CN115664283A - A sliding mode control method and system based on generalized parameter estimation observer - Google Patents

A sliding mode control method and system based on generalized parameter estimation observer Download PDF

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CN115664283A
CN115664283A CN202211444912.9A CN202211444912A CN115664283A CN 115664283 A CN115664283 A CN 115664283A CN 202211444912 A CN202211444912 A CN 202211444912A CN 115664283 A CN115664283 A CN 115664283A
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sliding mode
parameter estimation
axis current
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CN115664283B (en
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贺伟
王想
李涛
宋公飞
郑柏超
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Nanjing University of Information Science and Technology
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Abstract

The invention discloses a sliding mode control method and a system based on a generalized parameter estimation observer; converting a mathematical model under a natural coordinate system into a mathematical model under a d-q axis synchronous rotation coordinate system of the three-phase permanent magnet synchronous motor; converting state observation into parameter estimation based on a generalized parameter estimation observation theory, and determining a linear regression equation for estimating q-axis current and load torque; processing the linear regression equation to determine an estimated value of the q-axis current and an estimated value of the load torque; designing a sliding mode controller according to the estimation information of the generalized parameter estimation observer, obtaining a controlled variable according to the sliding mode controller, carrying out inverse Park coordinate transformation on the controlled variable, obtaining a driving signal of the three-phase inverter through an SVPWM module, and adjusting the output of the three-phase inverter according to the driving signal. The advantages are that: the anti-interference capability and robustness of the system are improved, the structure is simple, and on the premise of system stability, the use of the current sensor is reduced, so that the cost is saved.

Description

一种基于广义参数估计观测器的滑模控制方法及系统A sliding mode control method and system based on generalized parameter estimation observer

技术领域technical field

本发明涉及一种基于广义参数估计观测器的滑模控制方法及系统，属于永磁同步电机稳定控制技术领域。The invention relates to a sliding mode control method and system based on a generalized parameter estimation observer, and belongs to the technical field of permanent magnet synchronous motor stability control.

背景技术Background technique

近年来，永磁同步电机由于具有高功率密度、高动态性能、高效率、低惯性、低噪声、等诸多优良特性，已被广泛应用于机器人、计算机数控机床、航空等诸多工业领域。传统的PID控制稳定性好，结构简单，容易调整，比例环节将误差按一定的比例反映便于快速调节；积分环节主要用来消除系统的静态误差；微分环节可以预见系统偏差的变化趋势可以很好地改善系统的动态性能。但对于复杂的系统会存在较大的误差，产生超调。由于永磁同步电机是非线性的，并且存在建模误差、不可避免的干扰以及参数的变化，仅仅通过PID控制已无法获得满意的性能。In recent years, permanent magnet synchronous motors have been widely used in many industrial fields such as robots, computer numerical control machine tools, and aviation due to their high power density, high dynamic performance, high efficiency, low inertia, low noise, and many other excellent characteristics. The traditional PID control has good stability, simple structure, and is easy to adjust. The proportional link reflects the error according to a certain ratio for quick adjustment; the integral link is mainly used to eliminate the static error of the system; the differential link can predict the change trend of the system deviation and can be very good improve the dynamic performance of the system. However, for complex systems, there will be large errors, resulting in overshoot. Since permanent magnet synchronous motors are nonlinear, and there are modeling errors, inevitable disturbances and parameter changes, satisfactory performance cannot be obtained only by PID control.

发明内容Contents of the invention

本发明所要解决的技术问题是克服现有技术的缺陷，提供一种基于广义参数估计观测器的滑模控制方法及系统。The technical problem to be solved by the present invention is to overcome the defects of the prior art and provide a sliding mode control method and system based on a generalized parameter estimation observer.

为解决上述技术问题，本发明提供一种基于广义参数估计观测器的滑模控制方法，包括：In order to solve the above technical problems, the present invention provides a sliding mode control method based on a generalized parameter estimation observer, including:

获取三相永磁同步电机的自然坐标系下的数学模型，通过Clark坐标变换和Park坐标变换，并选取永磁同步电机q轴电流作为状态变量，机械角速度ω r 作为输出以及状态变量，将自然坐标系下的数学模型转换为三相永磁同步电机的d-q轴同步旋转坐标系下的数学模型；Obtain the mathematical model of the three-phase permanent magnet synchronous motor in the natural coordinate system, through Clark coordinate transformation and Park coordinate transformation, and select the q-axis current of the permanent magnet synchronous motor as the state variable, and the mechanical angular velocity ω r as the output and state variable, the natural The mathematical model under the coordinate system is converted into the mathematical model under the dq axis synchronous rotating coordinate system of the three-phase permanent magnet synchronous motor;

根据所述d-q轴同步旋转坐标系下的数学模型，基于广义参数估计观测理论将状态观测转化为参数估计，确定用于估计q轴电流i q 和负载转矩T L 的线性回归方程；According to the mathematical model under the dq-axis synchronous rotating coordinate system, the state observation is converted into parameter estimation based on the generalized parameter estimation observation theory, and the linear regression equation for estimating the q -axis current iq and the load torque T L is determined;

处理所述的线性回归方程，使其符合激励条件，根据预先设置的广义参数估计观测器，确定q轴电流的估计值

Figure 669418DEST_PATH_IMAGE001
和负载转矩T L 的估计值
Figure 146666DEST_PATH_IMAGE002
；Process the linear regression equation to make it meet the excitation conditions, estimate the observer according to the preset generalized parameters, and determine the estimated value of the q-axis current
Figure 669418DEST_PATH_IMAGE001
and an estimate of the load torque T L
Figure 146666DEST_PATH_IMAGE002
;

根据广义参数估计观测器的估计信息，设计滑模控制器，根据滑模控制器得到控制量u q ，对控制量u q 进行逆Park坐标变换后，经由SVPWM模块得到三相逆变器的驱动信号，根据所述驱动信号调节三相逆变器的输出。According to the estimated information of the generalized parameter estimation observer, the sliding mode controller is designed, and the control variable u q is obtained according to the sliding mode controller. After the inverse Park coordinate transformation is performed on the control variable u q , the drive of the three-phase inverter is obtained through the SVPWM module signal, and adjust the output of the three-phase inverter according to the drive signal.

进一步的，所述d-q轴同步旋转坐标系下的数学模型表示为：Further, the mathematical model under the d-q axis synchronously rotating coordinate system is expressed as:

Figure 731231DEST_PATH_IMAGE003
Figure 731231DEST_PATH_IMAGE003

其中，

Figure 226804DEST_PATH_IMAGE004
为q轴电流对时间的导数，i q 为q轴电流，R s 为定子电阻，L为电感，φ f 为永磁体与定子交链的磁链，u q 为q轴电压同时也是控制输入，ω r 为转子的机械角速度，
Figure 707464DEST_PATH_IMAGE005
为转子的机械角速度对时间的导数，P为电机的极对数，J为转动惯量，B为粘滞摩擦系数，T L 为负载转矩。in,
Figure 226804DEST_PATH_IMAGE004
is the derivative of the q -axis current to time, i q is the q- axis current, R s is the stator resistance, L is the inductance, φ f is the flux linkage between the permanent magnet and the stator, u q is the q-axis voltage and is also the control input, ω r is the mechanical angular velocity of the rotor,
Figure 707464DEST_PATH_IMAGE005
is the derivative of the mechanical angular velocity of the rotor with respect to time, P is the number of pole pairs of the motor, J is the moment of inertia, B is the coefficient of viscous friction, and T L is the load torque.

进一步的，所述线性回归方程为：Further, the linear regression equation is:

Figure 327801DEST_PATH_IMAGE006
Figure 327801DEST_PATH_IMAGE006

q e 为加入滤波器线性回归方程的可测量，m e 为加入滤波器线性回归方程的回归因子，

Figure 919319DEST_PATH_IMAGE007
为线性回归方程的中间变量，
Figure 410343DEST_PATH_IMAGE008
，i q0为q轴电流初始值误差； q e is the measurable added to the filter linear regression equation, m e is the regression factor added to the filter linear regression equation,
Figure 919319DEST_PATH_IMAGE007
is the intermediate variable of the linear regression equation,
Figure 410343DEST_PATH_IMAGE008
, i q 0 is the error of the initial value of the q-axis current;

Figure 717697DEST_PATH_IMAGE009
Figure 717697DEST_PATH_IMAGE009

Figure 497434DEST_PATH_IMAGE010
Figure 497434DEST_PATH_IMAGE010

Figure 689381DEST_PATH_IMAGE011
Figure 689381DEST_PATH_IMAGE011

s1为微分算子，α 1、α 2、β 1、β 2为滤波器参数，满足α 1，α 2≠0，β 1，β 2＞0，q1为未加入滤波器的线性回归方程的可测量，λ 1为观测器增益，λ 1＞0，m、ω为中间变量。s1 is a differential operator, α 1 , α 2 , β 1 , and β 2 are filter parameters, satisfying α 1 , α 2 ≠0, β 1 , β 2 >0, and q 1 is the linear regression equation without filter is measurable, λ 1 is the observer gain, λ 1 >0, m and ω are intermediate variables.

进一步的，求解中间变量m、ω，包括：Further, solve the intermediate variables m, ω , including:

基于广义参数估计观测器的理论，重构q轴电流i q ，得到下式：Based on the theory of generalized parameter estimation observer, the q-axis current i q is reconstructed, and the following formula is obtained:

Figure 644699DEST_PATH_IMAGE012
Figure 644699DEST_PATH_IMAGE012

其中，

Figure 263899DEST_PATH_IMAGE013
表示q轴电流i q 的重构状态的导数，ξ y 为q轴电流i q 的重构状态；in,
Figure 263899DEST_PATH_IMAGE013
Denotes the derivative of the reconstruction state of the q-axis current i q , ξ y is the reconstruction state of the q-axis current i q ;

基于线性系统理论得到重构状态ξ y 的状态转移矩阵X Ax ：The state transition matrix X Ax of the reconstructed state ξ y is obtained based on the linear system theory:

Figure 265353DEST_PATH_IMAGE014
Figure 265353DEST_PATH_IMAGE014

其中，

Figure 120045DEST_PATH_IMAGE015
为状态转移矩阵对时间的导数，X Ax (0)为状态转移矩阵的初始值；in,
Figure 120045DEST_PATH_IMAGE015
is the derivative of the state transition matrix with respect to time, and X Ax (0) is the initial value of the state transition matrix;

则q轴电流的真实值表示为：Then the true value of the q-axis current is expressed as:

Figure 523345DEST_PATH_IMAGE016
Figure 523345DEST_PATH_IMAGE016

其中，

Figure 579025DEST_PATH_IMAGE017
为初始值误差，i q (0)表示q轴电流的初始值，ξ y (0)表示q轴电流i q 的重构状态的初始值；in,
Figure 579025DEST_PATH_IMAGE017
is the initial value error, i q (0) represents the initial value of the q-axis current, ξ y (0) represents the initial value of the reconstruction state of the q-axis current i q ;

Figure 474300DEST_PATH_IMAGE018
Figure 474300DEST_PATH_IMAGE018

重构

Figure 211312DEST_PATH_IMAGE005
，表示为：refactor
Figure 211312DEST_PATH_IMAGE005
,Expressed as:

Figure 531435DEST_PATH_IMAGE019
Figure 531435DEST_PATH_IMAGE019

Figure 430121DEST_PATH_IMAGE020
Figure 430121DEST_PATH_IMAGE020

Figure 593118DEST_PATH_IMAGE021
Figure 593118DEST_PATH_IMAGE021

然后将m和ω的式子转换成微分方程的形式，表示为：Then convert the formulas of m and ω into the form of differential equations, expressed as:

Figure 868241DEST_PATH_IMAGE022
Figure 868241DEST_PATH_IMAGE022

Figure 777291DEST_PATH_IMAGE023
Figure 777291DEST_PATH_IMAGE023

其中，

Figure 50141DEST_PATH_IMAGE024
为状态转移矩阵的转置，m(0)为m的初始值；in,
Figure 50141DEST_PATH_IMAGE024
is the transposition of the state transition matrix, m (0) is the initial value of m ;

求解所述微分方程，得到中间变量m、ω。Solve the differential equation to obtain the intermediate variables m, ω .

进一步的，采用基于广义观测理论结合动态回归扩展方法确定所述q轴电流的估计值

Figure 44642DEST_PATH_IMAGE001
和负载转矩T L 的估计值
Figure 123456DEST_PATH_IMAGE002
。Further, the estimated value of the q-axis current is determined by using a generalized observation theory combined with a dynamic regression extension method
Figure 44642DEST_PATH_IMAGE001
and an estimate of the load torque T L
Figure 123456DEST_PATH_IMAGE002
.

进一步的，所述确定滑模控制器的过程，包括：Further, the process of determining the sliding mode controller includes:

以给定机械角速度与传感器测得的机械角速度之差作为滑模控制器的输入，The difference between the given mechanical angular velocity and the mechanical angular velocity measured by the sensor is used as the input of the sliding mode controller,

表示为：Expressed as:

Figure 542805DEST_PATH_IMAGE025
Figure 542805DEST_PATH_IMAGE025

其中，e为滑模控制器的输入，

Figure 783294DEST_PATH_IMAGE026
为转子的机械角速度的参考值；Among them, e is the input of the sliding mode controller,
Figure 783294DEST_PATH_IMAGE026
is the reference value of the mechanical angular velocity of the rotor;

设计滑模面s，表示为：The design sliding surface s is expressed as:

Figure 999511DEST_PATH_IMAGE027
Figure 999511DEST_PATH_IMAGE027

其中，c为滑模面参数，满足c＞0，

Figure 678754DEST_PATH_IMAGE028
表示输入误差对时间的导数；Among them, c is the sliding mode surface parameter, satisfying c > 0,
Figure 678754DEST_PATH_IMAGE028
Indicates the derivative of the input error with respect to time;

结合广义参数估计观测器，得到控制律u q 为：Combined with the generalized parameter estimation observer, the control law u q is obtained as:

Figure 437763DEST_PATH_IMAGE029
Figure 437763DEST_PATH_IMAGE029

其中，sgn(s)为符号函数，

Figure 849153DEST_PATH_IMAGE001
为q轴电流i q 的估计值，
Figure 83825DEST_PATH_IMAGE002
为负载转矩T L 的估计值，a为中间参数，
Figure 504442DEST_PATH_IMAGE030
，k为控制率参数，k＞0。Among them, sgn (s) is a symbolic function,
Figure 849153DEST_PATH_IMAGE001
is the estimated value of the q-axis current i q ,
Figure 83825DEST_PATH_IMAGE002
is the estimated value of load torque T L , a is an intermediate parameter,
Figure 504442DEST_PATH_IMAGE030
, k is the control rate parameter, k >0.

一种基于广义参数估计观测器的滑模控制系统，包括：A sliding mode control system based on a generalized parameter estimation observer, comprising:

变换模块，用于获取三相永磁同步电机的自然坐标系下的数学模型，通过Clark坐标变换和Park坐标变换，并选取永磁同步电机q轴电流作为状态变量，机械角速度ω r 作为输出以及状态变量，将自然坐标系下的数学模型转换为三相永磁同步电机的d-q轴同步旋转坐标系下的数学模型；The transformation module is used to obtain the mathematical model under the natural coordinate system of the three-phase permanent magnet synchronous motor, through Clark coordinate transformation and Park coordinate transformation, and select the q-axis current of the permanent magnet synchronous motor as the state variable, the mechanical angular velocity ω r as the output and The state variable converts the mathematical model under the natural coordinate system into a mathematical model under the dq axis synchronous rotating coordinate system of the three-phase permanent magnet synchronous motor;

第一确定模块，用于根据所述d-q轴同步旋转坐标系下的数学模型，基于广义参数估计观测理论将状态观测转化为参数估计，确定用于估计q轴电流i q 和负载转矩T L 的线性回归方程；The first determination module is used to convert the state observation into parameter estimation based on the generalized parameter estimation observation theory according to the mathematical model in the dq axis synchronous rotating coordinate system, and determine the parameters used to estimate the q-axis current i q and the load torque T L The linear regression equation;

第二确定模块，用于处理所述的线性回归方程，使其符合激励条件，根据预先设置的广义参数估计观测器，确定q轴电流的估计值

Figure 644523DEST_PATH_IMAGE001
和负载转矩T L 的估计值
Figure 492393DEST_PATH_IMAGE002
；The second determination module is used to process the linear regression equation to make it meet the excitation conditions, estimate the observer according to the preset generalized parameters, and determine the estimated value of the q-axis current
Figure 644523DEST_PATH_IMAGE001
and an estimate of the load torque T L
Figure 492393DEST_PATH_IMAGE002
;

输出模块，用于根据广义参数估计观测器的估计信息，设计滑模控制器，根据滑模控制器得到控制量u q ，对控制量u q 进行逆Park坐标变换后，经由SVPWM模块得到三相逆变器的驱动信号，根据所述驱动信号调节三相逆变器的输出。The output module is used to design the sliding mode controller based on the estimation information of the generalized parameter estimation observer, obtain the control variable u q according to the sliding mode controller, and perform the inverse Park coordinate transformation on the control variable u q , and obtain the three-phase through the SVPWM module The driving signal of the inverter, and the output of the three-phase inverter is adjusted according to the driving signal.

本发明所达到的有益效果：The beneficial effect that the present invention reaches:

（1）本发明基于广义参数估计观测器的滑模控制方法运用到永磁同步电机里，将状态观测转化为参数估计通过动态扩展与混合技术实现对q轴电流和负载转矩

Figure 214361DEST_PATH_IMAGE031
的同时估计。在保证系统稳定的前提下，减少了电流传感器的使用，降低了系统的成本，整个系统的可靠性也有所提高。(1) The sliding mode control method based on the generalized parameter estimation observer of the present invention is applied to the permanent magnet synchronous motor, and the state observation is transformed into parameter estimation. The q-axis current and load torque are realized through dynamic expansion and hybrid technology.
Figure 214361DEST_PATH_IMAGE031
estimated at the same time. Under the premise of ensuring the stability of the system, the use of current sensors is reduced, the cost of the system is reduced, and the reliability of the entire system is also improved.

（2）本发明基于广义参数估计观测器的滑模控制方法运用到永磁同步电机，获得了较好的动态性能又提高了闭环系统抗干扰的能力和鲁棒性，使本发明在工程上可以很好的应用。(2) The sliding mode control method based on the generalized parameter estimation observer of the present invention is applied to the permanent magnet synchronous motor, which obtains better dynamic performance and improves the anti-interference ability and robustness of the closed-loop system, making the present invention more effective in engineering Can be applied very well.

附图说明Description of drawings

图1是本发明的方法应用于永磁同步电机的控制框图；Fig. 1 is the control block diagram that method of the present invention is applied to permanent magnet synchronous motor;

图2为永磁同步电机q轴电流的估计值和真实值；Figure 2 shows the estimated value and real value of the q-axis current of the permanent magnet synchronous motor;

图3为永磁同步电机负载转矩T L 估计值和真实值；Fig. 3 is the estimated value and the real value of the load torque T L of the permanent magnet synchronous motor;

图4为q轴电流的初始值；Figure 4 is the initial value of the q-axis current;

图5为机械角速度的输出值。Figure 5 is the output value of the mechanical angular velocity.

具体实施方式Detailed ways

下面结合附图对本发明作进一步描述。以下实施例仅用于更加清楚地说明本发明的技术方案，而不能以此来限制本发明的保护范围。The present invention will be further described below in conjunction with the accompanying drawings. The following examples are only used to illustrate the technical solution of the present invention more clearly, but not to limit the protection scope of the present invention.

如附图1所示是本发明的一种基于广义参数估计观测器的滑模控制方法应用于永磁同步电机的控制框图，其中包括广义参数估计观测器回路、永磁同步电机速度环、光电编码器、滑模控制器；光电编码器得到转子位置角，通过计算得到机械角速度，送入到广义参数估计观测器中，滑模控制器根据给定的机械角速度与实际机械角速度作差作为输入，得到q轴的电压，给定的d轴电流与反馈电路中的d轴电流相减得到d轴电压。u d 和u q 通过了Park以及SVPWM产生脉冲信号然后进入三相逆变换器对永磁同步电机进行控制。广义参数估计观测器和滑模控制相结合，使系统对负载扰动和其他一些不确定因素具有较强的鲁棒性。采用所述装置实现的具体实现步骤如下：As shown in accompanying drawing 1 is a kind of sliding mode control method based on generalized parameter estimation observer of the present invention is applied to the control block diagram of permanent magnet synchronous motor, including generalized parameter estimation observer loop, permanent magnet synchronous motor speed loop, photoelectric Encoder and sliding mode controller; the photoelectric encoder obtains the rotor position angle, and the mechanical angular velocity is obtained through calculation, which is sent to the generalized parameter estimation observer. The sliding mode controller takes the difference between the given mechanical angular velocity and the actual mechanical angular velocity as input , to obtain the voltage of the q-axis, and subtract the given d-axis current from the d-axis current in the feedback circuit to obtain the d-axis voltage. U d and u q generate pulse signals through Park and SVPWM and then enter the three-phase inverter to control the permanent magnet synchronous motor. The combination of generalized parameter estimation observer and sliding mode control makes the system more robust to load disturbance and other uncertain factors. The concrete realization steps that adopt described device to realize are as follows:

步骤（1）：step 1):

为了简化永磁同步电机数学模型的建立采用Park变换和Clarke变换将自然坐标系下的数学模型转换为同步旋转坐标系下的数学模型，状态变量为i q ，ω r 既为状态变量又为输出模型如下：In order to simplify the establishment of the permanent magnet synchronous motor mathematical model, Park transformation and Clarke transformation are used to convert the mathematical model in the natural coordinate system into a mathematical model in the synchronous rotating coordinate system. The state variable is i q , and ω r is both the state variable and the output The model is as follows:

Figure 173090DEST_PATH_IMAGE003
Figure 173090DEST_PATH_IMAGE003

其中，

Figure 172270DEST_PATH_IMAGE004
为q轴电流对时间的导数，i q 为q轴电流，R s 为定子电阻，L为电感，φ f 为永磁体与定子交链的磁链，u q 为q轴电压同时也是控制输入，ω r 为转子的机械角速度，
Figure 191042DEST_PATH_IMAGE005
为转子的机械角速度对时间的导数，P为电机的极对数，J为转动惯量，B为粘滞摩擦系数，T L 为负载转矩。in,
Figure 172270DEST_PATH_IMAGE004
is the derivative of the q -axis current to time, i q is the q- axis current, R s is the stator resistance, L is the inductance, φ f is the flux linkage between the permanent magnet and the stator, u q is the q-axis voltage and is also the control input, ω r is the mechanical angular velocity of the rotor,
Figure 191042DEST_PATH_IMAGE005
is the derivative of the mechanical angular velocity of the rotor with respect to time, P is the number of pole pairs of the motor, J is the moment of inertia, B is the coefficient of viscous friction, and T L is the load torque.

步骤（2）：Step (2):

步骤21利用ω r 和u q 的信息进行状态的重构，基于广义参数观测理论，推导出用于估计q轴电流初始值误差i q0和负载转矩T L 的线性回归方程

Figure 134727DEST_PATH_IMAGE032
，其中
Figure 897146DEST_PATH_IMAGE008
。Step 21 Use the information of ω r and u q to reconstruct the state, and based on the generalized parameter observation theory, derive the linear regression equation for estimating the initial value error i q 0 of the q-axis current and the load torque T L
Figure 134727DEST_PATH_IMAGE032
,in
Figure 897146DEST_PATH_IMAGE008
.

为了获得测量未知q轴电流和负载转矩的线性回归方程，根据广义参数估计观测器的理论，先重构未知状态：In order to obtain the linear regression equation for measuring the unknown q -axis current and load torque, according to the theory of the generalized parameter estimation observer, the unknown state is reconstructed first:

Figure 101DEST_PATH_IMAGE012
Figure 101DEST_PATH_IMAGE012

其中，

Figure 189773DEST_PATH_IMAGE013
表示q轴电流i q 的重构状态的导数，ξ y 为q轴电流i q 的重构状态。in,
Figure 189773DEST_PATH_IMAGE013
Indicates the derivative of the reconstruction state of the q-axis current i q , and ξ y is the reconstruction state of the q-axis current i q .

然后获得状态转移矩阵：Then get the state transition matrix:

Figure 886334DEST_PATH_IMAGE014
Figure 886334DEST_PATH_IMAGE014

Figure 452445DEST_PATH_IMAGE015
为状态转移矩阵对时间的导数，X Ax 为状态转移矩阵，
Figure 895058DEST_PATH_IMAGE033
为状态转移矩阵的初始值。
Figure 452445DEST_PATH_IMAGE015
is the derivative of the state transition matrix with respect to time, X Ax is the state transition matrix,
Figure 895058DEST_PATH_IMAGE033
is the initial value of the state transition matrix.

则电流的真实值可以表示为：Then the real value of the current can be expressed as:

Figure 521212DEST_PATH_IMAGE016
Figure 521212DEST_PATH_IMAGE016

其中初始值误差为：The initial value error is:

Figure 377172DEST_PATH_IMAGE018
Figure 377172DEST_PATH_IMAGE018

i q (0)表示q轴电流的初始值，ξ y (0)表示q轴电流i q 的重构状态的初始值。 i q (0) represents the initial value of the q-axis current, and ξ y (0) represents the initial value of the reconstructed state of the q-axis current i q .

为了更易满足可激励条件且不使用

Figure 543711DEST_PATH_IMAGE034
导数的信息避免因为噪声过大影响观测器性能采用如下滤波器的方法：In order to more easily satisfy the incentive condition and do not use
Figure 543711DEST_PATH_IMAGE034
The information of the derivative avoids affecting the performance of the observer due to excessive noise, and adopts the following filter method:

Figure 434307DEST_PATH_IMAGE035
Figure 434307DEST_PATH_IMAGE035

Figure 152733DEST_PATH_IMAGE020
Figure 152733DEST_PATH_IMAGE020

Figure 495990DEST_PATH_IMAGE021
Figure 495990DEST_PATH_IMAGE021

整理成微分方程的形式可以得到：Putting it in the form of a differential equation, we get:

Figure 200641DEST_PATH_IMAGE022
Figure 200641DEST_PATH_IMAGE022

Figure 945743DEST_PATH_IMAGE023
Figure 945743DEST_PATH_IMAGE023

其中，

Figure 913699DEST_PATH_IMAGE024
为状态转移矩阵的转置，m(0)为m的初始值。in,
Figure 913699DEST_PATH_IMAGE024
is the transposition of the state transition matrix, m (0) is the initial value of m .

然后可以得到需要的线性回归方程：Then the required linear regression equation can be obtained:

Figure 681935DEST_PATH_IMAGE036
Figure 681935DEST_PATH_IMAGE036

其中，in,

Figure 127959DEST_PATH_IMAGE011
Figure 127959DEST_PATH_IMAGE011

Figure 55464DEST_PATH_IMAGE008
Figure 55464DEST_PATH_IMAGE008

m、ω为中间变量，λ 1为观测器增益，λ 1＞0

Figure 928742DEST_PATH_IMAGE037
m and ω are intermediate variables, λ 1 is the observer gain, λ 1 >0
Figure 928742DEST_PATH_IMAGE037

步骤22：Step 22:

运用动态回归扩展和混合的技术，使用滤波器对步骤21得到的线性回归方程

Figure 167963DEST_PATH_IMAGE036
进行扩展得到
Figure 417678DEST_PATH_IMAGE006
；然后两边同时乘以伴随矩阵adj｛Ω｝，混合后得到标量线性回归方程
Figure 199690DEST_PATH_IMAGE038
和
Figure 243869DEST_PATH_IMAGE039
，具体过程如下：Using the technique of dynamic regression extension and mixing, the linear regression equation obtained in step 21 is applied to the filter
Figure 167963DEST_PATH_IMAGE036
extended to get
Figure 417678DEST_PATH_IMAGE006
; Then both sides are multiplied by the adj { Ω } at the same time, and the scalar linear regression equation is obtained after mixing
Figure 199690DEST_PATH_IMAGE038
and
Figure 243869DEST_PATH_IMAGE039
, the specific process is as follows:

Figure 721118DEST_PATH_IMAGE009
Figure 721118DEST_PATH_IMAGE009

Figure 508945DEST_PATH_IMAGE010
Figure 508945DEST_PATH_IMAGE010

得到扩展后的线性回归方程：Get the extended linear regression equation:

Figure 348725DEST_PATH_IMAGE006
Figure 348725DEST_PATH_IMAGE006

根据动态回归扩展混合技术可以得到：Extending the hybrid technique according to dynamic regression gives:

Figure 626123DEST_PATH_IMAGE040
Figure 626123DEST_PATH_IMAGE040

然后可以得到：Then you can get:

Figure 918564DEST_PATH_IMAGE041
Figure 918564DEST_PATH_IMAGE041

其中, Y为可测量， Y 1、Y 2是Y的两个元素，s1为微分算子，

Figure 431454DEST_PATH_IMAGE042
， q e 、m e 、r、Ω、Δ为中间变量，α 1、α 2、β 1、β 2为滤波器参数，满足α 1，α 2≠0，β 1，β 2＞0，λ 2为增益系数，满足λ 2＞0。adj为伴随矩阵，det为行列式，r(0)为r的初始值，ω(0)为ω的初始值，
Figure 125740DEST_PATH_IMAGE043
为r的导数，
Figure 574039DEST_PATH_IMAGE044
为Ω的导数。Among them, Y is measurable, Y 1 and Y 2 are two elements of Y , s1 is a differential operator,
Figure 431454DEST_PATH_IMAGE042
, q e , me , r , Ω , Δ are intermediate variables, α 1 , α 2 , β 1 , β 2 are filter parameters, satisfying α 1 , α 2 ≠0, β 1 , β 2 >0, λ 2 is a gain coefficient, which satisfies λ 2 >0. adj is the companion matrix, det is the determinant, r (0) is the initial value of r , ω (0) is the initial value of ω ,
Figure 125740DEST_PATH_IMAGE043
is the derivative of r ,
Figure 574039DEST_PATH_IMAGE044
is the derivative of Ω .

步骤（3）：Step (3):

步骤31基于广义观测理论结合动态回归扩展技术估计状态

Figure 88197DEST_PATH_IMAGE045
：Step 31 Estimate the state based on the generalized observation theory combined with the dynamic regression extension technique
Figure 88197DEST_PATH_IMAGE045
:

为了解决没有足够激励，即（非一致可观性）的情况下仍能实现对参数的估计，基于上式得到的扩展后的线性回归方程在不使用滤波器的情况下推导出新的标量激励回归方程。In order to solve the problem of not having enough incentives, that is, (non-uniform observability), the estimation of parameters can still be achieved, based on the extended linear regression equation obtained by the above formula, a new scalar excitation regression is derived without using a filter equation.

为了得到新的回归变量，以未知量初始值误差

Figure 155510DEST_PATH_IMAGE017
为状态之一定义一个新的动力学方程：In order to get new regressors, the unknown initial value error
Figure 155510DEST_PATH_IMAGE017
Define a new kinetic equation for one of the states:

Figure 969882DEST_PATH_IMAGE046
Figure 969882DEST_PATH_IMAGE046

z 1是新动力学方程的状态，

Figure 526766DEST_PATH_IMAGE047
表示z 1对时间的导数，
Figure 590537DEST_PATH_IMAGE048
表示
Figure 523858DEST_PATH_IMAGE017
对时间的导数， u 1、u 2、u 3为动力学模型的系统参数，Y 1是步骤（2）最终得到的线性回归方程已知量的第一个元素，z 1(0)表示状态z 1的初始值； z1 is the state of the new kinetic equation,
Figure 526766DEST_PATH_IMAGE047
Denotes the derivative of z 1 with respect to time,
Figure 590537DEST_PATH_IMAGE048
express
Figure 523858DEST_PATH_IMAGE017
Derivatives with respect to time, u 1 , u 2 , u 3 are the system parameters of the dynamic model, Y 1 is the first element of the known quantity of the linear regression equation finally obtained in step (2), z 1 (0) represents the state initial value of z1 ;

然后重构上述动态方程：Then reconstruct the above dynamic equation:

Figure 114108DEST_PATH_IMAGE049
Figure 114108DEST_PATH_IMAGE049

其中，ξ 1为

Figure 841892DEST_PATH_IMAGE017
的重构状态、ξ 2为z 1的重构状态，ξ 1(0)表示ξ 1的初始值，ξ 2(0)表示ξ 2的初始值，Δ是步骤(2)最终得到的线性回归方程参数，
Figure 392959DEST_PATH_IMAGE050
表示ξ 1的导数，
Figure 129971DEST_PATH_IMAGE051
表示ξ 2的导数；Among them, ξ 1 is
Figure 841892DEST_PATH_IMAGE017
ξ 2 is the reconstruction state of z 1 , ξ 1 (0) represents the initial value of ξ 1 , ξ 2 (0) represents the initial value of ξ 2 , Δ is the final linear regression obtained in step (2) equation parameter,
Figure 392959DEST_PATH_IMAGE050
Denotes the derivative of ξ1 ,
Figure 129971DEST_PATH_IMAGE051
Represents the derivative of ξ 2 ;

重构动态方程后的状态转移矩阵记为

Figure 325460DEST_PATH_IMAGE052
，Φ11、Φ21、Φ12、Φ22为状态转移矩阵中的元素，可以由如下微分方程得到；The state transition matrix after reconstructing the dynamic equation is denoted as
Figure 325460DEST_PATH_IMAGE052
, Φ 11 , Φ 21 , Φ 12 , Φ 22 are the elements in the state transition matrix, which can be obtained by the following differential equation;

Figure 224146DEST_PATH_IMAGE053
Figure 224146DEST_PATH_IMAGE053

展开上述方程，得到关于Φ11、Φ21的微分方程如下：Expanding the above equations, the differential equations about Φ 11 and Φ 21 are obtained as follows:

Figure 465772DEST_PATH_IMAGE054
Figure 465772DEST_PATH_IMAGE054

Figure 803212DEST_PATH_IMAGE055
为Φ11的导数，
Figure 915525DEST_PATH_IMAGE056
为Φ21的导数；选取系统参数u 1、u 2、u 3为：
Figure 803212DEST_PATH_IMAGE055
is the derivative of Φ 11 ,
Figure 915525DEST_PATH_IMAGE056
is the derivative of Φ 21 ; select system parameters u 1 , u 2 , u 3 as:

Figure 437642DEST_PATH_IMAGE057
Figure 437642DEST_PATH_IMAGE057

通过解上述微分方程可以得到Φ11、Φ21。Φ 11 and Φ 21 can be obtained by solving the above differential equation.

定义新的已知量

Figure 635405DEST_PATH_IMAGE058
，然后得到新的回归方程为：Define a new known quantity
Figure 635405DEST_PATH_IMAGE058
, and then the new regression equation is obtained as:

Figure 776536DEST_PATH_IMAGE059
Figure 776536DEST_PATH_IMAGE059

为了估计参数采用新的回归方程并将上式代入：In order to estimate the parameters, a new regression equation is used and the above formula is substituted into:

Figure 743355DEST_PATH_IMAGE060
Figure 743355DEST_PATH_IMAGE060

Figure 187106DEST_PATH_IMAGE061
为
Figure 137744DEST_PATH_IMAGE017
的估计值，
Figure 754671DEST_PATH_IMAGE062
为
Figure 903892DEST_PATH_IMAGE061
的导数，γ 1为观测器增益,γ 1＞0；
Figure 187106DEST_PATH_IMAGE061
for
Figure 137744DEST_PATH_IMAGE017
the estimated value of
Figure 754671DEST_PATH_IMAGE062
for
Figure 903892DEST_PATH_IMAGE061
The derivative of , γ 1 is the observer gain, γ 1 >0;

然后可以得到q轴电流的估计值

Figure 580861DEST_PATH_IMAGE001
：An estimate of the q-axis current can then be obtained
Figure 580861DEST_PATH_IMAGE001
:

Figure 940167DEST_PATH_IMAGE063
。
Figure 940167DEST_PATH_IMAGE063
.

步骤32基于广义观测理论结合动态回归扩展技术估计负载转矩T L ：Step 32 estimates the load torque T L based on the generalized observation theory combined with the dynamic regression extension technique:

同上先以新定义的未知量

Figure 360784DEST_PATH_IMAGE064
为状态之一定义一个新的动力学方程：As above, the newly defined unknown
Figure 360784DEST_PATH_IMAGE064
Define a new kinetic equation for one of the states:

Figure 364512DEST_PATH_IMAGE065
Figure 364512DEST_PATH_IMAGE065

z 2是新动力学方程的状态，

Figure 212383DEST_PATH_IMAGE066
表示z 2对时间的导数，
Figure 809717DEST_PATH_IMAGE067
表示
Figure 34025DEST_PATH_IMAGE064
对时间的导数，u 12、u 22、u 32为动力学模型的系统参数，Y 2是步骤（2）最终得到的线性回归方程已知向量的第二个元素，z 2(0)表示状态z 2的初始值； z2 is the state of the new kinetic equation,
Figure 212383DEST_PATH_IMAGE066
Denotes the derivative of z 2 with respect to time,
Figure 809717DEST_PATH_IMAGE067
express
Figure 34025DEST_PATH_IMAGE064
Derivatives with respect to time, u 12 , u 22 , u 32 are the system parameters of the dynamic model, Y 2 is the second element of the known vector of the linear regression equation finally obtained in step (2), z 2 (0) represents the state initial value of z2 ;

然后重构上述动态方程，得到：Then reconstruct the above dynamic equations to get:

Figure 95522DEST_PATH_IMAGE068
Figure 95522DEST_PATH_IMAGE068

其中，ξ 12为

Figure 911031DEST_PATH_IMAGE064
的重构状态，ξ 22为z 2的重构状态，ξ 12(0)表示ξ 12的初始值，ξ 22(0)表示ξ 22的初始值，
Figure 57979DEST_PATH_IMAGE069
表示ξ 12的导数，
Figure 7349DEST_PATH_IMAGE070
表示ξ 22的导数；Among them, ξ 12 is
Figure 911031DEST_PATH_IMAGE064
ξ 22 is the reconstruction state of z 2 , ξ 12 (0) represents the initial value of ξ 12 , ξ 22 (0) represents the initial value of ξ 22 ,
Figure 57979DEST_PATH_IMAGE069
Denotes the derivative of ξ 12 ,
Figure 7349DEST_PATH_IMAGE070
Represents the derivative of ξ 22 ;

上述系统的状态转移矩阵记为

Figure 923353DEST_PATH_IMAGE071
，φ112、φ212、φ122、φ222为状态转移矩阵中的元素，可以由如下微分方程得到；The state transition matrix of the above system is written as
Figure 923353DEST_PATH_IMAGE071
, φ 112 , φ 212 , φ 122 , φ 222 are the elements in the state transition matrix, which can be obtained by the following differential equation;

Figure 175342DEST_PATH_IMAGE072
Figure 175342DEST_PATH_IMAGE072

展开上述方程，得到关于φ112、φ212的微分方程如下：Expanding the above equation, the differential equations about φ 112 and φ 212 are obtained as follows:

Figure 809586DEST_PATH_IMAGE073
Figure 809586DEST_PATH_IMAGE073

Figure 110117DEST_PATH_IMAGE074
为φ112的导数，
Figure 83890DEST_PATH_IMAGE075
为φ212的导数；选取系统参数u 12、u 22、u 32为：
Figure 110117DEST_PATH_IMAGE074
is the derivative of φ 112 ,
Figure 83890DEST_PATH_IMAGE075
is the derivative of φ 212 ; select system parameters u 12 , u 22 , u 32 as:

Figure 444464DEST_PATH_IMAGE076
Figure 444464DEST_PATH_IMAGE076

通过解上述微分方程可以得到φ112、φ212。By solving the above differential equations, φ 112 and φ 212 can be obtained.

定义新的已知量

Figure 362741DEST_PATH_IMAGE077
，然后得到新的回归方程为：Define a new known quantity
Figure 362741DEST_PATH_IMAGE077
, and then the new regression equation is obtained as:

Figure 466964DEST_PATH_IMAGE078
Figure 466964DEST_PATH_IMAGE078

根据上述回归方程，得到负载转矩的估计值

Figure 544510DEST_PATH_IMAGE002
：According to the above regression equation, the estimated value of the load torque is obtained
Figure 544510DEST_PATH_IMAGE002
:

Figure 75985DEST_PATH_IMAGE079
Figure 75985DEST_PATH_IMAGE079

其中，

Figure 684821DEST_PATH_IMAGE002
为负载转矩T L 的估计值，
Figure 389472DEST_PATH_IMAGE080
为
Figure 134574DEST_PATH_IMAGE002
的导数，γ 2＞0，γ 2为观测器增益。in,
Figure 684821DEST_PATH_IMAGE002
is the estimated value of load torque T L ,
Figure 389472DEST_PATH_IMAGE080
for
Figure 134574DEST_PATH_IMAGE002
The derivative of , γ 2 >0, γ 2 is the observer gain.

步骤（4）：Step (4):

光电编码器得到转子位置角，通过计算得到机械角速度，送入到广义参数估计观测器中，滑模控制器根据给定的机械角速度与实际机械角速度作差作为输入，得到q轴的电压，给定的d轴电流与反馈电路中的

Figure 774634DEST_PATH_IMAGE081
轴电流相减得到
Figure 605187DEST_PATH_IMAGE081
轴电压。u d 和u q 通过了Park以及SVPWM产生脉冲信号然后进入三相逆变换器对永磁同步电机进行控制。The photoelectric encoder obtains the rotor position angle, obtains the mechanical angular velocity through calculation, and sends it to the generalized parameter estimation observer. The sliding mode controller takes the difference between the given mechanical angular velocity and the actual mechanical angular velocity as input to obtain the voltage of the q-axis, and gives given d-axis current with the feedback circuit in the
Figure 774634DEST_PATH_IMAGE081
Subtract the shaft current to get
Figure 605187DEST_PATH_IMAGE081
shaft voltage. U d and u q generate pulse signals through Park and SVPWM and then enter the three-phase inverter to control the permanent magnet synchronous motor.

步骤41以给定机械角速度与传感器测得的机械角速度之差作为滑模控制器的输入：Step 41 takes the difference between the given mechanical angular velocity and the mechanical angular velocity measured by the sensor as the input of the sliding mode controller:

Figure 113528DEST_PATH_IMAGE025
Figure 113528DEST_PATH_IMAGE025

其中，

Figure 713137DEST_PATH_IMAGE026
为转子的机械角速度的参考值。in,
Figure 713137DEST_PATH_IMAGE026
is the reference value of the mechanical angular velocity of the rotor.

步骤42设计滑模面：Step 42 Design the sliding surface:

Figure 851994DEST_PATH_IMAGE027
Figure 851994DEST_PATH_IMAGE027

其中，c为滑模面参数，满足c＞0，

Figure 356794DEST_PATH_IMAGE028
表示滑模控制器的输入对时间的导数；Among them, c is the sliding mode surface parameter, satisfying c > 0,
Figure 356794DEST_PATH_IMAGE028
Indicates the time derivative of the input of the sliding mode controller;

步骤43结合广义参数估计观测器，得到控制律为u q ：Step 43 combines the generalized parameter estimation observer to obtain the control law u q :

Figure 606510DEST_PATH_IMAGE082
Figure 606510DEST_PATH_IMAGE082

其中，sgn(s)为符号函数，

Figure 122942DEST_PATH_IMAGE001
为q轴电流i q 的估计值，
Figure 167121DEST_PATH_IMAGE002
为负载转矩T L 的估计值，a为中间参数，
Figure 909949DEST_PATH_IMAGE030
，k为控制率参数，k＞0。Among them, sgn (s) is a symbolic function,
Figure 122942DEST_PATH_IMAGE001
is the estimated value of the q-axis current i q ,
Figure 167121DEST_PATH_IMAGE002
is the estimated value of load torque T L , a is an intermediate parameter,
Figure 909949DEST_PATH_IMAGE030
, k is the control rate parameter, k >0.

相应的本发明还提供一种基于广义参数估计观测器的滑模控制系统，其特征在于，包括：Correspondingly, the present invention also provides a sliding mode control system based on a generalized parameter estimation observer, which is characterized in that it includes:

变换模块，用于获取三相永磁同步电机的自然坐标系下的数学模型，通过Clark坐标变换和Park坐标变换，并选取永磁同步电机q轴电流作为状态变量，机械角速度ω r 作为输出以及状态变量，将自然坐标系下的数学模型转换为三相永磁同步电机的d-q轴同步旋转坐标系下的数学模型；The transformation module is used to obtain the mathematical model under the natural coordinate system of the three-phase permanent magnet synchronous motor, through Clark coordinate transformation and Park coordinate transformation, and select the q-axis current of the permanent magnet synchronous motor as the state variable, the mechanical angular velocity ω r as the output and The state variable converts the mathematical model under the natural coordinate system into a mathematical model under the dq axis synchronous rotating coordinate system of the three-phase permanent magnet synchronous motor;

第一确定模块，用于根据所述d-q轴同步旋转坐标系下的数学模型，基于广义参数估计观测理论将状态观测转化为参数估计，确定用于估计q轴电流i q 和负载转矩T L 的线性回归方程；The first determination module is used to convert the state observation into parameter estimation based on the generalized parameter estimation observation theory according to the mathematical model in the dq axis synchronous rotating coordinate system, and determine the parameters used to estimate the q-axis current i q and the load torque T L The linear regression equation;

第二确定模块，用于处理所述的线性回归方程，使其符合激励条件，根据预先设置的广义参数估计观测器，确定q轴电流的估计值

Figure 697777DEST_PATH_IMAGE001
和负载转矩T L 的估计值
Figure 334294DEST_PATH_IMAGE002
；The second determination module is used to process the linear regression equation to make it meet the excitation conditions, estimate the observer according to the preset generalized parameters, and determine the estimated value of the q-axis current
Figure 697777DEST_PATH_IMAGE001
and an estimate of the load torque T L
Figure 334294DEST_PATH_IMAGE002
;

输出模块，用于根据广义参数估计观测器的估计信息，设计滑模控制器，根据滑模控制器得到控制量u q ，对控制量u q 进行逆Park坐标变换后，经由SVPWM模块得到三相逆变器的驱动信号，根据所述驱动信号调节三相逆变器的输出。The output module is used to design the sliding mode controller based on the estimation information of the generalized parameter estimation observer, obtain the control variable u q according to the sliding mode controller, and perform the inverse Park coordinate transformation on the control variable u q , and obtain the three-phase through the SVPWM module The driving signal of the inverter, and the output of the three-phase inverter is adjusted according to the driving signal.

广义参数估计观测器结合动态混合扩展技术将状态观测转换为参数估计，不仅可以实现q轴电流i q 和负载转矩T L 的同时估计，减少了传感器的使用可以提高整个系统的稳定性。基于估计的信息设计滑模控制器以提高系统抗干扰的能力和鲁棒性。The generalized parameter estimation observer combines the dynamic hybrid extension technology to convert the state observation into parameter estimation, which not only realizes the simultaneous estimation of the q-axis current i q and load torque T L , but also reduces the use of sensors and improves the stability of the entire system. Based on the estimated information, a sliding mode controller is designed to improve the system's anti-disturbance ability and robustness.

为了验证本发明所设计的基于广义参数估计观测器的滑模控制方法的有效性，我们在Matlab/simulink仿真平台上测试本发明设计的控制器对永磁同步单机的控制性能。验证所设计的观测器能否准确的快速的估计出电机系统的q轴电流。永磁同步电机在仿真实验中所用参数如表1所示。由图2可以看出观测器可以立即跟踪观测到系统的电流。图3是对负载转矩的跟踪估计图，给定负载转矩T L 为1N·m，观测器可以在0.05s估计到负载转矩的值，图4输出机械角速度在0.05s内可以趋于稳定且和期望的输出值一致，图5输出机械角速度在0.05s内可以趋于稳定且和期望的输出值一致。In order to verify the effectiveness of the sliding mode control method based on the generalized parameter estimation observer designed by the present invention, we tested the control performance of the controller designed by the present invention on the permanent magnet synchronous single machine on the Matlab/simulink simulation platform. Verify that the designed observer can accurately and quickly estimate the q-axis current of the motor system. The parameters used in the simulation experiment of the permanent magnet synchronous motor are shown in Table 1. It can be seen from Figure 2 that the observer can immediately track the observed system current. Figure 3 is the tracking estimation diagram of the load torque, given that the load torque T L is 1N·m, the observer can estimate the value of the load torque within 0.05s, and the output mechanical angular velocity in Figure 4 can tend to Stable and consistent with the expected output value, the output mechanical angular velocity in Figure 5 can tend to be stable and consistent with the expected output value within 0.05s.

仿真结果表明，本发明可以实现对永磁同步电机角速度的控制。在负载转矩未知的情况下，依然可以保证闭环系统的稳定性，同时减少了电流传感器的使用，降低了成本，提高了可靠性，在工程上有很好的应用价值。Simulation results show that the invention can realize the control of the angular velocity of the permanent magnet synchronous motor. In the case of unknown load torque, the stability of the closed-loop system can still be guaranteed, and at the same time, the use of current sensors is reduced, the cost is reduced, and the reliability is improved, which has good application value in engineering.

表1Table 1

Figure 814954DEST_PATH_IMAGE083
Figure 814954DEST_PATH_IMAGE083

以上所述仅是本发明的优选实施方式，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明技术原理的前提下，还可以做出若干改进和变形，这些改进和变形也应视为本发明的保护范围。The above is only a preferred embodiment of the present invention, and it should be pointed out that for those of ordinary skill in the art, without departing from the technical principle of the present invention, some improvements and modifications can also be made. It should also be regarded as the protection scope of the present invention.

以上所述仅是本发明的优选实施方式，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明技术原理的前提下，还可以做出若干改进和变形，这些改进和变形也应视为本发明的保护范围。The above is only a preferred embodiment of the present invention, and it should be pointed out that for those of ordinary skill in the art, without departing from the technical principle of the present invention, some improvements and modifications can also be made. It should also be regarded as the protection scope of the present invention.

Claims (7)

1.一种基于广义参数估计观测器的滑模控制方法，其特征在于，包括：1. A sliding mode control method based on generalized parameter estimation observer, is characterized in that, comprises: 获取三相永磁同步电机的自然坐标系下的数学模型，通过Clark坐标变换和Park坐标变换，并选取永磁同步电机q轴电流作为状态变量，机械角速度ω r 作为输出以及状态变量，将自然坐标系下的数学模型转换为三相永磁同步电机的d-q轴同步旋转坐标系下的数学模型；Obtain the mathematical model of the three-phase permanent magnet synchronous motor in the natural coordinate system, through Clark coordinate transformation and Park coordinate transformation, and select the q-axis current of the permanent magnet synchronous motor as the state variable, and the mechanical angular velocity ω r as the output and state variable, the natural The mathematical model under the coordinate system is converted into the mathematical model under the dq axis synchronous rotating coordinate system of the three-phase permanent magnet synchronous motor; 根据所述d-q轴同步旋转坐标系下的数学模型，基于广义参数估计观测理论将状态观测转化为参数估计，确定用于估计q轴电流i q 和负载转矩T L 的线性回归方程；According to the mathematical model under the dq-axis synchronous rotating coordinate system, the state observation is converted into parameter estimation based on the generalized parameter estimation observation theory, and the linear regression equation for estimating the q -axis current iq and the load torque T L is determined; 处理所述线性回归方程，使其符合激励条件，根据预先设置的广义参数估计观测器，确定q轴电流的估计值
Figure 259197DEST_PATH_IMAGE001
和负载转矩T L 的估计值
Figure 775629DEST_PATH_IMAGE002
；Process the linear regression equation to make it meet the excitation conditions, estimate the observer according to the preset generalized parameters, and determine the estimated value of the q-axis current
Figure 259197DEST_PATH_IMAGE001
and an estimate of the load torque T L
Figure 775629DEST_PATH_IMAGE002
; 根据广义参数估计观测器的估计信息，设计滑模控制器，根据滑模控制器得到控制量u q ，对控制量u q 进行逆Park坐标变换后，经由SVPWM模块得到三相逆变器的驱动信号，根据所述驱动信号调节三相逆变器的输出。According to the estimated information of the generalized parameter estimation observer, the sliding mode controller is designed, and the control variable u q is obtained according to the sliding mode controller. After the inverse Park coordinate transformation is performed on the control variable u q , the drive of the three-phase inverter is obtained through the SVPWM module signal, and adjust the output of the three-phase inverter according to the drive signal. 2.根据权利要求1所述的基于广义参数估计观测器的滑模控制方法，其特征在于，所述d-q轴同步旋转坐标系下的数学模型表示为：2. the sliding mode control method based on generalized parameter estimation observer according to claim 1, is characterized in that, the mathematical model under described d-q axis synchronous rotating coordinate system is expressed as:
Figure 491912DEST_PATH_IMAGE003
Figure 491912DEST_PATH_IMAGE003
 其中，
Figure 93795DEST_PATH_IMAGE004
为q轴电流对时间的导数，i q 为q轴电流，R s 为定子电阻，L为电感，φ f 为永磁体与定子交链的磁链，u q 为q轴电压同时也是控制输入，ω r 为转子的机械角速度，
Figure 802994DEST_PATH_IMAGE005
为转子的机械角速度对时间的导数，P为电机的极对数，J为转动惯量，B为粘滞摩擦系数，T L 为负载转矩。in,
Figure 93795DEST_PATH_IMAGE004
is the derivative of the q -axis current to time, i q is the q- axis current, R s is the stator resistance, L is the inductance, φ f is the flux linkage between the permanent magnet and the stator, u q is the q-axis voltage and is also the control input, ω r is the mechanical angular velocity of the rotor,
Figure 802994DEST_PATH_IMAGE005
is the derivative of the mechanical angular velocity of the rotor with respect to time, P is the number of pole pairs of the motor, J is the moment of inertia, B is the coefficient of viscous friction, and T L is the load torque. 3.根据权利要求2所述的基于广义参数估计观测器的滑模控制方法，其特征在于，所述线性回归方程为：3. the sliding mode control method based on generalized parameter estimation observer according to claim 2, is characterized in that, described linear regression equation is:
Figure 173932DEST_PATH_IMAGE006
Figure 173932DEST_PATH_IMAGE006
 q e 为加入滤波器线性回归方程的可测量，m e 为加入滤波器线性回归方程的回归因子，
Figure 61117DEST_PATH_IMAGE007
为线性回归方程的中间变量，
Figure 884716DEST_PATH_IMAGE008
，i q0为q轴电流初始值误差； q e is the measurable added to the filter linear regression equation, m e is the regression factor added to the filter linear regression equation,
Figure 61117DEST_PATH_IMAGE007
is the intermediate variable of the linear regression equation,
Figure 884716DEST_PATH_IMAGE008
, i q 0 is the error of the initial value of the q-axis current;
Figure 397606DEST_PATH_IMAGE009
Figure 397606DEST_PATH_IMAGE009
Figure 623051DEST_PATH_IMAGE010
Figure 623051DEST_PATH_IMAGE010
Figure 681137DEST_PATH_IMAGE011
Figure 681137DEST_PATH_IMAGE011
 s1为微分算子，α 1、α 2、β 1、β 2为滤波器参数，满足α 1，α 2≠0，β 1，β 2＞0，q1为未加入滤波器的线性回归方程的可测量，λ 1为观测器增益，λ 1＞0，m、ω为中间变量。s1 is a differential operator, α 1 , α 2 , β 1 , and β 2 are filter parameters, satisfying α 1 , α 2 ≠0, β 1 , β 2 >0, and q 1 is the linear regression equation without filter is measurable, λ 1 is the observer gain, λ 1 >0, m and ω are intermediate variables. 4.根据权利要求3所述的基于广义参数估计观测器的滑模控制方法，其特征在于，求解中间变量m、ω，包括：4. the sliding mode control method based on generalized parameter estimation observer according to claim 3, is characterized in that, solving intermediate variable m, ω comprises: 基于广义参数估计观测器的理论，重构q轴电流i q ，得到下式：Based on the theory of generalized parameter estimation observer, the q-axis current i q is reconstructed, and the following formula is obtained:
Figure 257612DEST_PATH_IMAGE012
Figure 257612DEST_PATH_IMAGE012
 其中，
Figure 311543DEST_PATH_IMAGE013
表示q轴电流i q 的重构状态的导数，ξ y 为q轴电流i q 的重构状态；in,
Figure 311543DEST_PATH_IMAGE013
Denotes the derivative of the reconstruction state of the q-axis current i q , ξ y is the reconstruction state of the q-axis current i q ; 基于线性系统理论得到重构状态ξ y 的状态转移矩阵X Ax ：The state transition matrix X Ax of the reconstructed state ξ y is obtained based on the linear system theory:
Figure 391494DEST_PATH_IMAGE014
Figure 391494DEST_PATH_IMAGE014
 其中，
Figure 886061DEST_PATH_IMAGE015
为状态转移矩阵对时间的导数，X Ax (0)为状态转移矩阵的初始值；in,
Figure 886061DEST_PATH_IMAGE015
is the derivative of the state transition matrix with respect to time, and X Ax (0) is the initial value of the state transition matrix; 则q轴电流的真实值表示为：Then the true value of the q-axis current is expressed as:
Figure 418673DEST_PATH_IMAGE016
Figure 418673DEST_PATH_IMAGE016
 其中，
Figure 7786DEST_PATH_IMAGE017
为初始值误差，i q (0)表示q轴电流的初始值，ξ y (0)表示q轴电流i q 的重构状态的初始值；in,
Figure 7786DEST_PATH_IMAGE017
is the initial value error, i q (0) represents the initial value of the q-axis current, ξ y (0) represents the initial value of the reconstruction state of the q-axis current i q ;
Figure 207823DEST_PATH_IMAGE018
Figure 207823DEST_PATH_IMAGE018
 重构
Figure 873291DEST_PATH_IMAGE005
，表示为：refactor
Figure 873291DEST_PATH_IMAGE005
,Expressed as:
Figure 893200DEST_PATH_IMAGE019
Figure 893200DEST_PATH_IMAGE019
Figure 551583DEST_PATH_IMAGE020
Figure 551583DEST_PATH_IMAGE020
Figure 606127DEST_PATH_IMAGE021
Figure 606127DEST_PATH_IMAGE021
 然后将m和ω的式子转换成微分方程的形式，表示为：Then convert the formulas of m and ω into the form of differential equations, expressed as:
Figure 176916DEST_PATH_IMAGE022
Figure 176916DEST_PATH_IMAGE022
Figure 949700DEST_PATH_IMAGE023
Figure 949700DEST_PATH_IMAGE023
 其中，
Figure 146195DEST_PATH_IMAGE024
为状态转移矩阵的转置，m(0)为m的初始值；in,
Figure 146195DEST_PATH_IMAGE024
is the transposition of the state transition matrix, m (0) is the initial value of m ; 求解所述微分方程，得到中间变量m、ω。Solve the differential equation to obtain the intermediate variables m, ω . 5.根据权利要求4所述的基于广义参数估计观测器的滑模控制方法，其特征在于，采用基于广义观测理论结合动态回归扩展方法确定所述q轴电流的估计值
Figure 55246DEST_PATH_IMAGE001
和负载转矩T L 的估计值
Figure 62516DEST_PATH_IMAGE002
。5. the sliding mode control method based on generalized parameter estimation observer according to claim 4, is characterized in that, adopts to determine the estimated value of described q axis electric current based on generalized observation theory in conjunction with dynamic regression extension method
Figure 55246DEST_PATH_IMAGE001
and an estimate of the load torque T L
Figure 62516DEST_PATH_IMAGE002
. 6.根据权利要求4所述的基于广义参数估计观测器的滑模控制方法，其特征在于，所述确定滑模控制器的过程，包括：6. the sliding mode control method based on generalized parameter estimation observer according to claim 4, is characterized in that, the described process of determining sliding mode controller comprises: 以给定机械角速度与传感器测得的机械角速度之差作为滑模控制器的输入，The difference between the given mechanical angular velocity and the mechanical angular velocity measured by the sensor is used as the input of the sliding mode controller, 表示为：Expressed as:
Figure 57017DEST_PATH_IMAGE025
Figure 57017DEST_PATH_IMAGE025
 其中，e为滑模控制器的输入，
Figure 60132DEST_PATH_IMAGE026
为转子的机械角速度的参考值；Among them, e is the input of the sliding mode controller,
Figure 60132DEST_PATH_IMAGE026
is the reference value of the mechanical angular velocity of the rotor; 设计滑模面s，表示为：The design sliding surface s is expressed as:
Figure 89268DEST_PATH_IMAGE027
Figure 89268DEST_PATH_IMAGE027
 其中，c为滑模面参数，满足c＞0，
Figure 1860DEST_PATH_IMAGE028
表示输入误差对时间的导数；Among them, c is the sliding mode surface parameter, satisfying c > 0,
Figure 1860DEST_PATH_IMAGE028
Indicates the derivative of the input error with respect to time; 结合广义参数估计观测器，得到控制律u q 为：Combined with the generalized parameter estimation observer, the control law u q is obtained as:
Figure 483657DEST_PATH_IMAGE029
Figure 483657DEST_PATH_IMAGE029
 其中，sgn(s)为符号函数，
Figure 897321DEST_PATH_IMAGE001
为q轴电流i q 的估计值，
Figure 905597DEST_PATH_IMAGE002
为负载转矩T L 的估计值，a为中间参数，
Figure 113725DEST_PATH_IMAGE030
，k为控制率参数，k＞0。Among them, sgn (s) is a symbolic function,
Figure 897321DEST_PATH_IMAGE001
is the estimated value of the q-axis current i q ,
Figure 905597DEST_PATH_IMAGE002
is the estimated value of load torque T L , a is an intermediate parameter,
Figure 113725DEST_PATH_IMAGE030
, k is the control rate parameter, k >0. 7.一种基于广义参数估计观测器的滑模控制系统，其特征在于，包括：7. A sliding mode control system based on generalized parameter estimation observer, characterized in that, comprising: 变换模块，用于获取三相永磁同步电机的自然坐标系下的数学模型，通过Clark坐标变换和Park坐标变换，并选取永磁同步电机q轴电流作为状态变量，机械角速度ω r 作为输出以及状态变量，将自然坐标系下的数学模型转换为三相永磁同步电机的d-q轴同步旋转坐标系下的数学模型；The transformation module is used to obtain the mathematical model under the natural coordinate system of the three-phase permanent magnet synchronous motor, through Clark coordinate transformation and Park coordinate transformation, and select the q-axis current of the permanent magnet synchronous motor as the state variable, the mechanical angular velocity ω r as the output and The state variable converts the mathematical model under the natural coordinate system into a mathematical model under the dq axis synchronous rotating coordinate system of the three-phase permanent magnet synchronous motor; 第一确定模块，用于根据所述d-q轴同步旋转坐标系下的数学模型，基于广义参数估计观测理论将状态观测转化为参数估计，确定用于估计q轴电流i q 和负载转矩T L 的线性回归方程；The first determination module is used to convert the state observation into parameter estimation based on the generalized parameter estimation observation theory according to the mathematical model in the dq axis synchronous rotating coordinate system, and determine the parameters used to estimate the q-axis current i q and the load torque T L The linear regression equation; 第二确定模块，用于处理所述线性回归方程，使其符合激励条件，根据预先设置的广义参数估计观测器，确定q轴电流的估计值
Figure 958184DEST_PATH_IMAGE001
和负载转矩T L 的估计值
Figure 175539DEST_PATH_IMAGE002
；The second determination module is used to process the linear regression equation to make it meet the excitation conditions, estimate the observer according to the preset generalized parameters, and determine the estimated value of the q-axis current
Figure 958184DEST_PATH_IMAGE001
and an estimate of the load torque T L
Figure 175539DEST_PATH_IMAGE002
; 输出模块，用于根据广义参数估计观测器的估计信息，设计滑模控制器，根据滑模控制器得到控制量u q ，对控制量u q 进行逆Park坐标变换后，经由SVPWM模块得到三相逆变器的驱动信号，根据所述驱动信号调节三相逆变器的输出。The output module is used to design the sliding mode controller based on the estimation information of the generalized parameter estimation observer, obtain the control variable u q according to the sliding mode controller, and perform the inverse Park coordinate transformation on the control variable u q , and obtain the three-phase through the SVPWM module The driving signal of the inverter, and the output of the three-phase inverter is adjusted according to the driving signal.
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