CN106026803A

CN106026803A - Speed sensorless control method based on sliding-mode observer

Info

Publication number: CN106026803A
Application number: CN201610631269.9A
Authority: CN
Inventors: 张海刚; 张磊; 叶银忠; 徐兵; 王步来; 万衡; 华容; 卢建宁
Original assignee: Shanghai Institute of Technology
Current assignee: Shanghai Institute of Technology
Priority date: 2016-08-04
Filing date: 2016-08-04
Publication date: 2016-10-12

Abstract

The invention discloses a speed sensorless control method based on a sliding mode observer, which detects the position and speed of the motor rotor through a sliding mode observer that is easy to implement in engineering, and establishes the relationship between the sliding mode gain and the estimated counter electromotive force. Reduce system chattering, deduce the formula for calculating the rotation angle and speed, and build a permanent magnet synchronous motor model. The sliding mode observer involved can track the speed of the motor in a timely and accurate manner in the case of sudden changes in speed and load and corner changes. The invention has great research potential and application prospect in the field of sensorless control, provides key parameters for high-performance motor control and fault prediction, and has the characteristics of high control accuracy, good dynamic performance and strong robustness. In addition, It also has the advantages of low cost, simple control algorithm, high speed and precision of speed and position estimation.

Description

A Speed Sensorless Control Method Based on Sliding Mode Observer

技术领域technical field

本发明涉及无速度传感器测速技术领域，具体涉及一种基于滑模观测器的无速度传感器控制方法。The invention relates to the technical field of speed sensorless speed measurement, in particular to a speed sensorless control method based on a sliding mode observer.

背景技术Background technique

永磁同步电机(Permanent Magnet Synchronous Motor，简称PMSM)具有功率密度高、能量转换效率高、调速范围广、体积小、重量轻等优点，在工业、民用、军事等领域得到广泛的应用。Permanent Magnet Synchronous Motor (PMSM) has the advantages of high power density, high energy conversion efficiency, wide speed range, small size, light weight, etc., and has been widely used in industrial, civil, military and other fields.

永磁同步电机的控制需要获得电机转子的位置和速度信息，目前应用比较普遍的位置传感器包括光电编码器、旋转变压器等装置，而这些装置的使用不但增加了系统的体积和成本，降低了系统的可靠性，也限制了永磁同步电机在特殊环境下的应用，为解决机械传感器带来的诸多缺陷，无传感器控制技术的研究已成为国内外的研究热点，并取得了一定成果，但还存在许多问题。最重要的是目前还没有一种单一的无传感器技术能够适用于在各种运行条件下有效地控制电机。现有技术中，或适用于低速运行，或适用于高速运行，或受电机参数影响较大，或计算量很大、结构复杂，或稳定性不是很好。The control of the permanent magnet synchronous motor needs to obtain the position and speed information of the motor rotor. At present, the commonly used position sensors include photoelectric encoders, resolvers and other devices, and the use of these devices not only increases the size and cost of the system, but also reduces the system cost. The reliability of the sensorless control technology also limits the application of permanent magnet synchronous motors in special environments. In order to solve many defects caused by mechanical sensors, the research on sensorless control technology has become a research hotspot at home and abroad, and has achieved certain results. There are many problems. Most importantly, there is currently no single sensorless technology that can be applied to effectively control motors under various operating conditions. In the prior art, either it is suitable for low-speed operation, or it is suitable for high-speed operation, or it is greatly affected by the parameters of the motor, or it has a large amount of calculation, a complex structure, or poor stability.

当电机在中高速范围内运转时，基于滑模观测器的无传感器控制方法得到广泛的应用。这种方法首先通过构造滑模观测器首先观测电机的反电动势，然后从反电动势中直接或间接地估算出转子位置和速度，具有原理简单、稳定性好等特点。The sensorless control method based on the sliding mode observer is widely used when the motor is running in the middle and high speed range. This method first observes the back EMF of the motor by constructing a sliding mode observer, and then directly or indirectly estimates the rotor position and speed from the back EMF, which has the characteristics of simple principle and good stability.

发明内容Contents of the invention

为了克服现有的基于无速度传感器的永磁同步电机的转子角度、转速估计方法存在的原理复杂、计算量大以及慢动态特性使得整个系统的动态特性下降，甚至导致系统的不稳定问题，现在特别提出一种具有较高动态性能且易于工程实现的一种基于滑模观测器的无速度传感器控制方法。In order to overcome the existing speed sensor-based permanent magnet synchronous motor's rotor angle and rotational speed estimation method, the principle is complicated, the calculation amount is large, and the slow dynamic characteristics make the dynamic characteristics of the whole system decrease, and even lead to the instability of the system. Now In particular, a speed sensorless control method based on a sliding mode observer with high dynamic performance and easy engineering implementation is proposed.

为了达到上述发明目的，解决其技术问题所采用的技术方案如下：In order to achieve the above-mentioned purpose of the invention, the technical solution adopted to solve the technical problems is as follows:

一种基于滑模观测器的无速度传感器控制方法，包括以下步骤：A speed sensorless control method based on a sliding mode observer, comprising the following steps:

步骤1：选择d轴参考电流为0，交流永磁同步电机检测输出三相电流I_a、I_b和I_c；Step 1: Select the d-axis reference current is 0, the AC permanent magnet synchronous motor detects and outputs three-phase currents I _a , I _b and I _c ;

步骤2：三相电流I_a、I_b和I_c经过Clark变换，输出两相静止直角坐标系α-β下的两相定子电流i_α和i_β；Step 2: The three-phase currents I _a , I _b and I _c are transformed by Clark to output the two-phase stator currents i _α and i _{β in the two-phase stationary Cartesian coordinate system α-β} ;

步骤3：两相定子电流i_α和i_β经过Park变换，输出两相同步旋转坐标系d-q下的两相电流I_d和I_q；Step 3: The two-phase stator currents i _α and i _β undergo Park transformation, and output the two-phase currents I _d and I _q in the two-phase synchronous rotating coordinate system dq;

步骤4：逆变器输出的三相电压U_a、U_b和U_c经过Clark变换，输出两相静止直角坐标系α-β下的两相定子电压u_α和u_β；Step 4: The three-phase voltages U _a , U _b and U _c output by the inverter undergo Clark transformation, and output the two-phase stator voltages u _α and u _{β in the two-phase stationary Cartesian coordinate system α-β} ;

步骤5：将步骤2中所得的两相定子电流i_α和i_β与步骤4中所得的两相定子电压u_α和u_β一并输入滑模观测器进行估算处理，估算出转子转速的估计值和转子位置的估计值 Step 5: Input the two-phase stator currents i _α and i _β obtained in step 2 together with the two-phase stator voltages u _α and u _β obtained in step 4 into the sliding mode observer for estimation processing, and estimate the rotor speed value and an estimate of the rotor position

步骤6：将步骤5中估算出转子转速的估计值乘以一常数得到估算的转子转速n，并将估算的转子转速n与实际的转子转速n*进行作差，差值通过PI调节后输出q轴参考电流 Step 6: Apply the estimated value of the rotor speed estimated in Step 5 to Multiply by a constant to obtain the estimated rotor speed n, and make a difference between the estimated rotor speed n and the actual rotor speed n*, and the difference is adjusted by PI to output the q-axis reference current

步骤7：将q轴参考电流与步骤3中得到的电流I_q进行作差，差值通过PI调节后输出q轴参考电压 Step 7: Set the q-axis reference current Make a difference with the current I _q obtained in step 3, and output the q-axis reference voltage after the difference is adjusted by PI

步骤8：将d轴参考电流与步骤3中得到的电流I_d进行作差，差值通过PI调节后输出d轴参考电压 Step 8: Reference the d-axis to the current Make a difference with the current I _d obtained in step 3, and output the d-axis reference voltage after the difference is adjusted by PI

步骤9：将步骤7中输出的q轴参考电压和步骤8中输出的d轴参考电压经过Park反变换，输出两相静止直角坐标系α-β下的两相控制电压和 Step 9: Apply the q-axis reference voltage output in step 7 to and the d-axis reference voltage output in step 8 After Park inverse transformation, output the two-phase control voltage in the two-phase stationary Cartesian coordinate system α-β and

步骤10：将两相控制电压和进行空间矢量调制，输出PWM波形至逆变器，逆变器向永磁同步电机输入三相电压U_a、U_b和U_c，从而控制永磁同步电机。Step 10: Connect the two-phase control voltage and Perform space vector modulation, output PWM waveform to the inverter, and the inverter inputs three-phase voltages U _a , U _b and U _c to the permanent magnet synchronous motor to control the permanent magnet synchronous motor.

进一步的，在步骤5中，具体包括以下步骤：Further, in step 5, the following steps are specifically included:

步骤51：将步骤4中的两相定子电压u_α和u_β经过SMO优化算法计算后得到电流估算值和 Step 51: Calculate the two-phase stator voltage u _α and u _β in step 4 through the SMO optimization algorithm to obtain the current estimated value and

步骤52：将电流估算值和与步骤2中的两相定子电流i_α和i_β进行作差，得到αβ轴上的电流误差值和 Step 52: Convert the current estimate to and Make a difference with the two-phase stator currents i _α and i _β in step 2 to obtain the current error value on the αβ axis and

步骤53：将电流误差值和经过开关函数运算后得到反电动势e_α和e_β；Step 53: Convert the current error value to and After the switching function operation, the counter electromotive forces e _α and e _β are obtained;

步骤54：一方面，反电动势e_α和e_β传送回步骤51中，加入到SMO优化算法计算中；另一方面，反电动势e_α和e_β通过低通滤波器得到滑模观测器估算的反电动势估计值和 Step 54: On the one hand, the back electromotive force e _α and e _β are transmitted back to step 51 and added to the calculation of the SMO optimization algorithm; on the other hand, the back electromotive force e _α and e _β are estimated by the sliding mode observer through a low-pass filter Estimated value of back EMF and

步骤55：滑模观测器估算的反电动势估计值和通过转速估算得到转子转速的估计值 Step 55: Back EMF Estimated by Sliding Mode Observer and Estimation of rotor speed by speed estimation

步骤56：滑模观测器估算的反电动势估计值和通过位置估算得到转子位置未补偿前的估计值 Step 56: Back EMF Estimated by Sliding Mode Observer and The estimated value of the rotor position before compensation is obtained by position estimation

步骤57：通过对相位进行滞后补偿，得出相位补偿量 Step 57: Obtain the amount of phase compensation by performing lag compensation on the phase

步骤58：将步骤56中的转子位置未补偿前的估计值和步骤57中的相位补偿量进行求和，得到转子位置的估计值 Step 58: The estimated value of the rotor position in step 56 before compensation and the amount of phase compensation in step 57 are summed to obtain an estimate of the rotor position

作为一实施例，在步骤51中，具体包括以下步骤：As an embodiment, in step 51, the following steps are specifically included:

首先，建立交流永磁同步电机在两相静止直角坐标系α-β中的数学模型：First, establish the mathematical model of the AC permanent magnet synchronous motor in the two-phase stationary Cartesian coordinate system α-β:

$\overset{\cdot &Center Dot;}{{i i}_{α α}} = = - - \frac{{R R}_{s the s}}{{L L}_{s the s}} {i i}_{α α} - - \frac{11}{{L L}_{s the s}} {e e}_{α α} + + \frac{{u u}_{α α}}{{L L}_{s the s}} - - - - - - ((11))$

$\overset{\cdot &Center Dot;}{{i i}_{β β}} = = - - \frac{{R R}_{s the s}}{{L L}_{s the s}} {i i}_{β β} - - \frac{11}{{L L}_{s the s}} {e e}_{β β} + + \frac{{u u}_{β β}}{{L L}_{s the s}} - - - - - - ((22))$

其中，为电流i在α轴上的电流值i_α的导数，为电流i在β轴上的电流值i_β的导数，R_S为定子绕组电阻，Ls为等效电感，e_α为滑模观测器在α轴上的反电动势，e_β为滑模观测器在β轴上的反电动势，u_α为电压U在α轴上的电压值，u_β为电压U在β轴上的电压值；in, is the derivative of the current value i _α of the current i on the α axis, is the derivative of the current value i _β of the current i on the β axis, R _S is the stator winding resistance, Ls is the equivalent inductance, e _α is the back electromotive force of the sliding mode observer on the α axis, and e _β is the sliding mode observer The counter electromotive force on the β axis, u _α is the voltage value of the voltage U on the α axis, and u _β is the voltage value of the voltage U on the β axis;

其次，代入反电动势方程：Second, substitute into the back EMF equation:

e_α＝-ψ_fω_rsinθ (3)e _α ＝-ψ _f ω _r sinθ (3)

e_β＝ψ_fω_rcosθ (4)e _β = ψ _f ω _r cosθ (4)

其中，ψ_f为转子上永磁体产生的磁链，ω_r为同步转速，θ为转子角位置；Among them, ψ _f is the flux linkage generated by the permanent magnet on the rotor, ω _r is the synchronous speed, and θ is the angular position of the rotor;

再者，交流永磁同步电机在两相静止直角坐标系α-β中的SMO优化计算方程为：Furthermore, the SMO optimization calculation equation of the AC permanent magnet synchronous motor in the two-phase stationary Cartesian coordinate system α-β is:

$\overset{\cdot &Center Dot;}{\overset{^^}{{i i}_{α α}}} = = - - \frac{{R R}_{s the s}}{{L L}_{s the s}} \overset{^^}{{i i}_{α α}} + + \frac{{u u}_{α α}}{{L L}_{s the s}} - - \frac{k k}{{L L}_{s the s}} s the s i i g g n no ((\overset{^^}{{i i}_{α α}} - - {i i}_{α α})) - - - - - - ((55))$

$\overset{\cdot \cdot}{\overset{^^}{{i i}_{β β}}} = = - - \frac{{R R}_{s the s}}{{L L}_{s the s}} \overset{^^}{{i i}_{β β}} + + \frac{{u u}_{β β}}{{L L}_{s the s}} - - \frac{k k}{{L L}_{s the s}} s the s i i g g n no ((\overset{^^}{{i i}_{β β}} - - {i i}_{β β})) - - - - - - ((66))$

其中，分别为i_α、i_β的估算值，k为滑模切换增益；in, are the estimated values of i _α and i _β respectively, and k is the sliding mode switching gain;

最后，由上述可得电流估计误差方程：Finally, the current estimation error equation can be obtained from the above:

$\overset{\cdot &Center Dot;}{\overset{~ ~}{{i i}_{α α}}} = = - - \frac{{R R}_{s the s}}{{L L}_{s the s}} \overset{~ ~}{{i i}_{α α}} + + \frac{{e e}_{α α}}{{L L}_{s the s}} - - \frac{k k}{{L L}_{s the s}} s the s i i g g n no ((\overset{~ ~}{{i i}_{α α}})) - - - - - - ((77))$

$\overset{\cdot &Center Dot;}{\overset{~ ~}{{i i}_{β β}}} = = - - \frac{{R R}_{s the s}}{{L L}_{s the s}} \overset{~ ~}{{i i}_{β β}} + + \frac{{e e}_{β β}}{{L L}_{s the s}} - - \frac{k k}{{L L}_{s the s}} s the s i i g g n no ((\overset{~ ~}{{i i}_{β β}})) - - - - - - ((88))$

其中,为α轴上的电流误差值，为β轴上的电流误差值。in, is the current error value on the α axis, is the current error value on the β axis.

作为一实施例，在步骤52中，电流误差值和的计算方程为：As an example, in step 52, the current error value and The calculation equation is:

$\overset{~ ~}{{i i}_{α α}} = = {\overset{^^}{i i}}_{α α} - - {i i}_{α α} - - - - - - ((99))$

$\overset{~ ~}{{i i}_{β β}} = = {\overset{^^}{i i}}_{β β} - - {i i}_{β β} - - - - - - ((1010))$

其中，和i_α为α轴上的电流误差值、电流估算值和电流值，和i_β为β轴上的电流误差值、电流估算值和电流值。in, and i _α is the current error value, current estimation value and current value on the α axis, and i _β are the current error value, current estimated value and current value on the β axis.

作为一实施例，在步骤53中，反电动势e_α和e_β的计算过程分别包括以下步骤：As an embodiment, in step 53, the calculation process of counter electromotive force e _α and e _β includes the following steps respectively:

首先，选取sign开关函数进行开关函数运算，即：First, select the sign switch function to perform the switch function operation, namely:

$s the s i i g g n no = = \{\begin{matrix} 11 & x x > > 00 \\ - - 11 & x x < < 00 \end{matrix} - - - - - - ((1111))$

其次，选取李雅普诺夫函数：Second, choose the Lyapunov function:

$V V = = \frac{11}{22} {\overset{~ ~}{{i i}_{α α}}}^{22} + + \frac{11}{22} {\overset{~ ~}{{i i}_{β β}}}^{22} - - - - - - ((1212))$

对V求导，当k>max(|e_α|,|e_β|)时，则V＞0，由李雅普诺夫稳定性定理知，电流滑模观测器是稳定的，选取电流误差为滑模切换面，则当进入滑动模态时，有和时，Deriving V, when k>max(|e _α |,|e _β |), then V>0, from the Lyapunov stability theorem, the current sliding mode observer is stable, and the current error is selected as the sliding mode switching surface, then when entering the sliding mode, there is and hour,

${e e}_{α α} = = k k s the s i i g g n no ((\overset{~ ~}{{i i}_{α α}})) - - - - - - ((1313))$

${e e}_{β β} = = k k s the s i i g g n no ((\overset{~ ~}{{i i}_{β β}})) - - - - - - ((1414))$

其中，e_α和e_β为滑模观测器的反电动势，为α轴上的电流误差值，为β轴上的电流误差值，k为滑模切换增益。Among them, e _α and e _β are the back electromotive force of the sliding mode observer, is the current error value on the α axis, is the current error value on the β axis, and k is the sliding mode switching gain.

作为一实施例，在步骤54中，反电动势估计值和的计算过程包括：As an example, in step 54, the back electromotive force estimated value and The calculation process includes:

使用低通滤波器，将不连续的开关信号转换为等效的连续信号，相应计算公式如下：Use a low-pass filter to convert the discontinuous switching signal into an equivalent continuous signal, and the corresponding calculation formula is as follows:

${\overset{^^}{e e}}_{α α} = = \frac{{ω ω}_{c c}}{s the s + + {ω ω}_{c c}} {e e}_{α α} - - - - - - ((1515))$

${\overset{^^}{e e}}_{β β} = = \frac{{ω ω}_{c c}}{s the s + + {ω ω}_{c c}} {e e}_{β β} - - - - - - ((1616))$

其中，和为滑模观测器估算的反电动势估计值，ω_c为低通滤波器的截止频率，s为拉普拉斯算子，e_α和e_β为滑模观测器的反电动势。in, and is the estimated value of back electromotive force estimated by the sliding mode observer, ω _c is the cutoff frequency of the low-pass filter, s is the Laplacian operator, e _α and e _β are the back electromotive force of the sliding mode observer.

作为一实施例，在步骤55中，转子转速的估计值通过以下公式求得：As an embodiment, in step 55, the estimated value of the rotor speed is obtained by the following formula:

$\overset{^^}{ω ω} = = \frac{\sqrt{{\overset{^^}{{e e}_{α α}}}^{22} + + {\overset{^^}{{e e}_{β β}}}^{22}}}{{ψ ψ}_{f f}} - - - - - - ((1717))$

其中，为转子转速估算值，和为滑模观测器估算的反电动势，ψ_f为转子上永磁体产生的磁链。in, is the estimated rotor speed, and is the back electromotive force estimated by the sliding mode observer, and ψ _f is the flux linkage generated by the permanent magnet on the rotor.

作为一实施例，在步骤56中，转子位置的估计值通过以下公式求得：As an embodiment, in step 56, the estimated value of the rotor position is obtained by the following formula:

$\overset{^^}{{θ θ}_{c c}} = = - - a a r r c c t t a a n no ((\frac{\overset{^^}{{e e}_{α α}}}{\overset{^^}{{e e}_{β β}}})) - - - - - - ((1818))$

其中，为转子位置的估算值，和为滑模观测器估算的反电动势。in, is the estimated value of the rotor position, and Estimated back EMF for the sliding mode observer.

作为一实施例，在步骤57中，由于低通滤波器的使用，其相位具有一定的滞后性，须对相位进行滞后补偿，其相位补偿量为：As an embodiment, in step 57, due to the use of the low-pass filter, its phase has a certain lag, and the phase lag compensation must be performed, and the phase compensation amount is:

$Δ Δ \overset{^^}{θ θ} = = - - a a r r c c t t a a n no ((\frac{ω ω}{{ω ω}_{c c}})) - - - - - - ((1919))$

其中，是相位补偿量，ω为稳态时转速，ω_c为低通滤波器的截止频率。in, Is the amount of phase compensation, ω is the speed at steady state, and ω _c is the cut-off frequency of the low-pass filter.

本发明由于采用以上技术方案，使之与现有技术相比，具有以下的优点和积极效果：Compared with the prior art, the present invention has the following advantages and positive effects due to the adoption of the above technical solutions:

1、本发明一种基于滑模观测器的无速度传感器控制方法对系统扰动、参数摄动等不确定性因素具有鲁棒性，因此可以更好的实现永磁同步电机的无传感器控制；1. A speed sensorless control method based on a sliding mode observer of the present invention is robust to uncertain factors such as system disturbances and parameter perturbations, so the sensorless control of permanent magnet synchronous motors can be better realized;

2、本发明所设计的滑模观测器在转速突变以及负载突变的情况下，都能及时并准确的跟踪电动机的转速和转角变化，具有控制准确性高，动态性能好，鲁棒性强的特点，而且所设计的滑模观测器无论在硬件和软件上实施起来都较为方便，具有一定的实用性；2. The sliding mode observer designed by the present invention can timely and accurately track the change of the rotational speed and rotation angle of the motor in the case of sudden changes in the speed and load, and has the advantages of high control accuracy, good dynamic performance and strong robustness. characteristics, and the designed sliding mode observer is more convenient to implement both in hardware and software, and has certain practicability;

3、本发明通过采用滑模观测器实现状态估计，显著提高了转子位置与速度的估计精确度；3. The present invention significantly improves the estimation accuracy of rotor position and speed by using a sliding mode observer to realize state estimation;

4、本发明具有低成本、控制算法简单、转速及位置的估算速度及精度高等优点。4. The present invention has the advantages of low cost, simple control algorithm, high estimation speed and precision of rotational speed and position.

附图说明Description of drawings

为了更清楚地说明本发明实施例的技术方案，下面将对实施例描述中所需要使用的附图作简单的介绍。显而易见，下面描述中的附图仅仅是本发明的一些实施例，对于本领域技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。附图中：In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings that need to be used in the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention, and those skilled in the art can also obtain other drawings according to these drawings without creative work. In the attached picture:

图1是本发明一种基于滑模观测器的无速度传感器控制方法中滑模变结构控制系统的运动过程图；Fig. 1 is a motion process diagram of the sliding mode variable structure control system in a kind of speed sensorless control method based on the sliding mode observer of the present invention;

图2是本发明一种基于滑模观测器的无速度传感器控制方法中滑模观测器结构图；Fig. 2 is a structural diagram of the sliding mode observer in a speed sensorless control method based on the sliding mode observer of the present invention;

图3是本发明一种基于滑模观测器的无速度传感器控制方法中滑模观测器封装子模块图；Fig. 3 is a kind of sliding mode observer package submodule diagram in the speed sensorless control method based on sliding mode observer of the present invention;

图4是本发明一种基于滑模观测器的无速度传感器控制方法的整体流程图；Fig. 4 is the overall flowchart of a kind of speed sensorless control method based on sliding mode observer of the present invention;

图5是本发明一种基于滑模观测器的无速度传感器控制方法中的步骤5的具体流程图；Fig. 5 is the specific flowchart of step 5 in a kind of speed sensorless control method based on sliding mode observer of the present invention;

图6是本发明一种基于滑模观测器的无速度传感器控制方法所对应的系统仿真图；Fig. 6 is a system simulation diagram corresponding to a speed sensorless control method based on a sliding mode observer in the present invention;

图7是本发明一种基于滑模观测器的无速度传感器控制方法中转速突变转速波形图；Fig. 7 is a kind of speed sensorless control method based on the sliding mode observer of the present invention, the speed sudden change speed waveform diagram;

图8是本发明一种基于滑模观测器的无速度传感器控制方法中转速突变转角波形图；Fig. 8 is a waveform diagram of a sudden change in rotational speed in a speed sensorless control method based on a sliding mode observer of the present invention;

图9是本发明一种基于滑模观测器的无速度传感器控制方法中转矩突变转速波形图；Fig. 9 is a torque mutation speed waveform diagram in a speed sensorless control method based on a sliding mode observer of the present invention;

图10是本发明一种基于滑模观测器的无速度传感器控制方法中转矩突变转角波形图。Fig. 10 is a waveform diagram of a torque sudden change rotation angle in a speed sensorless control method based on a sliding mode observer according to the present invention.

具体实施方式detailed description

以下将结合本发明的附图，对本发明实施例中的技术方案进行清楚、完整的描述和讨论，显然，这里所描述的仅仅是本发明的一部分实例，并不是全部的实例，基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动的前提下所获得的所有其他实施例，都属于本发明的保护范围。The technical solutions in the embodiments of the present invention will be clearly and completely described and discussed below in conjunction with the accompanying drawings of the present invention. Obviously, what is described here is only a part of the examples of the present invention, not all examples. Based on 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.

参见图1，本发明专利中的现在考虑一般的情况，存在一个切换面s(x)＝s(x₁,x₂,···,x_n)＝0，它将x＝f(x)(x∈Rⁿ)这个系统的状态空间分成上下两个部分s>0和s<0。如图1所示，在切换面上有3种情况的运动点。点A为通常点，当到达切换面s＝0附近时，运动点穿越点A而过；点B为起始点，当到达切换面s＝0附近时，运动点从切换面两边离开点B；点C为终止点，当到达切换面s＝0附近时，运动点从切换面两边趋近于点C。Referring to Fig. 1, in the patent of the present invention, now considering the general situation, there is a switching surface s(x)=s(x ₁ ,x ₂ ,...,x _n )=0, which will x=f(x) (x∈R ⁿ ) The state space of this system is divided into upper and lower parts s>0 and s<0. As shown in Figure 1, there are three situations of motion points on the switching surface. Point A is a common point, and when it reaches near the switching surface s=0, the moving point passes through point A; Point B is the starting point, and when it reaches near the switching surface s=0, the moving point leaves point B from both sides of the switching surface; Point C is the end point, and when it reaches near the switching surface s=0, the moving point approaches point C from both sides of the switching surface.

在滑模变结构中，终止点有着特殊的意义，而起始点与通常点基本没有什么意义。当运动点在切换面上的某一段区域内都是终止点的时候，且一旦趋向于该区域时就会在此区域内运动。此时，称此区域为“滑动模态”区即“滑模”区，系统在此区域的运动叫做“滑模运动”。In the sliding mode variable structure, the end point has a special meaning, but the start point and the usual point basically have no meaning. When the moving point is the end point in a certain area on the switching surface, and once it tends to this area, it will move in this area. At this time, this area is called the "sliding mode" area, that is, the "sliding mode" area, and the movement of the system in this area is called "sliding mode motion".

参考图4，本发明公开了一种基于滑模观测器的无速度传感器控制方法，包括以下步骤：With reference to Fig. 4, the present invention discloses a kind of speed sensorless control method based on sliding mode observer, comprises the following steps:

步骤5：将步骤2中所得的两相定子电流i_α和i_β与步骤4中所得的两相定子电压u_α和u_β一并输入滑模观测器进行估算处理，估算出转子转速的估计值和转子位置的估计值如图3所示；Step 5: Input the two-phase stator currents i _α and i _β obtained in step 2 together with the two-phase stator voltages u _α and u _β obtained in step 4 into the sliding mode observer for estimation processing, and estimate the rotor speed value and an estimate of the rotor position As shown in Figure 3;

在步骤2中，将三相电流I_a、I_b和I_c经过Clark变换，输出两相静止直角坐标系α-β下的两相定子电流i_α和i_β具体涉及的换算公式如下：In step 2, the three-phase currents I _a , I _b and I _c are subjected to Clark transformation, and the two-phase stator currents i _α and i _β in the two-phase stationary Cartesian coordinate system α-β are output. The specific conversion formulas involved are as follows:

$[\begin{matrix} {i i}_{α α} \\ {i i}_{β β} \end{matrix}] = = \frac{22}{33} [\begin{matrix} 11 & - - 11 / / 22 & - - 11 / / 22 \\ 00 & \sqrt{33} / / 22 & - - \sqrt{33} / / 22 \end{matrix}] [\begin{matrix} {i i}_{a a} \\ {i i}_{b b} \\ {i i}_{c c} \end{matrix}]$

在步骤3中，将两相定子电流i_α和i_β经过Park变换，输出两相同步旋转坐标系d-q下的两相电流I_d和I_q具体涉及的换算公式如下：In step 3, the two-phase stator currents i _α and i _β are transformed by Park to output the two-phase currents I _d and I _q in the two-phase synchronous rotating coordinate system dq. The specific conversion formulas involved are as follows:

$[\begin{matrix} {I I}_{d d} \\ {I I}_{q q} \end{matrix}] = = [\begin{matrix} cos cos \overset{^^}{θ θ} & sin sin \overset{^^}{θ θ} \\ - - sin sin \overset{^^}{θ θ} & cos cos \overset{^^}{θ θ} \end{matrix}] [\begin{matrix} {i i}_{α α} \\ {i i}_{β β} \end{matrix}]$

其中，为估算的转子角。in, is the estimated rotor angle.

在步骤4中，将逆变器输出的三相电压U_a、U_b和U_c经过Clark变换，输出两相静止直角坐标系α-β下的两相定子电压u_α和u_β具体涉及的换算公式如下：In step 4, the three-phase voltages U _a , U _b and U _c output by the inverter are transformed by Clark, and the two-phase stator voltages u _α and u _β in the two-phase stationary Cartesian coordinate system α-β are output. The conversion formula is as follows:

$[\begin{matrix} {u u}_{α α} \\ {u u}_{β β} \end{matrix}] = = \frac{22}{33} [\begin{matrix} 11 & - - 11 / / 22 & - - 11 / / 22 \\ 00 & \sqrt{33} / / 22 & - - \sqrt{33} / / 22 \end{matrix}] [\begin{matrix} {U u}_{a a} \\ {U u}_{b b} \\ {U u}_{c c} \end{matrix}]$

进一步的，结合图2和图5，在步骤5中，具体包括以下步骤：Further, in conjunction with Fig. 2 and Fig. 5, in step 5, specifically include the following steps:

步骤51：将步骤4中的两相定子电压u_α和u_β经过SMO(Sliding modeobserver，滑模观测器)优化算法计算后得到电流估算值和 Step 51: Calculate the two-phase stator voltage u _α and u _β in step 4 through the SMO (Sliding mode observer, sliding mode observer) optimization algorithm to obtain the estimated current value and

e_α＝-ψ_fω_rsinθ (3)e _α ＝-ψ _f ω _r sinθ (3)

e_β＝ψ_fω_rcosθ (4)e _β = ψ _f ω _r cosθ (4)

$\overset{\cdot \cdot}{\overset{^^}{{i i}_{α α}}} = = - - \frac{{R R}_{s the s}}{{L L}_{s the s}} \overset{^^}{{i i}_{α α}} + + \frac{{u u}_{α α}}{{L L}_{s the s}} - - \frac{k k}{{L L}_{s the s}} s the s i i g g n no ((\overset{^^}{{i i}_{α α}} - - {i i}_{α α})) - - - - - - ((55))$

$\overset{\cdot \cdot}{\overset{~ ~}{{i i}_{β β}}} = = - - \frac{{R R}_{s the s}}{{L L}_{s the s}} \overset{~ ~}{{i i}_{β β}} + + \frac{{e e}_{β β}}{{L L}_{s the s}} - - \frac{k k}{{L L}_{s the s}} s the s i i g g n no ((\overset{~ ~}{{i i}_{β β}})) - - - - - - ((88))$

首先，选取sign开关函数进行开关函数运算，如图4所示，即：First, select the sign switch function to perform the switch function operation, as shown in Figure 4, namely:

其次，选取李雅普诺夫函数：Second, choose the Lyapunov function:

在步骤6中，步骤5中估算出转子转速的估计值与估算的转子转速n之间的关系为：In step 6, the estimate of the rotor speed was estimated in step 5 The relationship between and the estimated rotor speed n is:

$n no = = \frac{6060 \overset{^^}{ω ω}}{22 π π} = = 9.55 9.55 \overset{^^}{ω ω}$

即，所述常数为9.55。That is, the constant is 9.55.

在步骤9中，将步骤7中输出的q轴参考电压和步骤8中输出的d轴参考电压经过Park反变换，输出两相静止直角坐标系α-β下的两相控制电压和具体涉及以下换算公式：In step 9, the q-axis reference voltage output in step 7 and the d-axis reference voltage output in step 8 After Park inverse transformation, output the two-phase control voltage in the two-phase stationary Cartesian coordinate system α-β and Specifically, the following conversion formulas are involved:

$[\begin{matrix} {u u}_{α α}^{* *} \\ {u u}_{β β}^{* *} \end{matrix}] = = [\begin{matrix} cos cos \overset{^^}{θ θ} & - - sin sin \overset{^^}{θ θ} \\ sin sin \overset{^^}{θ θ} & cos cos \overset{^^}{θ θ} \end{matrix}] [\begin{matrix} {u u}_{d d}^{* *} \\ {u u}_{q q}^{* *} \end{matrix}]$

其中，为估算的转子角。in, is the estimated rotor angle.

为了验证本发明的有效性，构建了系统仿真图，如图6所示，本文使用的电动机参数见表1，通过仿真实现了实验结果。In order to verify the effectiveness of the present invention, a system simulation diagram is constructed, as shown in Figure 6, the motor parameters used in this paper are shown in Table 1, and the experimental results are realized through simulation.

参数含义Parameter meaning 取值value 极对数pnumber of pole pairs p 44 定子电阻Rs/ΩStator resistance Rs/Ω 2.87502.8750 电感Ld和Lq/mHInductance Ld and Lq/mH 8.58.5 转动惯量J/(kg.m2)Moment of inertia J/(kg.m2) 0.0050.005 直流母线电压VDC/VDC bus voltage VDC/V 500500 磁链/WbMagnetic link/Wb 0.1750.175

表1永磁同步电机驱动系统主要参数Table 1 Main parameters of permanent magnet synchronous motor drive system

图7、图8、图9、图10表明了该发明专利所设计的滑模观测器在转速突变以及负载突变的情况下，都能及时并准确的跟踪电动机的转速和转角变化，具有控制准确性高，动态性能好，鲁棒性强的特点，而且所设计的滑模观测器无论在硬件和软件上实施起来都较为方便，具有一定的实用性。Figure 7, Figure 8, Figure 9, and Figure 10 show that the sliding mode observer designed in this invention patent can track the speed and rotation angle changes of the motor in a timely and accurate manner in the case of sudden changes in speed and load, and has accurate control High performance, good dynamic performance, and strong robustness, and the designed sliding mode observer is more convenient to implement in both hardware and software, and has certain practicability.

以上所述，仅为本发明较佳的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，可轻易想到的变化或替换，都应涵盖在本发明的保护范围之内。因此，本发明的保护范围应该以权利要求的保护范围为准。The above is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed in the present invention can easily think of changes or Replacement should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the protection scope of the claims.

Claims

1. A speed-sensor-free control method based on a sliding-mode observer is characterized by comprising the following steps:

step 1: selecting a d-axis reference current0, the alternating current permanent magnet synchronous motor detects and outputs three-phase current I_a、I_bAnd I_c；

Step 2: three-phase current I_a、I_bAnd I_cAfter Clark conversion, outputTwo-phase stator current i under two-phase static rectangular coordinate system α - β_αAnd i_β；

And step 3: two-phase stator current i_αAnd i_βAfter Park conversion, two-phase current I under a two-phase synchronous rotating coordinate system d-q is output_dAnd I_q；

And 4, step 4: three-phase voltage U output by inverter_a、U_bAnd U_cThe two-phase stator voltage u under a two-phase static rectangular coordinate system α - β is output through Clark conversion_αAnd u_β；

And 5: the two-phase stator current i obtained in the step 2 is processed_αAnd i_βAnd the two-phase stator voltage u obtained in the step 4_αAnd u_βInputting the data into a sliding mode observer for estimation processing to estimate the estimated value of the rotor rotating speedAnd an estimate of rotor position

Step 6: estimating the rotor speed in step 5Multiplying a constant to obtain an estimated rotor speed n, subtracting the estimated rotor speed n from the actual rotor speed n, and outputting q-axis reference current after the difference value is regulated by PI

And 7: reference q-axis currentWith the current I obtained in step 3_qPerforming difference making, and outputting q-axis reference voltage after the difference value is regulated by PI

And 8: reference d-axis currentWith the current I obtained in step 3_dPerforming difference making, and outputting d-axis reference voltage after the difference value is regulated by PI

And step 9: the q-axis reference voltage output in the step 7 is comparedAnd the d-axis reference voltage output in step 8After Park inverse transformation, two-phase control voltage under a two-phase static rectangular coordinate system α - β is outputAnd

step 10: two phases of control voltageAndspace vector modulation is carried out, PWM waveform is output to an inverter, and the inverter inputs three-phase voltage U to the permanent magnet synchronous motor_a、U_bAnd U_cThereby controlling the permanent magnet synchronous motor.

2. The method for controlling the non-speed sensor based on the sliding-mode observer according to claim 1, wherein in the step 5, the method specifically comprises the following steps:

step 51: the two-phase stator voltage u in the step 4 is measured_αAnd u_βObtaining a current estimated value after calculation of an SMO optimization algorithmAnd

step 52: estimating the currentAndwith the two-phase stator current i in step 2_αAnd i_βPerforming difference to obtain αβ axis current error valueAnd

step 53: error value of currentAndobtaining back electromotive force e after the operation of a switching function_αAnd e_β；

Step 54: on the one hand, back electromotive force e_αAnd e_βTransmitting back to step 51, and adding into calculation of the SMO optimization algorithm; on the other hand, back electromotive force e_αAnd e_βObtaining the back electromotive force estimated value of the sliding mode observer through a low-pass filterAnd

step 55: back electromotive force estimated value estimated by sliding-mode observerAndobtaining an estimate of rotor speed by speed estimation

Step 56: back electromotive force estimated value estimated by sliding-mode observerAndobtaining estimated value before rotor position uncompensation through position estimation

And 57: obtaining the phase compensation quantity by performing lag compensation on the phase

Step 58: the rotor position estimate in step 56 before uncompensationAnd the amount of phase compensation in step 57Summing to obtain the estimated value of the rotor position

3. The method for controlling the non-speed sensor based on the sliding-mode observer according to claim 2, wherein in step 51, the method specifically comprises the following steps:

firstly, establishing a mathematical model of the alternating current permanent magnet synchronous motor in a two-phase static rectangular coordinate system alpha-beta:

\overset{\cdot}{i_{α}} = - \frac{R_{s}}{L_{s}} i_{α} - \frac{1}{L_{s}} e_{α} + \frac{u_{α}}{L_{s}} - - - (1)

\overset{\cdot}{i_{β}} = - \frac{R_{s}}{L_{s}} i_{β} - \frac{1}{L_{s}} e_{β} + \frac{u_{β}}{L_{s}} - - - (2)

wherein,is the current value i of the current i on the α axis_αThe derivative of (a) of (b),is the current value i of the current i on the β axis_βDerivative of (A), R_SIs stator winding resistance, Ls is equivalent inductance, e_αBack EMF on α axis for sliding mode observer, e_βFor the back EMF of the sliding-mode observer on the β axis_αIs the voltage value of voltage U on α axis_βIs the voltage value of the voltage U on the β axis;

next, the back emf equation is substituted:

e_α＝-ψ_fω_rsinθ (3)

e_β＝ψ_fω_rcosθ (4)

wherein psi_fFlux linkage, omega, produced for permanent magnets on the rotor_rFor synchronous speed, θ is the rotor angular position;

furthermore, an SMO optimization calculation equation of the alternating current permanent magnet synchronous motor in a two-phase static rectangular coordinate system alpha-beta is as follows:

\overset{\cdot}{\hat{i_{α}}} = - \frac{R_{s}}{L_{s}} \hat{i_{α}} + \frac{u_{α}}{L_{s}} - \frac{k}{L_{s}} s i g n (\hat{i_{α}} - i_{α}) - - - (5)

\overset{\cdot}{\hat{i_{β}}} = - \frac{R_{s}}{L_{s}} \hat{i_{β}} + \frac{u_{β}}{L_{s}} - \frac{k}{L_{s}} s i g n (\hat{i_{β}} - i_{β}) - - - (6)

wherein,are respectively asK is the sliding mode switching gain;

finally, from the above available current estimation error equation:

\overset{\cdot}{\tilde{i_{α}}} = - \frac{R_{s}}{L_{s}} \tilde{i_{α}} + \frac{e_{α}}{L_{s}} - \frac{k}{L_{s}} s i g n (\tilde{i_{α}}) - - - (7)

\overset{\cdot}{\tilde{i_{β}}} = - \frac{R_{s}}{L_{s}} \tilde{i_{β}} + \frac{e_{β}}{L_{s}} - \frac{k}{L_{s}} s i g n (\tilde{i_{β}}) - - - (8)

wherein,is the current error value on the α axis,is the current error value on the β axis.

4. The sliding-mode observer-based method for sensorless control according to claim 2, wherein in step 52, the current error valueAndthe calculation equation of (a) is:

\tilde{i_{α}} = \hat{i_{α}} - i_{α} - - - (9)

\tilde{i_{β}} = {\hat{i}}_{β} - i_{β} - - - (10)

wherein,and i_αFor the current error value on axis α, the current estimate value and the current value,and i_βCurrent error value, current estimate value and current value on axis β.

5. The sliding-mode observer-based speed sensorless control method according to claim 2, wherein in step 53, back electromotive force e_αAnd e_βIs calculated byRespectively comprises the following steps:

firstly, a sign switching function is selected to perform switching function operation, namely:

s i g n = \{\begin{matrix} 1 & x > 0 \\ - 1 & x < 0 \end{matrix} - - - (11)

secondly, selecting a Lyapunov function:

V = \frac{1}{2} {\tilde{i_{α}}}^{2} + \frac{1}{2} {\tilde{i_{β}}}^{2} - - - (12)

derivative of V when k>max(|e_α|,|e_βIf | thenV is more than 0, the current sliding mode observer is stable according to the Lyapunov stability theorem, the current error is selected as the sliding mode switching surface, and when the sliding mode enters, the current sliding mode observer hasAndwhen the temperature of the water is higher than the set temperature,

e_{α} = k s i g n (\tilde{i_{α}}) - - - (13)

e_{β} = k s i g n (\tilde{i_{β}}) - - - (14)

wherein e is_αAnd e_βIs the back electromotive force of the sliding-mode observer,is the current error value on the α axis,for the current error value on the β axis, k is the sliding mode switching gain.

6. The sliding-mode observer-based sensorless control method of claim 2, wherein in step 54, the back electromotive force estimate isAndthe calculation process of (2) includes:

using a low-pass filter, the discontinuous switching signal is converted into an equivalent continuous signal, and the corresponding calculation formula is as follows:

{\hat{e}}_{α} = \frac{ω_{c}}{s + ω_{c}} e_{α} - - - (15)

{\hat{e}}_{β} = \frac{ω_{c}}{s + ω_{c}} e_{β} - - - (16)

wherein,andestimated back electromotive force, ω, for sliding mode observer estimation_cIs the cut-off frequency of the low-pass filter, s is the Laplace operator, e_αAnd e_βIs the back electromotive force of the sliding mode observer.

7. The sliding-mode observer-based sensorless control method according to claim 2, wherein in step 55, the estimated value of the rotor speed is obtained by the following formula:

\hat{ω} = \frac{\sqrt{{\hat{e_{α}}}^{2} + {\hat{e_{β}}}^{2}}}{ψ_{f}} - - - (17)

wherein,in order to estimate the rotational speed of the rotor,andback electromotive force, psi, estimated for sliding mode observer_fThe flux linkage generated by the permanent magnets on the rotor.

8. The method of claim 2 for the speed sensorless control based on the sliding-mode observer,

characterized in that, in step 56, the estimated value of the rotor position is obtained by the following formula:

\hat{θ_{c}} = - a r c t a n (\frac{\hat{e_{α}}}{\hat{e_{β}}}) - - - (18)

wherein,for the estimation of the position of the rotor,andback emf estimated for a sliding mode observer.

9. The method for controlling a sensor without speed based on a sliding-mode observer according to claim 2, wherein in step 57, the phase has a certain hysteresis due to the use of a low-pass filter, and the phase is required to be compensated for, and the phase compensation amount is:

Δ \hat{θ} = - a r c t a n (\frac{ω}{ω_{c}}) - - - (19)

wherein,is the phase compensation quantity, omega is the rotation speed at steady state, omega_cThe cut-off frequency of the low-pass filter.