移，m是转子质量，

Figure BDA00022163349100001010
为转子位移的一阶导数，Kx为力位移刚度系数，Ki为力电流刚度系数，u为积分模糊滑模控制器的第一输出；Among them, x represents the displacement of the rotor in the X direction, m is the mass of the rotor,
Figure BDA00022163349100001010
is the first derivative of the rotor displacement, K x is the force-displacement stiffness coefficient, K i is the force-current stiffness coefficient, and u is the first output of the integral fuzzy sliding mode controller;

令积分滑模面w的一阶导数

Figure BDA00022163349100001011
计算等效控制器421的输出为：Let the first derivative of the integral sliding mode surface w
Figure BDA00022163349100001011
The output of the computationally equivalent controller 421 is:

Figure BDA00022163349100001012
Figure BDA00022163349100001012

计算切换控制器422的输出：Calculate the output of switching controller 422:

us＝mηsgn(w)/(Kik2)，u s =mηsgn(w)/(K i k 2 ),

其中，m是转子质量，η为大于零的常数，sgn(·)为符号函数；where m is the rotor mass, η is a constant greater than zero, and sgn( ) is a sign function;

计算积分模糊滑模控制器420的第一输出u为：Calculate the first output u of the integral fuzzy sliding mode controller 420 as:

u＝ueq+us，u=u eq +u s ,

其中，ueq为等效控制器的输出，us为切换控制器的输出；所述第一输出u的稳定性判定公式为：Wherein, u eq is the output of the equivalent controller, and u s is the output of the switching controller; the stability determination formula of the first output u is:

Figure BDA0002216334910000111
Figure BDA0002216334910000111

优选的，所述积分模糊滑模控制器420计算积分模糊滑模控制器420的第二输出包括：Preferably, the integral fuzzy sliding mode controller 420 calculates the second output of the integral fuzzy sliding mode controller 420 including:

根据积分滑模面w的系数k1和k2，以及积分模糊滑模控制器420的第一输出u，确定模糊控制器423的模糊规则Rule n为According to the coefficients k 1 and k 2 of the integral sliding mode surface w and the first output u of the integral fuzzy sliding mode controller 420 , the fuzzy rule Rule n of the fuzzy controller 423 is determined as:

Figure BDA0002216334910000112
Figure BDA0002216334910000112

其中，

Figure BDA0002216334910000113
和αn分别为输入和输出的模糊集合，n表示N个模糊规则中的第n个；in,
Figure BDA0002216334910000113
and α n are the fuzzy sets of input and output, respectively, and n represents the nth of the N fuzzy rules;

采用重心法进行反模糊化，得到模糊控制器423的输出：Defuzzification is carried out using the center of gravity method, and the output of the fuzzy controller 423 is obtained:

Figure BDA0002216334910000114
Figure BDA0002216334910000114

其中，ωn和αn分别为第n条规则中前提隶属度和结论的隶属度；Among them, ω n and α n are the premise membership degree and the conclusion membership degree respectively in the nth rule;

计算积分模糊滑模控制器420的第二输出：Calculate the second output of the integral fuzzy sliding mode controller 420:

u′＝ueq+ufzus，u′=u eq +u fz u s ,

其中，ueq为等效控制器421的输出，us为切换控制器422的输出，ufz为模糊控制器423的输出。Among them, ue eq is the output of the equivalent controller 421 , u s is the output of the switching controller 422 , and u fz is the output of the fuzzy controller 423 .

上述实施例中的采用具有积分滑模面的模糊滑模控制方法及设备，其能够在推力主动磁悬浮轴承系统受到扰动时，推力主动磁悬浮轴承仍能够实现正常工作，提高推力主动磁悬浮轴承的控制精度并有效减轻与消除滑模抖振，具有较强的鲁棒干扰能力。The fuzzy sliding mode control method and device with integral sliding mode surface in the above-mentioned embodiments can still achieve normal operation of the thrust active magnetic suspension bearing when the thrust active magnetic suspension bearing system is disturbed, and improve the control accuracy of the thrust active magnetic suspension bearing. And effectively reduce and eliminate sliding mode chattering, with strong robust interference ability.

以下根据实际推力主动磁悬浮轴承系统的具体参数，通过仿真来对比传统等效滑模控制方法与具有积分滑模面的模糊滑模控制方法在相同仿真条件下得到的位置跟踪结果来验证具有积分滑模面的模糊滑模控制方法的有效性。According to the specific parameters of the actual thrust active magnetic suspension bearing system, the position tracking results obtained by the traditional equivalent sliding mode control method and the fuzzy sliding mode control method with integral sliding mode surface under the same simulation conditions are compared through simulation to verify that the integral sliding mode control method has integral sliding mode. Effectiveness of fuzzy sliding mode control methods for die surfaces.

图5是本发明提供的控制方法应用于控制对象之后的效果图，当系统从启动到稳定运行时，系统在积分模糊滑模控制作用下能够在0.15s(秒)迅速稳定下来，没有振荡现象且其稳定后的偏离值小于±0.001mm(毫米)满足对系统稳定偏离值的要求。Figure 5 is the effect diagram after the control method provided by the present invention is applied to the control object. When the system starts to run stably, the system can quickly stabilize within 0.15s (seconds) under the action of integral fuzzy sliding mode control, and there is no oscillation phenomenon. And its stable deviation value is less than ±0.001mm (mm) to meet the requirements of the system stable deviation value.

图6是本发明和现有的传统等效滑模控制效果对比图，从图6可以看出现有的传统等效滑模控制方法应用于该系统后的效果图，当系统从启动到稳定运行时，系统在传统等效滑模控制作用下发生了振荡现象并在0.21s稳定下来，稳定后的偏离值为+0.001mm～+0.002mm之间，部分满足对系统稳定偏离值的要求。通过对比，可以得出以下结论：具有积分滑模面的模糊滑模控制方法在该系统中比现有的传统等效滑模控制方法达到稳定运行所需要的时间更短，相对于位移参考指令的偏离值更小，且没有振荡现象，具有更强的鲁棒干扰能力。Figure 6 is a comparison diagram of the effect of the present invention and the existing traditional equivalent sliding mode control. It can be seen from Figure 6 that the existing traditional equivalent sliding mode control method is applied to the system. When the system starts to run stably When , the system oscillates under the traditional equivalent sliding mode control and stabilizes in 0.21s. The deviation value after stabilization is between +0.001mm and +0.002mm, which partially meets the requirements for the stable deviation value of the system. By comparison, the following conclusions can be drawn: the time required for the fuzzy sliding mode control method with integral sliding mode surface to achieve stable operation in this system is shorter than that of the existing traditional equivalent sliding mode control method, compared with the displacement reference command The deviation value is smaller, and there is no oscillation phenomenon, which has a stronger robust interference ability.

以上的所述乃是本发明的具体实施例及所运用的技术原理，若依本发明的构想所作的改变，其所产生的功能作用仍未超出说明书及附图所涵盖的精神时，仍应属本发明的保护范围。The above descriptions are the specific embodiments of the present invention and the technical principles used. If changes are made according to the concept of the present invention, if the functions produced by them still do not exceed the spirit covered by the description and the accompanying drawings, they should still be It belongs to the protection scope of the present invention.

Claims (7)

1. An integral fuzzy sliding mode control method of a thrust active magnetic suspension bearing is characterized by comprising the following steps:
step 1, calculating a mechanical equation of a rotor in the X direction according to the displacement of the rotor of the thrust active magnetic suspension bearing in the X direction, and obtaining a transfer function of the thrust active magnetic suspension bearing through Laplace transformation;
step 2, converting a transfer function of the thrust active magnetic suspension bearing into a state equation;
step 3, calculating a first output of the integral fuzzy sliding mode controller according to a state equation;
step 4, adjusting equivalent control and switching control weight through a fuzzy rule according to the parameters of the integral sliding mode surface and the first output, calculating a second output of the integral fuzzy sliding mode controller, and controlling the position of the thrust active magnetic suspension bearing rotor by using the second output;
wherein, in the step 3, calculating the first output of the integral fuzzy sliding mode controller according to the state equation comprises:
step 301, calculating a reference position command according to a state equation
Figure FDA0003714339260000011
And position error
Figure FDA0003714339260000012
Wherein X r As a reference position instruction x r In the form of a matrix of (a),
Figure FDA0003714339260000013
as a reference position instruction x r X is the matrix form of the rotor displacement X, E is the matrix form of the position error E,
Figure FDA0003714339260000014
is the first derivative of the position error e;
step 302, defining the formula of the integral sliding mode surface w as
Figure FDA0003714339260000015
Wherein, the integral sliding mode surface parameter k 1 And k 2 Is a non-zero positive constant, t represents the time of rotor operation, 0 represents the start of rotor operation,
Figure FDA0003714339260000016
as a reference position instruction x r The second derivative of (a);
calculating the first derivative of integral sliding-mode surface w:
Figure FDA0003714339260000017
where X denotes the displacement of the rotor in the X direction, m is the rotor mass,
Figure FDA0003714339260000018
as the first derivative of rotor displacement, K x Is a force displacement stiffness coefficient, K i The force current stiffness coefficient is, and u is a first output of the integral fuzzy sliding mode controller;
integral first derivative of sliding mode surface w
Figure FDA0003714339260000021
The output of the equivalent controller is calculated as:
Figure FDA0003714339260000022
step 303, calculate the output of the switching controller:
u s ＝mηsgn(w)/(K i k 2 )，
wherein m is the rotor mass, η is a constant greater than zero, sgn (·) is a sign function;
step 304, calculating a first output u of the integral fuzzy sliding mode controller as:
u＝u eq +u s ，
wherein u is eq Is an output of the equivalent controller, u s Is the output of the switching controller; the stability determination formula of the first output u is:
Figure FDA0003714339260000023
2. the method of claim 1, wherein step 1 comprises:
according to the displacement X of the thrust active magnetic suspension bearing rotor in the X direction, calculating a mechanical equation of the rotor in the X direction:
Figure FDA0003714339260000024
obtaining a Laplace transformation formula through Laplace transformation:
ms 2 X(s)＝K x X(s)+K i I(s)；
further obtaining a transfer function G(s) of the thrust active magnetic suspension bearing:
Figure FDA0003714339260000025
where X denotes the displacement of the rotor in the X direction, m is the rotor mass,
Figure FDA0003714339260000026
for the second derivative of rotor displacement, i is the control current in the X direction, K x Is a force displacement stiffness coefficient, K i For force current stiffness coefficient, s is a variable of a transfer function of the thrust active magnetic suspension bearing rotor, X(s) represents an output quantity of the transfer function, and I(s) represents an input quantity of the transfer function.
3. The method of claim 1, wherein the expression of the state equation of step 2 is:
Figure FDA0003714339260000031
wherein the matrix of rotor displacements x
Figure FDA0003714339260000032
Figure FDA0003714339260000033
Is the first derivative, matrix, of the rotor displacement x
Figure FDA0003714339260000034
Being the first derivative of the matrix X, the matrix
Figure FDA0003714339260000035
Matrix array
Figure FDA0003714339260000036
The matrix U 'is the matrix of the second output U' of the integral fuzzy sliding mode controller, m is the rotor mass, K x Is a force displacement stiffness coefficient, K i Is the force current stiffness coefficient.
4. The method of claim 1, wherein step 4 comprises:
step 401, according to the parameter k of the integral sliding mode surface w 1 And k 2 And a first output u of the integral fuzzy sliding mode controller, determining a fuzzy Rule n of the fuzzy controller as
Figure FDA0003714339260000037
Wherein,
Figure FDA0003714339260000038
and alpha n Fuzzy sets which are input and output respectively, wherein N represents the nth fuzzy rule in the N fuzzy rules;
step 402, performing defuzzification by using a gravity center method to obtain the output of a fuzzy controller:
Figure FDA0003714339260000039
wherein, ω is n And alpha n Membership degrees of the antecedents and the conclusions in the nth rule respectively;
step 403, calculating a second output of the integral fuzzy sliding mode controller:
u'＝u eq +u fz u s ，
wherein u is eq Is an output of the equivalent controller, u s For switching the controllerOutput of u fz Is the output of the fuzzy controller;
and step 404, taking the second output u' of the integral fuzzy sliding mode controller as a control signal, and applying the control signal to the thrust active magnetic suspension bearing system to change the position of the rotor.
5. The utility model provides an integral fuzzy sliding mode controlgear of thrust initiative magnetic suspension bearing, is connected with thrust initiative magnetic suspension bearing which characterized in that includes:
the mechanical conversion module of the magnetic suspension bearing rotor is used for calculating a mechanical equation of the thrust active magnetic suspension bearing rotor in the X direction and obtaining a transfer function of the thrust active magnetic suspension bearing through Laplace transformation; converting the transfer function into a state equation;
the integral fuzzy sliding mode controller comprises an equivalent controller, a switching controller and a fuzzy controller and is used for calculating first output of the integral fuzzy sliding mode controller according to a state equation; obtaining the output of a fuzzy controller through a fuzzy rule according to the parameters of the integral sliding mode surface and the first output, adjusting the weights of the equivalent controller and the switching controller by using the output of the fuzzy controller, and calculating the second output of the integral fuzzy sliding mode controller; controlling a position of a thrust active magnetic bearing rotor using the second output;
the integral fuzzy sliding mode controller is used for calculating the first output of the integral fuzzy sliding mode controller according to a state equation, and comprises the following steps:
calculating a reference position command from a state equation
Figure FDA0003714339260000041
And position error
Figure FDA0003714339260000042
Wherein X r As a reference position instruction x r In the form of a matrix of (a),
Figure FDA0003714339260000043
as a reference position instruction x r First order ofNumber, X is the matrix form of the rotor displacement X, E is the matrix form of the position error E,
Figure FDA0003714339260000044
is the first derivative of the position error e;
defining an integral sliding mode surface as
Figure FDA0003714339260000045
Wherein k is 1 And k 2 Is a non-zero positive constant, t represents the time of rotor operation, 0 represents the start of rotor operation,
Figure FDA0003714339260000046
as a reference position instruction x r The second derivative of (a);
calculating the first derivative of integral sliding-mode surface w:
Figure FDA0003714339260000051
where X denotes the displacement of the rotor in the X direction, m is the rotor mass,
Figure FDA0003714339260000052
as the first derivative of rotor displacement, K x Is a force displacement stiffness coefficient, K i Is a force current stiffness coefficient, and u is a first output of the integral fuzzy sliding mode controller;
integral first derivative of sliding mode surface w
Figure FDA0003714339260000053
The output of the equivalent controller is calculated as:
Figure FDA0003714339260000054
compute the output of the switching controller:
u s ＝mηsgn(w)/(K i k 2 )，
wherein m is the rotor mass, η is a constant greater than zero, sgn (·) is a sign function;
calculating a first output u of the integral fuzzy sliding mode controller as:
u＝u eq +u s ，
wherein u is eq Is an output of the equivalent controller, u s Is the output of the switching controller; the stability determination formula of the first output u is:
Figure FDA0003714339260000055
6. the apparatus according to claim 5, characterized in that the mechanical transformation module of the magnetic bearing rotor is specifically configured to:
according to the displacement X of the thrust active magnetic suspension bearing rotor in the X direction, calculating a mechanical equation of the rotor in the X direction:
Figure FDA0003714339260000056
obtaining a Laplace transformation formula through Laplace transformation:
ms 2 X(s)＝K x X(s)+K i I(s)；
further obtaining a transfer function G(s) of the thrust active magnetic suspension bearing:
Figure FDA0003714339260000061
where X denotes the displacement of the rotor in the X direction, m is the rotor mass,
Figure FDA0003714339260000062
for the second derivative of rotor displacement, i is the control current in the X direction, K x Is a force displacement steelCoefficient of degree, K i For a force current stiffness coefficient, s is a variable of a transfer function of a thrust active magnetic suspension bearing rotor, X(s) represents an output quantity of the transfer function, and I(s) represents an input quantity of the transfer function;
converting the transfer function to a state equation as:
Figure FDA0003714339260000063
wherein the matrix of rotor displacements x
Figure FDA0003714339260000064
Figure FDA0003714339260000065
Is the first derivative, matrix, of the rotor displacement x
Figure FDA0003714339260000066
Being the first derivative of the matrix X, the matrix
Figure FDA0003714339260000067
Matrix array
Figure FDA0003714339260000068
The matrix U 'is the matrix of the second output U' of the integral fuzzy sliding mode controller, m is the rotor mass, K x Is a force displacement stiffness coefficient, K i Is the force current stiffness coefficient.
7. The apparatus of claim 5, wherein the integral fuzzy sliding mode controller calculating the second output of the integral fuzzy sliding mode controller comprises:
parameter k from integral sliding mode surface w 1 And k 2 And a first output u of the integral fuzzy sliding mode controller, determining a fuzzy Rule n of the fuzzy controller as
Figure FDA0003714339260000069
Wherein,
Figure FDA00037143392600000610
and alpha n Fuzzy sets which are input and output respectively, wherein N represents the nth fuzzy rule in the N fuzzy rules;
performing defuzzification by adopting a gravity center method to obtain the output of a fuzzy controller:
Figure FDA0003714339260000071
wherein, ω is n And alpha n Membership degrees of the antecedents and the conclusions in the nth rule respectively;
calculating a second output of the integrating fuzzy sliding mode controller:
u'＝u eq +u fz u s ，
wherein u is eq Is an output of the equivalent controller, u s For switching the output of the controller, u fz Is the output of the fuzzy controller.
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