WO2023237018A1 - 一种适用于双轴永磁伺服系统的非线性预测位置控制方法 - Google Patents

一种适用于双轴永磁伺服系统的非线性预测位置控制方法 Download PDF

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WO2023237018A1
WO2023237018A1 PCT/CN2023/098959 CN2023098959W WO2023237018A1 WO 2023237018 A1 WO2023237018 A1 WO 2023237018A1 CN 2023098959 W CN2023098959 W CN 2023098959W WO 2023237018 A1 WO2023237018 A1 WO 2023237018A1
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permanent magnet
axis
magnet synchronous
synchronous motor
dual
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PCT/CN2023/098959
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English (en)
French (fr)
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曹彦飞
夏长亮
李晨
周湛清
耿强
史婷娜
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浙江大学先进电气装备创新中心
浙江大学
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Publication of WO2023237018A1 publication Critical patent/WO2023237018A1/zh

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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/18—Estimation of position or speed
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/22—Current control, e.g. using a current control loop
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P70/00—Climate change mitigation technologies in the production process for final industrial or consumer products
    • Y02P70/10—Greenhouse gas [GHG] capture, material saving, heat recovery or other energy efficient measures, e.g. motor control, characterised by manufacturing processes, e.g. for rolling metal or metal working

Definitions

  • the invention relates to a control method for a permanent magnet synchronous motor, and in particular to a nonlinear predictive position control method suitable for a dual-axis permanent magnet synchronous motor.
  • Permanent magnet synchronous motors have the advantages of simple structure, high power density, and wide speed range, and are widely used in precision machining of CNC machine tools, semiconductor micromachining, robots and other applications.
  • the performance of the dual-axis permanent magnet synchronous motor drive system deteriorates and the contour tracking accuracy decreases. Therefore, it is of great significance to study the permanent magnet synchronous motor position tracking control strategy to achieve efficient and stable operation of the dual-axis permanent magnet synchronous motor drive system.
  • Literature [1] is based on generalized model predictive control, and adds the tracking error of permanent magnet synchronous motor as a control target to the value function.
  • the solution is to obtain a single-axis drive motor cascade generalized predictive controller to drive each axis motor, and combine it with cross-coupling control decoupling. Realize the contour tracking control of the dual-axis permanent magnet synchronous motor drive system.
  • Literature [2] combines the model predictive control method, introduces the tracking error and the contour error as the control objectives at the same time into the value function, and solves the control law based on the optimal control theory, determines the controller structure of the system, and realizes the drive control of the dual-axis motor.
  • traditional model predictive control methods mostly use a cascade controller structure to control dual-axis drive motors.
  • the controller structure is relatively redundant and has limited dynamic response performance.
  • the technical problem to be solved by the present invention is to provide a nonlinear predictive position control method that can improve the dynamic response capability of a dual-axis drive motor and improve the contour tracking accuracy of a dual-axis permanent magnet synchronous motor drive system.
  • the invention has a simple structure, fast dynamic response and high position tracking accuracy, and is of great significance for improving the accuracy of biaxial contour tracking.
  • a value function and its constraints for the dual-axis permanent magnet synchronous motor drive system are constructed, and the value function is solved to obtain the voltage control quantity of the permanent magnet synchronous motor.
  • the voltage control quantity of the permanent magnet synchronous motor is input to the fixed voltage of the permanent magnet synchronous motor. sub-voltage input terminal, thereby achieving nonlinear predictive position adjustment control of the dual-axis permanent magnet synchronous motor drive system.
  • J is the value function value used by the predictive controller
  • T 1 and T 2 are the prediction step sizes of the permanent magnet synchronous motor current loop and position loop respectively
  • H 1 and H 2 respectively represent the value function weight coefficient matrix
  • Y 1 and Y 2 respectively represent the value function output evaluation vector
  • t represents the time
  • ⁇ represents the future control time domain
  • y 1 (t) , y 2 (t) respectively represent the first component and the second component of the actual output vector of the control system at time t
  • Respectively represent the second derivative of the second component of the actual output vector of the control system at time t respectively
  • Respectively represent the first derivatives of the first component and the second component of the control system reference output vector at time t represent the second-order derivative and the third-order derivative of the
  • the above value function enables the permanent magnet synchronous motor system to track the given value as quickly as possible.
  • x(t) represents the state variable at time t
  • i qi represents the actual value of the q-axis current of the two permanent magnet synchronous motors
  • ⁇ i is the mechanical angular velocity of the two permanent magnet synchronous motors
  • u(t) represents the motor control system at time t
  • Input vectors u di and u qi respectively represent the voltage control quantities of the d-axis and q-axis of the permanent magnet synchronous motor
  • b di , b qi , b ⁇ i , and b ⁇ i respectively represent the changes in the d-axis parameters in the permanent magnet synchronous motor system.
  • f() represents the nonlinear function of the motor control system
  • h() represents the output function of the motor control system
  • b(t) represents the uncertain disturbance vector at time t
  • g 1 (), g 2 () represent the coefficient matrix functions of the input vector and disturbance vector respectively
  • R s , L s , ⁇ f , p, J m and B are the stator resistance, inductance and rotor of the permanent magnet synchronous motor respectively. Permanent magnet flux linkage, number of pole pairs, moment of inertia and friction coefficient;
  • the voltage control quantity u(t) of the permanent magnet synchronous motor is obtained by minimizing the value function equation, that is, Solve for the goal.
  • the uncertain disturbance b(t) is obtained by establishing a nonlinear disturbance observer.
  • the above-mentioned nonlinear disturbance observer of the present invention can realize high-precision control of trajectory tracking of the dual-axis permanent magnet synchronous motor drive system and perform real-time estimation of the uncertain disturbance b(t) of the permanent magnet synchronous motor system.
  • q() is the nonlinear function to be designed for the nonlinear observer
  • L is the gain matrix of the nonlinear observer
  • l 1 , l 2 , l 3 , l 4 represents the first, second, third and fourth gain coefficients of the nonlinear observer respectively, and the gain coefficients l 1 , l 2 , l 3 , l 4 >0
  • G() represents the coefficient matrix related to the motor parameters in the voltage control quantity; and Represents the coefficient related to the prediction step in the voltage control variable; K 1 and K 2 respectively represent the constant matrix in the voltage control variable; represents the Lie derivative symbol.
  • the method of the present invention applies the nonlinear predictive control algorithm to the position control of the permanent magnet synchronous motor of the dual-axis system, and establishes the optimal control value function of the nonlinear predictive position control.
  • the present invention uses a nonlinear predictive control algorithm to construct a single-axis motor non-cascade controller, simplifying the transmission
  • the system cascade controller structure at the same time, the present invention adopts the optimization principle to solve the nonlinear prediction value function, which can effectively reduce the system calculation amount, improve the system dynamic response performance, and thereby improve the contour tracking accuracy of the dual-axis permanent magnet synchronous motor drive system.
  • the present invention can effectively suppress the influence of parameter uncertainty disturbance on the position tracking of the motor in the dual-axis system.
  • Figure 1 is a schematic diagram of an embodiment of a control system under the method of the present invention
  • Figure 2 is the schematic diagram of the nonlinear predictive control algorithm of a single-axis motor.
  • the present invention constructs a cascaded single-loop nonlinear predictive position controller based on a nonlinear predictive control algorithm, thereby improving the dynamic response performance of the system.
  • a nonlinear disturbance observer is constructed to observe uncertainty disturbances such as system parameter mismatch and load mutation to suppress the impact of system uncertainty disturbances.
  • the position correction link is combined to realize compensation for the given position of the dual-axis drive motor.
  • Figure 1 is a system block diagram using the nonlinear predictive position control method of the dual-axis permanent magnet synchronous motor drive system of the present invention.
  • ⁇ x and ⁇ y are the actual values of the x and y axis motor rotor positions respectively
  • ⁇ x and ⁇ y are the x and y axis motor mechanical angular velocities respectively
  • i dx and i dy are the actual values of the d-axis current of the x- and y-axis motors respectively
  • i qx and i qy are the actual values of the q-axis current of the x- and y-axis motors, respectively.
  • ⁇ cx and ⁇ cy are the given position corrections output by the cross-coupled control structure
  • p* and p are the given position and actual position matrices of the dual-axis system respectively
  • C x , C y is the contour error compensation coefficient of each axis
  • C c is the gain coefficient of the cross-coupling controller
  • e is the dual-axis contour error.
  • the uncertain disturbance b(t) is obtained by establishing a nonlinear disturbance observer.
  • the voltage control quantity u(t) of the permanent magnet synchronous motor is obtained by minimizing the value function equation, that is, Solve for the goal.
  • Figure 2 is a schematic diagram of the nonlinear position prediction algorithm for a single-axis motor.
  • the d-axis current given value of the permanent magnet synchronous motor is used control mode, and the dual-axis permanent magnet synchronous motor drive system is given the contour trajectory corresponding to the mechanical rotor position angle of each axis of the motor
  • the control of each axis permanent magnet synchronous motor is realized.

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Control Of Ac Motors In General (AREA)

Abstract

本发明公开了一种适用于双轴永磁伺服系统的非线性预测位置控制方法。考虑到双轴永磁同步电机驱动系统存在不确定性扰动，构建针对双轴永磁同步电机驱动系统的价值函数及其约束条件，对价值函数进行求解获得永磁同步电机的电压控制量，将永磁同步电机的电压控制量输入到永磁同步电机的定子电压输入端，进而实现双轴永磁同步电机驱动系统的非线性预测位置的调节控制。本发明通过构建非线性扰动观测器估计系统不确定扰动，可有效抑制参数不确定性扰动给双轴系统电机位置跟踪影响，简化了传统级联控制器结构，有效减小系统计算量，提高系统动态响应性能。

Description

一种适用于双轴永磁伺服系统的非线性预测位置控制方法 技术领域
本发明涉及一种永磁同步电机的控制方法，特别是涉及了一种适用于双轴永磁同步电机非线性预测位置控制方法。
背景技术
永磁同步电机具有结构简单、功率密度大、调速范围宽等优点被广泛应用数控机床精密加工、半导体微加工、机器人等应用场合。然而，在实际工作过程中，由于参考轮廓轨迹发生转折、双轴驱动电机负载不平衡等因素导致双轴永磁同步电机驱动系统性能发生恶化，轮廓跟踪精度降低。因此，研究永磁同步电机位置跟踪控制策略，以实现双轴永磁同步电机驱动系统高效、稳定的运行具有重要意义。
近年来，国内外学者对双轴轮廓控制方法进行了深入研究。其中，模型预测控制方法凭借其动态响应速度快等优点被广泛应用于多电机控制系统。文献[1]基于广义模型预测控制，将永磁同步电机跟踪误差作为控制目标加入至价值函数中，求解获得单轴驱动电机级联广义预测控制器驱动各轴电机，并结合交叉耦合控制解耦实现双轴永磁同步电机驱动系统的轮廓跟踪控制。文献[2]结合模型预测控制方法，将跟踪误差与轮廓误差作为控制目标同时引入价值函数中，并基于最优控制理论求解控制律，确定系统的控制器结构，实现对双轴电机的驱动控制。然而，传统的模型预测控制方法大多采用一种级联控制器结构实现对双轴驱动电机的控制，其控制器结构相对冗余，动态响应性能有限。
发明内容
本发明所要解决的技术问题是，提供一种能够提高双轴驱动电机动态响应能力，提高双轴永磁同步电机驱动系统轮廓跟踪精度的非线性预测位置控制方法。本发明结构简单，动态响应快，位置跟踪精度高，对改善双轴轮廓跟踪精度具有重要意义。
本发明所采用的技术方案是：
考虑到双轴永磁同步电机驱动系统存在不确定性扰动，构建针对双轴永磁同步电机驱动系统的价值函数及其约束条件，对价值函数进行求解获得永磁同步电机的电压控制量，将永磁同步电机的电压控制量输入到永磁同步电机的定 子电压输入端，进而实现双轴永磁同步电机驱动系统的非线性预测位置的调节控制。
构建以下针对双轴永磁同步电机驱动系统的价值函数为：
H1＝[1 τ]，

其中，J为预测控制器采用的价值函数值，T1、T2分别为永磁同步电机电流环和位置环的预测步长；分别表示价值函数参考输出向量，H1、H2分别表示价值函数权重系数矩阵，Y1、Y2分别表示价值函数输出评估向量，t表示时刻，τ表示未来控制时域；y1(t)、y2(t)分别表示t时刻控制系统实际输出向量的第一分量和第二分量；分别表示t时刻控制系统实际输出向量第一分量和第二分量的一阶导数；分别表示t时刻控制系统实际输出向量第二分量的二阶导数；分别表示t时刻控制系统参考输出向量的第一分量和第二分量；分别表示t时刻控制系统参考输出向量第一分量和第二分量的一阶导数；分别表示t时刻控制系统参考输出向量第二分量的二阶导数和三阶导数；idi(t)、分别表示t时刻两台永磁同步电机d轴电流的实际值和参考值，θi(t)、分别表示t时刻的两台永磁同步电机位置角的实际值和参考值，i＝1,2表示两台永磁同步电机的标号；
上述的价值函数能够使永磁同步电机系统尽可能快速的跟踪给定值。
所述的价值函数下还建立以下针对双轴系统永磁同步电机构建的永磁同步电机非线性约束：



x(t)＝[idi iqi ωi θi]T
u(t)＝[udi uqi]T
y(t)＝[y1 y2]T
b(t)＝[bdi bqi bωi bθi]T
式中，x(t)表示t时刻的状态变量，表示t时刻的状态变量的一阶导数，iqi表示两台永磁同步电机q轴电流实际值，ωi为两台永磁同步电机的机械角速度，u(t)表示t时刻电机控制系统的输入向量，udi、uqi分别表示永磁同步电机的d轴、q轴的电压控制量；bdi、bqi、bωi、bθi分别表示永磁同步电机系统中由d轴参数变化、q轴参数变化、外部负载变化和机械干扰引入的扰动；f()表示电机控制系统的非线性函数，h()表示电机控制系统的输出函数，b(t)表示t时刻的不确定扰动向量，g1()、g2()分别表示输入向量和扰动向量的系数矩阵函数；Rs、Ls、ψf、p、Jm、B分别为永磁同步电机的定子电阻、电感、转子永磁磁链、极对数、转动惯量和摩擦系数；
然后通过对价值函数式以最小化为目标求解得到永磁同步电机的电压控制量u(t)，即以为目标求解。
将永磁同步电机的电压控制量u(t)中的d轴、q轴的电压控制量udi uqi输入到永磁同步电机的定子电压输入端，进而实现双轴永磁同步电机驱动系统的非 线性预测位置的调节控制。
所述的不确定扰动b(t)是建立非线性扰动观测器处理获得。
本发明上述的非线性扰动观测器能够实现双轴永磁同步电机驱动系统轨迹跟踪的高精度控制，对永磁同步电机系统不确定扰动b(t)进行实时估计。
所述的非线性扰动观测器如下：


q(x(t))＝[[l1idi l2iqi l3ωi l4θi]]T
式中，表示扰动观测值；z和分别表示非线性观测器内部的状态变量及其一阶导数；q()为非线性观测器待设计的非线性函数；L为非线性观测器的增益矩阵；l1，l2，l3，l4分别表示非线性观测器的第一、第二、第三、第四增益系数，且增益系数l1，l2，l3，l4>0；分别表示bdi、bqi、bωi、bθi的观测值；
通过上述非线性扰动观测器处理获得扰动观测值将扰动观测值作为不确定扰动b(t)代入到价值函数中。
方法求解获得的永磁同步电机的电压控制量u(t)具体计算为：


K1＝[1 0 0 0]，
式中，G()表示电压控制量中与电机参数相关的系数矩阵；和表示电压控制量中与预测步长相关的系数；K1、K2分别表示电压控制量中的常数矩阵；表示李导数符号。
本发明的特点及有益效果是：
本发明方法将非线性预测控制算法应用于双轴系统永磁同步电机的位置控制上，建立了非线性预测位置控制的最优控制价值函数。
本发明采用非线性预测控制算法构建了单轴电机非级联控制器，简化了传 统级联控制器结构；同时本发明采用优化原理求解非线性预测价值函数，可有效减小系统计算量，提高系统动态响应性能，进而提高双轴永磁同步电机驱动系统轮廓跟踪精度。
本发明通过构建非线性扰动观测器估计系统不确定扰动，可有效抑制参数不确定性扰动给双轴系统电机位置跟踪影响。
附图说明
图1是本发明方法下的控制系统实施例的原理图；
图2为单轴电机非线性预测控制算法的原理图。
具体实施方式
下面结合实施例和附图对本发明做出详细说明，所描述的具体实施例仅对本发明进行解释说明，并不用于限制本发明。
针对传统双轴轮廓控制结构存在动态响应慢、轮廓误差较大等问题，本发明基于非线性预测控制算法，构建了级联单环非线性预测位置控制器，从而提高系统动态响应性能。同时，构建非线性扰动观测器用于观测系统参数失配与负载突变等不确定性扰动，以抑制系统不确定性扰动带来的影响。此外，为协调控制两个轴，结合位置修正环节实现对双轴驱动电机给定位置的补偿。
本发明的具体实施情况如下：
图1为应用本发明的双轴永磁同步电机驱动系统非线性预测位置控制方法的系统框图。图中，分别为x、y轴电机转子位置给定值，θx、θy分别为x、y轴电机转子位置实际值，ωx、ωy分别为x、y轴电机机械角速度，分别为x、y轴电机d轴给定电流，idx、idy分别为x、y轴电机的d轴电流实际值，iqx、iqy分别为x、y轴电机q轴电流实际值，分别为x、y轴电机的扰动观测值，θcx、θcy为交叉耦合控制结构输出的给定位置修正量；p*、p分别为双轴系统给定位置与实际位置矩阵；Cx、Cy为各轴轮廓误差补偿系数；Cc为交叉耦合控制器增益系数；e为双轴轮廓误差。
构建以下针对双轴永磁同步电机驱动系统的价值函数为：

H1＝[1 τ]，

价值函数下还建立以下针对双轴系统永磁同步电机构建的永磁同步电机非线性约束：



x(t)＝[idi iqi ωi θi]T
u(t)＝[udi uqi]T
y(t)＝[y1 y2]T
b(t)＝[bdi bqi bωi bθi]T
其中的不确定扰动b(t)是建立非线性扰动观测器处理获得，非线性扰动观测器如下：


q(x(t))＝[[l1idi l2iqi l3ωi l4θi]]T
通过上述非线性扰动观测器处理获得扰动观测值将扰动观测值作为不确定扰动b(t)代入到价值函数中。
然后通过对价值函数式以最小化为目标求解得到永磁同步电机的电压控制量u(t)，即以为目标求解。
最终求解获得的永磁同步电机的电压控制量u(t)具体计算为：


K1＝[1 0 0 0]，
将永磁同步电机的电压控制量u(t)中的d轴、q轴的电压控制量udi uqi输入到永磁同步电机的定子电压输入端，进而实现双轴永磁同步电机驱动系统的非线性预测位置的调节控制。
图2为单轴电机非线性预测位置算法原理图。非线性预测位置控制具体实施过程中采用永磁同步电机d轴电流给定值控制方式，并将双轴永磁同步电机驱动系统给定轮廓轨迹对应的各轴电机机械转子位置角作为非线性预测位置控制器的给定输入，结合非线性扰动观测器实现对各轴永磁同步电机的控制。
上面结合图对本发明进行了描述，但是本发明并不局限于上述的具体实施方式，上述的具体实施方式仅仅是示意性的，而不是限制性的，本领域的普通技术人员在本发明的启示下，在不脱离本发明宗旨的情况下，还可以作出很多变形，这些均属本发明的保护之内。

Claims (6)

  1. 一种适用于双轴永磁伺服系统的非线性预测位置控制方法，其特征在于：方法包括：所述的双轴永磁伺服系统为双轴永磁同步电机驱动系统，考虑到双轴永磁同步电机驱动系统存在不确定性扰动，构建针对双轴永磁同步电机驱动系统的价值函数及其约束条件，对价值函数进行求解获得永磁同步电机的电压控制量，将永磁同步电机的电压控制量输入到永磁同步电机的定子电压输入端，进而实现双轴永磁同步电机驱动系统的非线性预测位置的调节控制。
  2. 根据权利要求1所述的一种适用于双轴永磁伺服系统的非线性预测位置控制方法，其特征在于：构建以下针对双轴永磁同步电机驱动系统的价值函数为：

    H1＝[1 t]，

    其中，J为价值函数值，T1、T2分别为永磁同步电机电流环和位置环的预测步长；Y1 ref、Y2 ref分别表示价值函数参考输出向量，H1、H2分别表示价值函数权重系数矩阵，Y1、Y2分别表示价值函数输出评估向量，t表示时刻，t表示未来控制时域；y1(t)、y2(t)分别表示t时刻控制系统实际输出向量的第一分量和第二分量；分别表示t时刻控制系统实际输出向量第一分量和第二分量的一阶导数；分别表示t时刻控制系统实际输出向量第二分量的二阶导数；分别表示t时刻控制系统参考输出向量的第一分量和第二分量；分别表示t时刻控制系统参考输出向量第一分量和第二分量的一阶导数；分别表示t时刻控制系统参考输出向量第二分量的二阶导数和三阶导数；idi(t)、分别表示t时刻两台永磁同步电机d轴电流的实际值和参考值，qi(t)、分别表示t时刻的两台永磁同步电机位置角的实际值和参考值，i＝1,2表示两台永磁同步电机的标号；
    所述的价值函数下还建立以下永磁同步电机非线性约束：



    x(t)＝[idi iqi wi qi]T
    u(t)＝[udi uqi]T
    y(t)＝[y1 y2]T
    b(t)＝[bdi bqi bwi bqi]T
    式中，x(t)表示t时刻的状态变量，x&(t)表示t时刻的状态变量的一阶导数，iqi表示两台永磁同步电机q轴电流实际值，wi为两台永磁同步电机的机械角速度，u(t)表示t时刻电机控制系统的输入向量，udi、uqi分别表示永磁同步电机的d轴、q轴的电压控制量；bdi、bqi、bwi、bqi分别表示永磁同步电机系统中由d轴参数变化、q轴参数变化、外部负载变化和机械干扰引入的扰动；f()表示电机控制系统的非线性函数，h()表示电机控制系统的输出函数，b(t)表示t时刻的不确定扰动向量，g1()、g2()分别表示输入向量和扰动向量的系数矩阵函数；Rs、Ls、ψf、p、Jm、B分别为永磁同步电机的定子电阻、电感、转子永磁磁链、极对数、转动惯量和摩擦系数；
    然后通过对价值函数式以最小化为目标求解得到永磁同步电机的电压控制量u(t)。
  3. 根据权利要求2所述的一种适用于双轴永磁伺服系统的非线性预测位置控制方法，其特征在于：将永磁同步电机的电压控制量u(t)中的d轴、q轴的电压控制量udi uqi输入到永磁同步电机的定子电压输入端，进而实现双轴永磁同步电机驱动系统的非线性预测位置的调节控制。
  4. 根据权利要求1所述的一种适用于双轴永磁伺服系统的非线性预测位置控制方法，其特征在于：所述的不确定扰动b(t)是建立非线性扰动观测器处理获得。
  5. 根据权利要求4所述的一种适用于双轴永磁伺服系统的非线性预测位置控制方法，其特征在于：所述的非线性扰动观测器如下：


    q(x(t))＝[l1idi l2iqi l3wi l4qi]T
    式中，表示扰动观测值；z和分别表示非线性观测器内部的状态变量及其一阶导数；q()为非线性观测器待设计的非线性函数；L为非线性观测器的增益矩阵；l1，l2，l3，l4分别表示非线性观测器的第一、第二、第三、第四增益系数，且增益系数l1，l2，l3，l4>0；分别表示bdi、bqi、bwi、bqi的观测值；
    通过上述非线性扰动观测器处理获得扰动观测值将扰动观测值作为不确定扰动b(t)代入到价值函数中。
  6. 根据权利要求2所述的一种适用于双轴永磁伺服系统的非线性预测位置控制方法，其特征在于：
    方法求解获得的永磁同步电机的电压控制量u(t)具体计算为：


    K1＝[1 0 0 0]，
    式中，G()表示电压控制量中与电机参数相关的系数矩阵；和表示 电压控制量中与预测步长相关的系数；K1、K2分别表示电压控制量中的常数矩阵。
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