CN115347841A - Dead-beat prediction current loop control method for permanent magnet synchronous motor - Google Patents
Dead-beat prediction current loop control method for permanent magnet synchronous motor Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
- H02P21/0007—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
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Abstract
Description
技术领域technical field
本发明属于电机控制技术领域。The invention belongs to the technical field of motor control.
背景技术Background technique
在永磁同步电机驱动系统中,传统的控制方法主要有矢量控制和直接转矩控制。但对于高速发展的工业领域而言,传统的控制策略并不能满足不断发展的工业需求,因此一些新型现代控制方法相继被学者们提出。模型预测控制自问世以来已经在复杂工业过程中取得了巨大成功,从原来的启发式控制算法发展成为了工业领域新的学科分支。无差拍预测电流控制作为一种典型的基于模型的方法,系统模型的失配会严重降低控制器的性能。通过设计一个观测器来估计扰动与不确定性变量,然后将估计到的干扰补偿到预测控制器中是一种十分有效的方法,但是现有的补偿过程中存在电流环中参数失配问题和速度环中参数和负载的干扰性强的问题。In the permanent magnet synchronous motor drive system, the traditional control methods mainly include vector control and direct torque control. However, for the rapidly developing industrial field, traditional control strategies cannot meet the continuously developing industrial needs, so some new modern control methods have been proposed by scholars one after another. Model predictive control has achieved great success in complex industrial processes since its inception, and has developed from the original heuristic control algorithm to a new branch of the industry. Deadbeat predictive current control is a typical model-based method, and the mismatch of the system model will seriously degrade the performance of the controller. It is a very effective method to estimate the disturbance and uncertainty variables by designing an observer, and then compensate the estimated disturbance to the predictive controller, but the existing compensation process has the problem of parameter mismatch in the current loop and The problem of strong interference of parameters and loads in the speed loop.
发明内容Contents of the invention
本发明目的是为了解决现有补偿过程中存在电流环中参数失配问题和速度环中参数和负载的干扰性强的问题,提供了一种永磁同步电机无差拍预测电流控制方法。The purpose of the present invention is to solve the problem of parameter mismatch in the current loop and the strong interference of parameters and loads in the speed loop in the existing compensation process, and to provide a permanent magnet synchronous motor deadbeat prediction current control method.
本发明所述一种永磁同步电机无差拍预测电流控制方法,包括:A deadbeat predictive current control method for a permanent magnet synchronous motor according to the present invention, comprising:
步骤一、建立永磁同步电机的数学模型,利用所述数学模型,获取电流环超螺旋滑模观测器;
建立带有扰动的电机运动方程,设计速度环高阶滑模观测器;Establish the motion equation of the motor with disturbance, and design a high-order sliding mode observer for the speed loop;
步骤二、利用速度环超螺旋滑模观测器对电机的速度环扰动进行观测,获取扰动观测结果;
步骤三、利用电机实际转速和转速给定值对滑模趋近律改进,将所述扰动观测结果补偿到改进后的滑模趋近律中,获得速度控制律;
步骤四、利用电流环超螺旋滑模观测器对电流环进行观测,将电流环超螺旋滑模观测器的观测值和速度控制律输入到无差拍电流控制器,获取电流环控制信号。Step 4: Use the current loop superhelical sliding mode observer to observe the current loop, and input the observation value and speed control law of the current loop superhelical sliding mode observer to the deadbeat current controller to obtain the current loop control signal.
进一步地,本发明中,建立永磁同步电机的数学模型的方法为:Further, in the present invention, the method for establishing the mathematical model of the permanent magnet synchronous motor is:
建立永磁同步电机在dq坐标系下的定子电流方程:Establish the stator current equation of the permanent magnet synchronous motor in the dq coordinate system:
其中:ud,uq分别为dq坐标系下的定子电压的d轴分量和q轴分量;id,iq分别为dq坐标系下定子电流的d轴分量和q轴分量;R为定子电阻;Ld,Lq分别为d、q轴定子电感;ωe为电机的角速度;ψf为转子永磁体磁链幅值;Among them: u d , u q are the d-axis component and q-axis component of the stator voltage in the dq coordinate system; id and i q are the d -axis component and q-axis component of the stator current in the dq coordinate system; R is the stator voltage Resistance; L d , L q are d and q axis stator inductance respectively; ω e is the angular velocity of the motor; ψ f is the flux amplitude of the permanent magnet of the rotor;
采用前向欧拉法对所述定子电流方程进行离散化,在一个调制周期后控制实际电流矢量i(k+1)达到参考电流值i*(k+1),i(k+1)=i*(k+1),获取永磁同步电机的离散电流模型:The forward Euler method is used to discretize the stator current equation, and after one modulation cycle, the actual current vector i(k+1) is controlled to reach the reference current value i * (k+1), i(k+1)= i * (k+1), to obtain the discrete current model of the permanent magnet synchronous motor:
其中,ud(k)是dq坐标系下定子电压第k个调制周期的d轴分量;uq(k)是dq坐标系下定子电压第k个调制周期的q轴分量;Ts为采样周期,id(k)是dq坐标系下定子电流第k个调制周期的d轴分量,id(k)是dq坐标系下定子电流第k个调制周期的q轴分量,是dq坐标系下定子电流第k+1个调制周期的d轴分量的给定值,是dq坐标系下定子电流第k+1个调制周期的q轴分量的给定值。Among them, u d (k) is the d-axis component of the k-th modulation cycle of the stator voltage in the dq coordinate system; u q (k) is the q-axis component of the k-th modulation cycle of the stator voltage in the dq coordinate system; T s is the sampling period, id (k) is the d -axis component of the kth modulation period of the stator current in the dq coordinate system, and id (k) is the q-axis component of the kth modulation period of the stator current in the dq coordinate system, is the given value of the d-axis component of the k+1th modulation period of the stator current in the dq coordinate system, It is the given value of the q-axis component of the k+1th modulation period of the stator current in the dq coordinate system.
进一步地,本发明中,步骤一中,利用所述数学模型,获取电流环超螺旋滑模观测器的方法为:Further, in the present invention, in
利用所述数学模型建立包含参数不确定性的电压方程,根据所述包含参数不确定性的电压方程,获取电流环超螺旋滑模观测器表达式为:Using the mathematical model to establish a voltage equation containing parameter uncertainty, according to the voltage equation containing parameter uncertainty, the expression of the current loop superhelical sliding mode observer is obtained as:
其中,为id的观测值,为iq的观测值,k1为d轴电流观测器的第一控制参数,k2为d轴电流观测器的第二控制参数,k3为d轴电流观测器的第三控制参数;k4为q轴电流观测器的第一控制参数,k5为q轴电流观测器的第二控制参数,k6为q轴电流观测器的第三控制参数,Fd,Fq分别为fd,fq的导数,分别为的导数,为Fq的观测值,为Fd的观测值,为Fq的导数,为的导数,sgn()为符号函数,为fd的观测值,为fq的观测值,fd、fq分别为d轴和q轴参数的扰动。in, is the observed value of i d , is the observed value of i q , k 1 is the first control parameter of the d-axis current observer, k 2 is the second control parameter of the d-axis current observer, k 3 is the third control parameter of the d-axis current observer; k 4 is the first control parameter of the q-axis current observer, k 5 is the second control parameter of the q-axis current observer, k 6 is the third control parameter of the q-axis current observer, F d and F q are respectively f d , the derivative of f q , respectively derivative of is the observed value of F q , is the observed value of F d , is the derivative of F q , for The derivative of , sgn() is a symbolic function, is the observed value of f d , is the observed value of f q , and f d and f q are the disturbances of the d-axis and q-axis parameters respectively.
进一步地,本发明中,还包括对电流环超螺旋滑模观测器进行离散的步骤,具体为:Further, in the present invention, the step of discretizing the superhelical sliding mode observer of the current loop is also included, specifically:
利用前向欧拉法,使观测的电流和扰动的误差在有限时间内收敛到零,电流环超螺旋滑模观测器的离散时间方程为:Using the forward Euler method, the observed current and disturbance errors converge to zero within a finite time, and the discrete time equation of the current loop superhelical sliding mode observer is:
其中,k为调制周期个数,Ts表示调制周期,为id在第k+1个调制周期时的观测值,为iq在第k+1个调制周期时的观测值,为fd在第k个调制周期时的观测值,为fd在第k+1个调制周期时的观测值,为Fd在第k+1个调制周期时的观测值,为Fd在第k个调制周期时的观测值,为fq第k个调制周期时的观测值,为fq第k+1个调制周期时的观测值,为Fq第k+1个调制周期时的观测值,为Fq第k个调制周期时的观测值,为id在第k个调制周期时的观测值。Among them, k is the number of modulation cycles, T s represents the modulation cycle, is the observed value of i d at the k+1th modulation period, is the observed value of i q at the k+1th modulation period, is the observed value of f d at the kth modulation period, is the observed value of f d at the k+1th modulation period, is the observed value of F d at the k+1th modulation cycle, is the observed value of F d at the kth modulation period, is the observed value of f q at the kth modulation period, is the observed value of f q at the k+1th modulation cycle, is the observed value of F q at the k+1th modulation period, is the observed value of F q at the kth modulation period, is the observed value of i d at the kth modulation period.
进一步地,本发明中,步骤一种,带有扰动的电机运动方程为:Further, in the present invention, in step one, the motor motion equation with disturbance is:
其中,Pn为磁极对数;ωm为电机机械角速度;B为摩擦系数;J为转动惯量,ρ为参数摄动和外部负载的总扰动。Among them, P n is the number of magnetic pole pairs; ω m is the mechanical angular velocity of the motor; B is the friction coefficient; J is the moment of inertia, and ρ is the total disturbance of parameter perturbation and external load.
进一步地,本发明中,步骤一中,速度环高阶滑模观测器为:Further, in the present invention, in
式中,为速度观测误差,为ρ的观测值,D为ρ的导数,为D的观测值,kw1为速度环高阶滑模观测器的第一控制参数,kw2为速度环高阶滑模观测器的第二控制参数,kw3为速度环高阶滑模观测器的第三控制参数,为电机机械角速度ωm的观测值。In the formula, is the velocity observation error, is the observed value of ρ, D is the derivative of ρ, is the observed value of D, k w1 is the first control parameter of the speed loop high-order sliding mode observer, k w2 is the second control parameter of the speed loop high-order sliding mode observer, k w3 is the speed loop high-order sliding mode observation The third control parameter of the device, is the observed value of the motor mechanical angular velocity ω m .
进一步地,本发明中,步骤一中,还包括对速度环高阶滑模观测器进行离散化的步骤,具体为:Further, in the present invention,
其中,为电机机械角速度第k+1个调制周期时的观测值,ωm(k)为电机机械角速度第k个调制周期时的观测值,为D第k个调制周期时的观测值。in, is the observed value at the k+1th modulation cycle of the motor mechanical angular velocity, ω m (k) is the observed value at the kth modulation cycle of the motor mechanical angular velocity, is the observed value at the kth modulation period of D.
进一步地,本发明中,步骤三中,利用电机实际转速和转速给定值对滑模趋近律改进的方法为:Further, in the present invention, in
定义滑模面:Define the sliding surface:
其中,ew为转速误差;c为积分型滑模面的积分系数;s为滑模面;Among them, e w is the speed error; c is the integral coefficient of the integral sliding mode surface; s is the sliding mode surface;
式中,为转速给定值;In the formula, is the speed given value;
改进滑模趋近律为:The improved sliding mode reaching law is:
式中,为滑模面s的导数,ks为切换增益,ε为可变项ε+(1-ε)e-δ|s|的增益,kt为线性增益,δ为指数项e-δ|s|的增益,且ks>0,kt>0,δ>0,0<ε<1,当系统远离滑模面时,符号函数前面的系数趋近于ks|e|/ε,的值大于ks,加快了收敛速度,当系统到达滑模面时,符号函数前面的系数趋近于ks|ew|,的值小于ks,实现限制抖振。In the formula, is the derivative of the sliding mode surface s, k s is the switching gain, ε is the gain of the variable term ε+(1-ε)e -δ|s| , k t is the linear gain, and δ is the exponential term e -δ|s | , and k s >0, k t >0, δ>0, 0<ε<1, when the system is far away from the sliding mode surface, the coefficient in front of the sign function tends to k s |e|/ε, The value of is greater than k s , which speeds up the convergence speed. When the system reaches the sliding mode surface, the coefficient in front of the sign function tends to k s |e w |, A value of less than k s achieves limited chattering.
进一步地,本发明中,步骤三中,获得速度控制律的方法为:Further, in the present invention, in
将观测的参数摄动和外部负载的总扰动ρ补偿到控制律中,可得速度控制律为:Compensating the observed parameter perturbation and the total disturbance ρ of the external load into the control law, the speed control law can be obtained as:
为电机机械角速度给定值,为的导数。 is the given value of the mechanical angular velocity of the motor, for derivative of .
本发明所设计的高阶(三阶,本领域定义二阶以上为高阶)超螺旋滑模观测器可以估计未来电流值和参数失配引起的集中扰动,并有效地消除参数失配的影响,提高电流环的抗扰性能。此外,在速度环中采用改进的滑模趋近律设计速度控制器并设计三阶超螺旋滑模观测器估计参数摄动和外部负载的总扰动补偿到速度控制器中,为电流环提供稳定的电流参考值。The high-order (third-order, defined in the art as high-order above second-order) superhelical sliding mode observer designed by the present invention can estimate the concentrated disturbance caused by future current value and parameter mismatch, and effectively eliminate the influence of parameter mismatch , improve the anti-interference performance of the current loop. In addition, an improved sliding mode reaching law is used in the speed loop to design the speed controller and a third-order super-helical sliding mode observer is designed to estimate the parameter perturbation and the total disturbance of the external load to be compensated in the speed controller to provide stability for the current loop current reference value.
附图说明Description of drawings
图1为本发明基于高阶滑模观测器的永磁同步电机无差拍预测电流控制原理框图;Fig. 1 is the principle block diagram of the present invention's deadbeat prediction current control of permanent magnet synchronous motor based on high-order sliding mode observer;
图2为速度环采用PI控制,电流环采用传统的无差拍预测电流控制且电阻参数变标称参数的10倍,id,iq电流效果图;Figure 2 is the effect diagram of i d , i q current when the speed loop adopts PI control, the current loop adopts traditional deadbeat predictive current control and the resistance parameter becomes 10 times of the nominal parameter;
图3为速度环采用PI控制,电流环采用传统的无差拍预测电流控制且电感参数变标称参数的2倍,id,iq电流效果图;Figure 3 is the current effect diagram of i d and i q when the speed loop adopts PI control, the current loop adopts traditional deadbeat predictive current control and the inductance parameter becomes twice the nominal parameter;
图4为速度环采用PI控制,电流环采用传统的无差拍预测电流控制且磁链参数变标称参数的4倍,id,iq电流效果图;Figure 4 is the current effect diagram of i d and i q when the speed loop adopts PI control, the current loop adopts traditional deadbeat predictive current control and the flux linkage parameter is changed to 4 times of the nominal parameter;
图5为速度环采用PI控制,电流环采用无差拍预测电流控制结合高阶滑模观测器且电阻参数变标称参数的10倍,id,iq电流效果图;Fig. 5 is the speed loop adopts PI control, the current loop adopts deadbeat predictive current control combined with high-order sliding mode observer and the resistance parameter becomes 10 times of the nominal parameter, i d , i q current effect diagram;
图6为速度环采用PI控制,电流环采用无差拍预测电流控制结合高阶滑模观测器且电感参数变标称参数的2倍,id,iq电流效果图;Fig. 6 is the speed loop adopts PI control, the current loop adopts deadbeat predictive current control combined with high-order sliding mode observer, and the inductance parameter becomes twice the nominal parameter, the current effect diagram of i d and i q ;
图7为速度环采用PI控制,电流环采用无差拍预测电流控制结合高阶滑模观测器且磁链参数变标称参数的4倍,id,iq电流效果图;Fig. 7 is the speed loop adopts PI control, the current loop adopts deadbeat predictive current control combined with high-order sliding mode observer and the flux linkage parameter becomes 4 times of the nominal parameter, i d , i q current effect diagram;
图8为采用的改进滑模趋近律速度控制方法的转速图;Fig. 8 is the rotating speed diagram of the improved sliding mode reaching law speed control method adopted;
图9为采用改进滑模趋近律结合高阶滑模观测器控制方法的转速图。Fig. 9 is a diagram of the rotational speed using the improved sliding mode reaching law combined with the high-order sliding mode observer control method.
具体实施方式Detailed ways
下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例仅仅是本发明一部分实施例,而不是全部的实施例。基于本发明中的实施例,本领域普通技术人员在没有作出创造性劳动的前提下所获得的所有其他实施例,都属于本发明保护的范围。The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.
需要说明的是,在不冲突的情况下,本发明中的实施例及实施例中的特征可以相互组合。It should be noted that, in the case of no conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.
具体实施方式一:下面结合图1说明本实施方式,本实施方式所述一种永磁同步电机无差拍预测电流控制方法,包括:Specific Embodiment 1: The present embodiment will be described below in conjunction with FIG. 1 . A dead-beat predictive current control method for a permanent magnet synchronous motor described in this embodiment includes:
步骤一、建立永磁同步电机的数学模型,利用所述数学模型,获取电流环超螺旋滑模观测器;
建立带有扰动的电机运动方程,设计速度环高阶滑模观测器;Establish the motion equation of the motor with disturbance, and design a high-order sliding mode observer for the speed loop;
步骤二、利用速度环超螺旋滑模观测器对电机的速度环扰动进行观测,获取扰动观测结果;
步骤三、利用电机实际转速和转速给定值对滑模趋近律改进,将所述扰动观测结果补偿到改进后的滑模趋近律中,获得速度控制律;
步骤四、利用电流环超螺旋滑模观测器对电流环进行观测,将电流环超螺旋滑模观测器的观测值和速度控制律输入到无差拍电流控制器,获取电流环控制信号。Step 4: Use the current loop superhelical sliding mode observer to observe the current loop, and input the observation value and speed control law of the current loop superhelical sliding mode observer to the deadbeat current controller to obtain the current loop control signal.
本发明提高了永磁同步电机速度和电流抗扰性能和跟踪精度。本发明将参数变化和外部负载变化视为集总扰动,建立内置式永磁同步电机的数学模型,进而构造了两个三阶超螺旋滑模观测器来分别估计速度和电流回路中的集总扰动,并将估计出的扰动前馈到对应的控制器中进行补偿,以提高系统电流环鲁棒性和跟踪精度。此外,为了得到稳定的电流环给定值,在转速控制中采用了一种改进的滑模趋近律,不仅降低了控制信号中的抖振和缩短系统状态到达滑模面所需的时间,还进一步提高了抗扰性能。实验结果证明了本发明的有效性。本发明中,在获取电流环控制信号,将电流环控制信号输入至电流控制器,电流控制器产生电压控制信号经过坐标变换变为进入SVPMW调制模块,产生控制脉冲给到逆变器模块以驱动永磁同步电机转动。The invention improves the speed and current anti-disturbance performance and tracking precision of the permanent magnet synchronous motor. The present invention regards parameter changes and external load changes as lumped disturbances, establishes a mathematical model of the built-in permanent magnet synchronous motor, and then constructs two third-order superhelical sliding mode observers to estimate the lumped disturbance in the speed and current loops respectively. Disturbance, and the estimated disturbance is fed forward to the corresponding controller for compensation, so as to improve the system current loop robustness and tracking accuracy. In addition, in order to obtain a stable current loop given value, an improved sliding mode approach law is used in the speed control, which not only reduces the chattering in the control signal and shortens the time required for the system state to reach the sliding mode surface, The anti-interference performance is further improved. Experimental results prove the effectiveness of the present invention. In the present invention, after obtaining the current loop control signal, the current loop control signal is input to the current controller, and the current controller generates the voltage control signal After coordinate transformation into Enter the SVPMW modulation module to generate control pulses to the inverter module to drive the permanent magnet synchronous motor to rotate.
进一步地,本发明中,建立永磁同步电机的数学模型的方法为:Further, in the present invention, the method for establishing the mathematical model of the permanent magnet synchronous motor is:
建立永磁同步电机在dq坐标系下的定子电流方程:Establish the stator current equation of the permanent magnet synchronous motor in the dq coordinate system:
其中:ud,uq分别为dq坐标系下的定子电压的d轴分量和q轴分量;id,iq分别为dq坐标系下定子电流的d轴分量和q轴分量;R为定子电阻;Ld,Lq分别为d、q轴定子电感;ωe为电机的角速度;ψf为转子永磁体磁链幅值;Among them: u d , u q are the d-axis component and q-axis component of the stator voltage in the dq coordinate system; id and i q are the d -axis component and q-axis component of the stator current in the dq coordinate system; R is the stator voltage Resistance; L d , L q are d and q axis stator inductance respectively; ω e is the angular velocity of the motor; ψ f is the flux amplitude of the permanent magnet of the rotor;
采用前向欧拉法对所述定子电流方程进行离散化,在一个调制周期后控制实际电流矢量i(k+1)达到参考电流值i*(k+1),i(k+1)=i*(k+1),获取永磁同步电机的离散电流模型:The forward Euler method is used to discretize the stator current equation, and after one modulation cycle, the actual current vector i(k+1) is controlled to reach the reference current value i * (k+1), i(k+1)= i * (k+1), to obtain the discrete current model of the permanent magnet synchronous motor:
其中,ud(k)是dq坐标系下定子电压第k个调制周期的d轴分量;uq(k)是dq坐标系下定子电压第k个调制周期的q轴分量;Ts为采样周期,id(k)是dq坐标系下定子电流第k个调制周期的d轴分量,id(k)是dq坐标系下定子电流第k个调制周期的q轴分量,是dq坐标系下定子电流第k+1个调制周期的d轴分量的给定值,是dq坐标系下定子电流第k+1个调制周期的q轴分量的给定值,。Among them, u d (k) is the d-axis component of the k-th modulation cycle of the stator voltage in the dq coordinate system; u q (k) is the q-axis component of the k-th modulation cycle of the stator voltage in the dq coordinate system; T s is the sampling period, id (k) is the d -axis component of the kth modulation period of the stator current in the dq coordinate system, and id (k) is the q-axis component of the kth modulation period of the stator current in the dq coordinate system, is the given value of the d-axis component of the k+1th modulation period of the stator current in the dq coordinate system, is the given value of the q-axis component of the k+1th modulation period of the stator current in the dq coordinate system,.
进一步地,本发明中,步骤一中,利用所述数学模型,获取电流环超螺旋滑模观测器的方法为:Further, in the present invention, in
利用所述数学模型建立包含参数不确定性的电压方程,根据所述包含参数不确定性的电压方程,获取电流环超螺旋滑模观测器表达式为:Using the mathematical model to establish a voltage equation containing parameter uncertainty, according to the voltage equation containing parameter uncertainty, the expression of the current loop superhelical sliding mode observer is obtained as:
其中,为id的观测值,为iq的观测值,k1为d轴电流观测器的第一控制参数,k2为d轴电流观测器的第二控制参数,k3为d轴电流观测器的第三控制参数;k4为q轴电流观测器的第一控制参数,k5为q轴电流观测器的第二控制参数,k6为q轴电流观测器的第三控制参数,Fd,Fq分别为fd,fq的导数,分别为的导数,为Fq的观测值,为Fd的观测值,为Fq的导数,为的导数,sgn()为符号函数,为fd的观测值,为fq的观测值,fd、fq分别为d轴和q轴参数的扰动。in, is the observed value of i d , is the observed value of i q , k 1 is the first control parameter of the d-axis current observer, k 2 is the second control parameter of the d-axis current observer, k 3 is the third control parameter of the d-axis current observer; k 4 is the first control parameter of the q-axis current observer, k 5 is the second control parameter of the q-axis current observer, k 6 is the third control parameter of the q-axis current observer, F d and F q are respectively f d , the derivative of f q , respectively derivative of is the observed value of F q , is the observed value of F d , is the derivative of F q , for The derivative of , sgn() is a symbolic function, is the observed value of f d , is the observed value of f q , and f d and f q are the disturbances of the d-axis and q-axis parameters respectively.
进一步地,本发明中,还包括对电流环超螺旋滑模观测器进行离散的步骤,具体为:Further, in the present invention, the step of discretizing the superhelical sliding mode observer of the current loop is also included, specifically:
利用前向欧拉法,使观测的电流和扰动的误差在有限时间内收敛到零,电流环超螺旋滑模观测器的离散时间方程为:Using the forward Euler method, the observed current and disturbance errors converge to zero within a finite time, and the discrete time equation of the current loop superhelical sliding mode observer is:
其中,k为调制周期个数,Ts表示调制周期,为id在第k+1个调制周期时的观测值,为iq在第k+1个调制周期时的观测值,为fd在第k个调制周期时的观测值,为fd在第k+1个调制周期时的观测值,为Fd在第k+1个调制周期时的观测值,为Fd在第k个调制周期时的观测值,为fq第k个调制周期时的观测值,为fq第k+1个调制周期时的观测值,第k+1个调制周期时的观测值,为Fq第k个调制周期时的观测值,为id在第k个调制周期时的观测值。Among them, k is the number of modulation cycles, T s represents the modulation cycle, is the observed value of i d at the k+1th modulation period, is the observed value of i q at the k+1th modulation cycle, is the observed value of f d at the kth modulation period, is the observed value of f d at the k+1th modulation period, is the observed value of F d at the k+1th modulation cycle, is the observed value of F d at the kth modulation period, is the observed value of f q at the kth modulation period, is the observed value of f q at the k+1th modulation cycle, The observed value at the k+1th modulation period, is the observed value of F q at the kth modulation period, is the observed value of i d at the kth modulation period.
进一步地,本发明中,步骤一种,带有扰动的电机运动方程为:Further, in the present invention, in step one, the motor motion equation with disturbance is:
其中,Pn为磁极对数;ωm为电机机械角速度;B为摩擦系数;J为转动惯量,ρ为参数摄动和外部负载的总扰动。Among them, P n is the number of magnetic pole pairs; ω m is the mechanical angular velocity of the motor; B is the friction coefficient; J is the moment of inertia, and ρ is the total disturbance of parameter perturbation and external load.
进一步地,本发明中,步骤一中,速度环高阶滑模观测器为:Further, in the present invention, in
式中,为速度观测误差,为ρ的观测值,D为ρ的导数,为D的观测值,kw1为速度环高阶滑模观测器的第一控制参数,kw2为速度环高阶滑模观测器的第二控制参数,kw3为速度环高阶滑模观测器的第三控制参数,为电机机械角速度ωm的观测值。In the formula, is the velocity observation error, is the observed value of ρ, D is the derivative of ρ, is the observed value of D, k w1 is the first control parameter of the speed loop high-order sliding mode observer, k w2 is the second control parameter of the speed loop high-order sliding mode observer, k w3 is the speed loop high-order sliding mode observation The third control parameter of the device, is the observed value of the motor mechanical angular velocity ω m .
进一步地,本发明中,步骤一中,还包括对速度环高阶滑模观测器进行离散化的步骤,具体为:Further, in the present invention,
其中,为电机机械角速度第k+1个调制周期时的观测值,ωm(k)为电机机械角速度第k个调制周期时的观测值,为D第k个调制周期时的观测值。in, is the observed value at the k+1th modulation cycle of the motor mechanical angular velocity, ω m (k) is the observed value at the kth modulation cycle of the motor mechanical angular velocity, is the observed value at the kth modulation period of D.
进一步地,本发明中,步骤三中,利用电机实际转速和转速给定值对滑模趋近律改进的方法为:Further, in the present invention, in
定义滑模面:Define the sliding surface:
其中,ew为转速误差;c为积分型滑模面的积分系数;s为滑模面;Among them, e w is the speed error; c is the integral coefficient of the integral sliding mode surface; s is the sliding mode surface;
式中,为转速给定值;In the formula, is the speed given value;
改进滑模趋近律为:The improved sliding mode reaching law is:
式中,为滑模面s的导数,ks为切换增益,ε为可变项ε+(1-ε)e-δ|s|的增益,kt为线性增益,δ为指数项e-δ|s|的增益,且ks>0,kt>0,δ>0,0<ε<1,当系统远离滑模面时,符号函数前面的系数趋近于ks|e|/ε,的值大于ks,加快了收敛速度,当系统到达滑模面时,符号函数前面的系数趋近于ks|ew|,的值小于ks,实现限制抖振。In the formula, is the derivative of the sliding mode surface s, k s is the switching gain, ε is the gain of the variable term ε+(1-ε)e -δ|s| , k t is the linear gain, and δ is the exponential term e -δ|s | , and k s >0, k t >0, δ>0, 0<ε<1, when the system is far away from the sliding mode surface, the coefficient in front of the sign function tends to k s |e|/ε, The value of is greater than k s , which speeds up the convergence speed. When the system reaches the sliding mode surface, the coefficient in front of the sign function tends to k s |e w |, A value of less than k s achieves limited chattering.
进一步地,本发明中,步骤三中,获得速度控制律的方法为:Further, in the present invention, in
将观测的参数摄动和外部负载的总扰动ρ补偿到控制律中,可得速度控制律为:Compensating the observed parameter perturbation and the total disturbance ρ of the external load into the control law, the speed control law can be obtained as:
为电机机械角速度给定值,为的导数。 is the given value of the mechanical angular velocity of the motor, for derivative of .
本发明中,步骤一中采用内置式永磁同步电机在dq坐标系下的定子电流方程为:In the present invention, the stator current equation of the built-in permanent magnet synchronous motor under the dq coordinate system in
电磁转矩方程:Electromagnetic torque equation:
运动方程:Motion equation:
其中:ud,uq;id,iq分别为dq坐标系下的定子电压和定子电流;R为定子电阻;Ld,Lq分别为dq轴电感;ωe为电角速度;ψf为转子永磁体磁链幅值;Te为电磁转矩;Pn为磁极对数;ωm为机械角速度;TL为负载转矩;B为摩擦系数;J为转动惯量。Among them: u d , u q ; id , i q are stator voltage and stator current in dq coordinate system respectively; R is stator resistance; L d , L q are dq axis inductance respectively; ω e is electrical angular velocity; ψ f T e is the electromagnetic torque; P n is the number of magnetic pole pairs; ω m is the mechanical angular velocity; T L is the load torque; B is the friction coefficient; J is the moment of inertia.
应用前向欧拉法对(1)中所示的模型进行离散化,永磁同步电机的离散电流模型可以表示为:Apply forward Euler method to discretize the model shown in (1), the discrete current model of permanent magnet synchronous motor can be expressed as:
其中,Ts为采样周期。根据离散的永磁同步电机的离散电流模型,在一个调制周期后,使实际电流矢量达到参考电流即i(k+1)=i*(k+1),此时定子电压表达式如下:Among them, T s is the sampling period. According to the discrete current model of the discrete permanent magnet synchronous motor, after one modulation cycle, the actual current vector reaches the reference current i(k+1)=i * (k+1), at this time the expression of the stator voltage is as follows:
随着电机运行或外部条件的变化,控制器中设置的参数可能与实际不同。包含参数不确定性的电压方程表示为:As the motor runs or the external conditions change, the parameters set in the controller may be different from the actual ones. The voltage equation including parameter uncertainties is expressed as:
其中,fd、fq为参数扰动。Among them, f d and f q are parameter perturbations.
用实验结果说明本发明的有效性,本发明的系统参数如表1,本发明的整体控制框图如图1所示。电机空载启动,给定转速为1500r/min,并在运行过程中负载转矩突变为12N·m。在图2到图7的对比可知,电阻的变化对于系统的电流的影响并不明显,但当电感和磁链变化时,传统控制方法的电流脉动变大,跟踪精度下降。且在磁链变化时最为明显,电流iq完全跟踪不上参考电流iqref。本发明所设计的系统在电阻、电感、磁链发生变化时,表现出更好的动态和稳态性能。由图8和图9可知,本发明所设计的系统在负载发生变化时,转速的调节时间更小,且转速跌落也更小。实验表明本发明所设计的系统具有更好的动态和稳态性能。Illustrate effectiveness of the present invention with experimental result, system parameter of the present invention is as table 1, and overall control block diagram of the present invention is as shown in Figure 1. The motor starts without load, the given speed is 1500r/min, and the load torque suddenly changes to 12N·m during operation. From the comparison of Figure 2 to Figure 7, it can be seen that the change of resistance has no obvious influence on the current of the system, but when the inductance and flux linkage change, the current ripple of the traditional control method becomes larger and the tracking accuracy decreases. And it is most obvious when the flux linkage changes, and the current i q cannot track the reference current i qref completely . The system designed by the invention shows better dynamic and steady-state performance when the resistance, inductance and flux linkage change. It can be seen from Fig. 8 and Fig. 9 that when the load changes in the system designed by the present invention, the adjustment time of the speed is shorter, and the speed drop is also smaller. Experiments show that the system designed by the present invention has better dynamic and steady-state performance.
表1Table 1
虽然在本文中参照了特定的实施方式来描述本发明,但是应该理解的是,这些实施例仅仅是本发明的原理和应用的示例。因此应该理解的是,可以对示例性的实施例进行许多修改,并且可以设计出其他的布置,只要不偏离所附权利要求所限定的本发明的精神和范围。应该理解的是,可以通过不同于原始权利要求所描述的方式来结合不同的从属权利要求和本文中所述的特征。还可以理解的是,结合单独实施例所描述的特征可以使用在其他所述实施例中。Although the invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It is therefore to be understood that numerous modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the invention as defined by the appended claims. It shall be understood that different dependent claims and features described herein may be combined in a different way than that described in the original claims. It will also be appreciated that features described in connection with individual embodiments can be used in other described embodiments.
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CN116317747A (en) * | 2023-01-18 | 2023-06-23 | 北京航空航天大学 | Full-rotation-speed range tracking method for ultra-high-speed permanent magnet synchronous motor |
CN117811445A (en) * | 2024-02-28 | 2024-04-02 | 华侨大学 | Novel ultra-spiral sliding mode robust load observation method for permanent magnet synchronous motor |
CN119051500A (en) * | 2024-08-15 | 2024-11-29 | 山东科技大学 | Dead beat prediction control method for PIR type permanent magnet synchronous motor with disturbance suppression |
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CN116317747A (en) * | 2023-01-18 | 2023-06-23 | 北京航空航天大学 | Full-rotation-speed range tracking method for ultra-high-speed permanent magnet synchronous motor |
CN117811445A (en) * | 2024-02-28 | 2024-04-02 | 华侨大学 | Novel ultra-spiral sliding mode robust load observation method for permanent magnet synchronous motor |
CN117811445B (en) * | 2024-02-28 | 2024-05-21 | 华侨大学 | Ultra-spiral sliding mode robust load observation method for permanent magnet synchronous motor |
CN119051500A (en) * | 2024-08-15 | 2024-11-29 | 山东科技大学 | Dead beat prediction control method for PIR type permanent magnet synchronous motor with disturbance suppression |
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