CN116094400A - A MTPA predictive control method for permanent magnet synchronous motor - Google Patents
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Abstract
本发明公开了一种永磁同步电机MTPA预测控制方法，包括：建立永磁同步电机的基于MTPA的电流预测的多项目价值函数；将当前时刻的采样的永磁同步电机电流与电压值带入价值函数求解得到当前时刻满足电机最优控制的变量，并根据该最优控制的变量中的电流值计算出下一时刻即k时刻的电流值；将电机转速参考值和得到电流值输入PI调节器后获得该时刻的电磁转矩参考值；将获得的电磁转矩参考值、预测到的下一时刻的d轴预测电流作为MTPA模块的输入，MTPA模块输出其工作时的q轴电流以及d轴电流。本发明在电流预测控制的基础上，通过上一个周期预测的当前周期的d轴电流近似获取MTPA工作点电流，有效简化公式法中电流计算方法。
The invention discloses a MTPA predictive control method for a permanent magnet synchronous motor, which includes: establishing a multi-item value function based on MTPA current prediction of the permanent magnet synchronous motor; bringing the current and voltage values of the permanent magnet synchronous motor sampled at the current moment into Solve the value function to obtain the variable that satisfies the optimal control of the motor at the current moment, and calculate the current value at the next moment, that is, the k time according to the current value in the variable of the optimal control; input the motor speed reference value and the obtained current value into the PI adjustment The electromagnetic torque reference value at this moment is obtained after the controller; the obtained electromagnetic torque reference value and the predicted d-axis predicted current at the next moment are used as the input of the MTPA module, and the MTPA module outputs the q-axis current and d shaft current. On the basis of current predictive control, the present invention approximates the current of the MTPA working point through the d-axis current of the current cycle predicted in the previous cycle, and effectively simplifies the current calculation method in the formula method.
Description
技术领域Technical Field
本发明涉及交流伺服控制技术领域，具体涉及一种永磁同步电机MTPA预测控制方法。The present invention relates to the technical field of AC servo control, and in particular to a permanent magnet synchronous motor MTPA predictive control method.
背景技术Background Art
永磁同步电机因其结构简单、功率密度高、重量轻、低损耗和效率高等性能，在汽车工业等多个领域得到广泛的应用。随着控制理论和计算机技术的发展，越来越多先进的控制方法被应用到永磁同步电机的控制中，常用的如改进PI控制、滑模控制、MTPA控制、预测控制等。Permanent magnet synchronous motors are widely used in many fields such as the automotive industry due to their simple structure, high power density, light weight, low loss and high efficiency. With the development of control theory and computer technology, more and more advanced control methods are applied to the control of permanent magnet synchronous motors, such as improved PI control, sliding mode control, MTPA control, predictive control, etc.
最大转矩电流比MTPA(Maximum Torque per Ampere)控制是一种提升电机运行效率的控制方法，它使得电流一定的情况下输出最大电磁转矩。MTPA控制主要分为三类：查表法，信号注入法和公式法。公式法是MTPA控制中常用的一种方法，公式法MTPA通过建立电磁转矩和定子电流约束条件，并通过极值求解得到电磁转矩与交轴、直轴电流之间的关系，进而得到直轴和交轴电流给定值。现有的公式法如附图2所示中，不仅包括原有公式法MTPA、还包括超前角公式法MTPA；MTPA法直观易懂，但其中通过转矩获得电流的公式中含有高次多项式、反三角函数等运算，计算复杂且量大。Maximum torque per current ratio MTPA (Maximum Torque per Ampere) control is a control method to improve the operating efficiency of the motor. It enables the maximum electromagnetic torque to be output when the current is constant. MTPA control is mainly divided into three categories: table lookup method, signal injection method and formula method. The formula method is a commonly used method in MTPA control. The formula method MTPA establishes electromagnetic torque and stator current constraints, and obtains the relationship between the electromagnetic torque and the quadrature axis and direct axis currents through extreme value solution, and then obtains the direct axis and quadrature axis current given values. The existing formula method is shown in Figure 2, which includes not only the original formula method MTPA, but also the lead angle formula method MTPA; the MTPA method is intuitive and easy to understand, but the formula for obtaining current through torque contains high-order polynomials, inverse trigonometric functions and other operations, and the calculation is complex and large.
模型预测控制MPC(Model Predictive Control)是在建立在系统数学模型基础上，实现在当前时刻预测下一时刻的状态。而永磁同步电机连续电流预测控制是将参考电流与运行电流之间的误差进行约束求解，然后将下一个控制周期的最优控制电压用于电机控制,动态性能好。因此需要更好的方法来解决如何在永磁同步电机电流预测控制的基础上研究一种计算更为简单的MTPA控制方法。Model Predictive Control (MPC) is based on the mathematical model of the system to predict the state of the next moment at the current moment. The continuous current predictive control of permanent magnet synchronous motors solves the error between the reference current and the operating current, and then uses the optimal control voltage of the next control cycle for motor control, which has good dynamic performance. Therefore, a better method is needed to solve how to study a MTPA control method with simpler calculations based on the current predictive control of permanent magnet synchronous motors.
发明内容Summary of the invention
1.所要解决的技术问题：1. Technical problems to be solved:
针对上述技术问题，本发明提供一种永磁同步电机MTPA预测控制方法，本方法能够简化MTPA工作点求解方法，同时在电流控制中引入基于MTPA的预测控制方案，确保电流轨迹能够按照最大转矩电流比曲线运行，提升电机运行效率。In view of the above technical problems, the present invention provides a permanent magnet synchronous motor MTPA predictive control method, which can simplify the MTPA operating point solution method and introduce a MTPA-based predictive control scheme into current control to ensure that the current trajectory can operate according to the maximum torque current ratio curve and improve the motor operation efficiency.
2.技术方案：2. Technical solution:
一种永磁同步电机MTPA预测控制方法，其特征在于：包括以下步骤：A permanent magnet synchronous motor MTPA predictive control method, characterized in that it comprises the following steps:
步骤一：在d-q旋转坐标系下建立永磁同步电机的基于MTPA的电流预测的多项目价值函数；所述多项目价值函数包括电流误差优化、最大转矩电流比优化以及电压误差优化；Step 1: Establish a multi-item value function for current prediction based on MTPA of a permanent magnet synchronous motor in a d-q rotating coordinate system; the multi-item value function includes current error optimization, maximum torque current ratio optimization, and voltage error optimization;
步骤二：通过价值函数求出当前k时刻电机控制最优电压，并根据该最优控制电压和永磁同步电机得电流预测模型预测下一个k+1时刻的d轴电流值；Step 2: Calculate the optimal voltage of the motor control at the current k moment through the value function, and predict the d-axis current value at the next k+1 moment based on the optimal control voltage and the current prediction model of the permanent magnet synchronous motor;
步骤三：将电机转速参考值和电机当前运行转速值输入PI调节器后获得该时刻的电磁转矩参考值Te *(k)；Step 3: Input the motor speed reference value and the current running speed value of the motor into the PI regulator to obtain the electromagnetic torque reference value T e * (k) at that moment;
步骤四：将步骤三获得的电磁转矩参考值、根据在k-1时刻预测到的k时刻的d轴预测电流作为MTPA模块的输入，MTPA模块输出其工作时的q轴电流以及d轴电流。Step 4: The electromagnetic torque reference value obtained in step 3 and the predicted d-axis current at time k predicted at time k-1 are used as inputs of the MTPA module, and the MTPA module outputs the q-axis current and d-axis current during its operation.
进一步地，所述步骤一具体包括：Furthermore, the
S11：永磁同步电机电流方程为：S11: The current equation of the permanent magnet synchronous motor is:
公式(1)中id为d轴电流，i q为q轴电流；Rs为电阻；Ld为d轴磁导、Lq为q轴磁导；P为电机极对数；ud为d轴电压，uq为q轴电压；ωm为机械转速；φf为磁链；In formula (1), i d is the d-axis current, i q is the q-axis current; R s is the resistance; L d is the d-axis permeance, Lq is the q-axis permeance; P is the number of motor pole pairs; ud is the d-axis voltage, u q is the q-axis voltage; ω m is the mechanical speed; φ f is the flux linkage;
S12：将永磁同步电机电流方程离散化；得到永磁同步电机的电流离散模型如下式(2)：S12: Discretize the permanent magnet synchronous motor current equation; obtain the current discrete model of the permanent magnet synchronous motor as follows (2):
(2)式中，T为采样周期，k表示k个采样时刻；(2) In the formula, T is the sampling period, k represents k sampling moments;
S13：将公式(2)改写为状态空间模型得到如下式(3)的状态空间方程：S13: Rewrite formula (2) into a state space model to obtain the state space equation of formula (3):
x(k+1)＝Ax(k)+Bu(k)x(k+1)＝Ax(k)+Bu(k)
y(k)＝Cx(k) (3)；y(k)＝Cx(k) (3);
(3)式中，
S14：永磁同步电机采用MTPA模式运行时轨迹为MTPA控制曲线，即d、q轴电流满足公式：
(4)式中，kid为当前d轴电流与d轴参考电流之
进一步地，步骤二中通过对价值函数分别进行对△ud和△uq求偏导数，即：Furthermore, in
从而得到当前k时刻的最优控制电压增量△ud和△uq；然后根据公式(5)获得k时刻最优电压，并将求得的该电压用于永磁同步电机控制；Thus, the optimal control voltage increments △u d and △u q at the current time k are obtained; then the optimal voltage at the time k is obtained according to formula (5), and the obtained voltage is used for permanent magnet synchronous motor control;
ud(k)＝ud(k-1)+△ud(k)u d (k)＝u d (k-1)+△u d (k)
uq(k)＝uq(k-1)+△uq(k) (5)；u q (k)=u q (k-1)+Δu q (k) (5);
将上式中获取的d、q轴电压带入公式(6)，得到k+1时刻的d轴电流idmiddle(k+1)，作为MTPA工作点求解的中间变量：Substituting the d-axis and q-axis voltages obtained in the above formula into formula (6), we can obtain the d-axis current i dmiddle (k+1) at time k+1, which is used as the intermediate variable for solving the MTPA operating point:
进一步地，步骤三具体为：Furthermore, step three is specifically as follows:
永磁同步电机速度公式如下：The speed formula of permanent magnet synchronous motor is as follows:
利用上式公式，将电机速度参考值和当前时刻电机的速度反馈值输入PI调节器并得到电机的电磁转矩参考值Te *(k)。By using the above formula, the motor speed reference value and the speed feedback value of the motor at the current moment are input into the PI regulator to obtain the electromagnetic torque reference value Te * (k) of the motor.
进一步地，将步骤三获得的电磁转矩参考值Te *(k)、步骤一中的d轴预测电流idpre(k+1)作为MTPA算法模块的输入求解电机MTPA控制时的工作点，具体如下：Furthermore, the electromagnetic torque reference value Te * (k) obtained in step 3 and the d-axis predicted current i dpre (k+1) in
S41:永磁同步电机电磁转矩方程如(8)所示，S41: The electromagnetic torque equation of the permanent magnet synchronous motor is shown in (8),
将电磁转矩Te *(k)、预测电流idmiddle(k)代入公式(8)，可以得到MTPA工作时的q轴电流：Substituting the electromagnetic torque Te * (k) and the predicted current i dmiddle (k) into formula (8), the q-axis current when MTPA is working can be obtained:
S42:由于当永磁同步电机采用MTPA模式运行时，其d、q轴电流满足下式(10)：S42: When the permanent magnet synchronous motor is operated in MTPA mode, its d-axis and q-axis currents satisfy the following equation (10):
因此将得到的中iqmtpa(k)带入公式(10)，即得到MTPA模板工作时的d轴工作电流，如下式(11)：Therefore, the obtained i qmtpa (k) is substituted into formula (10), and the d-axis working current of the MTPA template when working is obtained, which is as follows (11):
3.有益效果：3. Beneficial effects:
(1)本发明提供了的一种MTPA工作点电流的计算方法，在电流预测控制的基础上，通过上一个周期预测的当前周期的d轴电流近似获取MTPA工作点电流，附图2中公开的是现有技术中的公式法、超前角公式法以及本申请中公开的改进MTPA的计算公式，从中不难看出本申请公开的方法能够简化公式法中电流计算方法，消除了传统的公式法中的开方等运算。(1) The present invention provides a method for calculating the MTPA operating point current. On the basis of current prediction control, the MTPA operating point current is approximately obtained by predicting the d-axis current of the current cycle from the previous cycle. Attached Figure 2 discloses the formula method in the prior art, the lead angle formula method and the calculation formula of the improved MTPA disclosed in the present application. It is not difficult to see that the method disclosed in the present application can simplify the current calculation method in the formula method and eliminate the square root operation and the like in the traditional formula method.
(2)本发明还提供了一种MTPA电流预测控制方法，在电流预测价值函数中除了电流误差、电压误差外，增加了MTPA工作轨迹误差，使得永磁同步电机d轴、q轴电流尽可能沿着最大转矩电流比轨迹运行。同时，电流预测中获得的下一时刻的d轴电流作为MTPA工作点求解的变量，用于简化MTPA工作点求解的公式。(2) The present invention also provides an MTPA current prediction control method. In addition to the current error and voltage error, the MTPA working trajectory error is added to the current prediction value function, so that the d-axis and q-axis currents of the permanent magnet synchronous motor run along the maximum torque current ratio trajectory as much as possible. At the same time, the d-axis current at the next moment obtained in the current prediction is used as a variable for solving the MTPA working point, which is used to simplify the formula for solving the MTPA working point.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为本发明的系统控制框图；FIG1 is a system control block diagram of the present invention;
图2为本发明中MTPA公式与现有技术中的MTPA公式。FIG. 2 shows the MTPA formula in the present invention and the MTPA formula in the prior art.
具体实施方式DETAILED DESCRIPTION
下面结合附图对本发明进行具体的说明。The present invention will be described in detail below with reference to the accompanying drawings.
现有的技术方案,如公式法、查表法等,在准确性、计算量、实施速度等方面具有一定的不足。Existing technical solutions, such as formula method, table lookup method, etc., have certain shortcomings in terms of accuracy, calculation amount, implementation speed, etc.
公式求解方法是应用广泛的一种MTPA工作点电流的求解方法。现有的MTPA公式法主要有电流求解法、超前角求解法等，如附图2中所示。电流求解法以速度环输出电磁转矩，并根据公式求解出d、q轴电流，用于MTPA控制，该公式较为计算复杂；超前角电流法相对于直接公式法公式形式简单，但设计到三角函数，计算也较为复杂。本申请提出的改进的MTPA控制算法首先采用预测控制保持系统性能的稳定，在此基础上利用预测控制的预测电流作为MTPA工作点计算的输入，简化了直接公式法(1)中的工作点q轴电流的求解。The formula solving method is a widely used method for solving the MTPA working point current. The existing MTPA formula methods mainly include the current solving method, the lead angle solving method, etc., as shown in Figure 2. The current solving method uses the speed loop to output the electromagnetic torque, and solves the d and q axis currents according to the formula for MTPA control. The formula is relatively complex to calculate; the lead angle current method is simpler than the direct formula method, but it is designed with trigonometric functions and the calculation is also relatively complex. The improved MTPA control algorithm proposed in this application first adopts predictive control to maintain the stability of system performance, and on this basis uses the predicted current of predictive control as the input for MTPA working point calculation, which simplifies the solution of the working point q axis current in the direct formula method (1).
如附图1所示，一种永磁同步电机MTPA预测控制方法，其特征在于：包括以下步骤：As shown in FIG1 , a permanent magnet synchronous motor MTPA predictive control method is characterized by comprising the following steps:
步骤一：在d-q旋转坐标系下建立永磁同步电机的基于MTPA的电流预测的多项目价值函数；所述多项目价值函数包括电流误差优化、最大转矩电流比优化以及电压误差优化；Step 1: Establish a multi-item value function for current prediction based on MTPA of a permanent magnet synchronous motor in a d-q rotating coordinate system; the multi-item value function includes current error optimization, maximum torque current ratio optimization, and voltage error optimization;
步骤二：通过价值函数求出当前k时刻电机控制最优电压，并根据该最优控制电压和永磁同步电机得电流预测模型预测下一个k+1时刻的d轴电流值；Step 2: Calculate the optimal voltage of the motor control at the current k moment through the value function, and predict the d-axis current value at the next k+1 moment based on the optimal control voltage and the current prediction model of the permanent magnet synchronous motor;
步骤三：将电机转速参考值和电机当前运行转速值输入PI调节器后获得该时刻的电磁转矩参考值Te *(k)；Step 3: Input the motor speed reference value and the current running speed value of the motor into the PI regulator to obtain the electromagnetic torque reference value T e * (k) at that moment;
步骤四：将步骤三获得的电磁转矩参考值、根据在k-1时刻预测到的k时刻的d轴预测电流作为MTPA模块的输入，MTPA模块输出其工作时的q轴电流以及d轴电流。Step 4: The electromagnetic torque reference value obtained in step 3 and the predicted d-axis current at time k predicted at time k-1 are used as inputs of the MTPA module, and the MTPA module outputs the q-axis current and d-axis current during its operation.
进一步地，所述步骤一具体包括：Furthermore, the
S11：永磁同步电机电流方程为：S11: The current equation of the permanent magnet synchronous motor is:
公式(1)中id为d轴电流，i q为q轴电流；Rs为电阻；Ld为d轴磁导、Lq为q轴磁导；P为电机极对数；ud为d轴电压，uq为q轴电压；ωm为机械转速；φf为磁链；In formula (1), i d is the d-axis current, i q is the q-axis current; R s is the resistance; L d is the d-axis permeance, Lq is the q-axis permeance; P is the number of motor pole pairs; ud is the d-axis voltage, u q is the q-axis voltage; ω m is the mechanical speed; φ f is the flux linkage;
S12：将永磁同步电机电流方程离散化；得到永磁同步电机的电流离散模型如下式(2)：S12: Discretize the permanent magnet synchronous motor current equation; obtain the current discrete model of the permanent magnet synchronous motor as follows (2):
(2)式中，T为采样周期，k表示k个采样时刻；(2) In the formula, T is the sampling period, k represents k sampling moments;
S13：将公式(2)改写为状态空间模型得到如下式(3)的状态空间方程：S13: Rewrite formula (2) into a state space model to obtain the state space equation of formula (3):
x(k+1)＝Ax(k)+Bu(k)x(k+1)＝Ax(k)+Bu(k)
y(k)＝Cx(k) (3)y(k)＝Cx(k) (3)
(3)式中，
S14：永磁同步电机采用MTPA模式运行时轨迹为MTPA控制曲线，即d、q轴电流满足公式：
(4)式中，kid为当前d轴电流与d轴参考电流之
进一步地，步骤二中通过对价值函数分别进行对△ud和△uq求偏导数，即：Furthermore, in
从而得到当前k时刻的最优控制电压增量△ud和△uq；然后根据公式(5)获得k时刻最优电压，并将求得的该电压用于永磁同步电机控制；Thus, the optimal control voltage increments △u d and △u q at the current time k are obtained; then the optimal voltage at the time k is obtained according to formula (5), and the obtained voltage is used for permanent magnet synchronous motor control;
ud(k)＝ud(k-1)+△ud(k)u d (k)＝u d (k-1)+△u d (k)
uq(k)＝uq(k-1)+△uq(k) (5)；u q (k)=u q (k-1)+Δu q (k) (5);
将上式中获取的d、q轴电压带入公式(6)，得到k+1时刻的d轴电流idmiddle(k+1)，作为MTPA工作点求解的中间变量：Substituting the d-axis and q-axis voltages obtained in the above formula into formula (6), we can obtain the d-axis current i dmiddle (k+1) at
进一步地，步骤三具体为：Furthermore, step three is specifically as follows:
永磁同步电机速度公式如下：The speed formula of permanent magnet synchronous motor is as follows:
利用上式公式，将电机速度参考值和当前时刻电机的速度反馈值输入PI调节器并得到电机的电磁转矩参考值Te *(k)。By using the above formula, the motor speed reference value and the speed feedback value of the motor at the current moment are input into the PI regulator to obtain the electromagnetic torque reference value Te * (k) of the motor.
进一步地，将步骤三获得的电磁转矩参考值Te *(k)、步骤一中的d轴预测电流idpre(k+1)作为MTPA算法模块的输入求解电机MTPA控制时的工作点，具体如下：Furthermore, the electromagnetic torque reference value Te * (k) obtained in step 3 and the d-axis predicted current i dpre (k+1) in
S41:永磁同步电机电磁转矩方程如(8)所示，S41: The electromagnetic torque equation of the permanent magnet synchronous motor is shown in (8),
将电磁转矩Te *(k)、预测电流idmiddle(k)代入公式(8)，可以得到MTPA工作时的q轴电流：Substituting the electromagnetic torque Te * (k) and the predicted current i dmiddle (k) into formula (8), the q-axis current when MTPA is working can be obtained:
S42:由于当永磁同步电机采用MTPA模式运行时，其d、q轴电流满足下式(10)：S42: When the permanent magnet synchronous motor is operated in MTPA mode, its d-axis and q-axis currents satisfy the following equation (10):
因此将得到的中iqmtpa(k)带入公式(10)，即得到MTPA模板工作时的d轴工作电流，如下式(11)：Therefore, the obtained i qmtpa (k) is substituted into formula (10), and the d-axis working current of the MTPA template when working is obtained, which is as follows (11):
虽然本发明已以较佳实施例公开如上，但它们并不是用来限定本发明的，任何熟习此技艺者，在不脱离本发明之精神和范围内，自当可作各种变化或润饰，因此本发明的保护范围应当以本申请的权利要求保护范围所界定的为准。Although the present invention has been disclosed as above in terms of preferred embodiments, they are not intended to limit the present invention. Anyone skilled in the art can make various changes or modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection defined by the claims of this application.
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