WO2022100371A1 - 一种新型双滑模观测器spmsm无传感器复合控制方法 - Google Patents

一种新型双滑模观测器spmsm无传感器复合控制方法 Download PDF

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WO2022100371A1
WO2022100371A1 PCT/CN2021/124411 CN2021124411W WO2022100371A1 WO 2022100371 A1 WO2022100371 A1 WO 2022100371A1 CN 2021124411 W CN2021124411 W CN 2021124411W WO 2022100371 A1 WO2022100371 A1 WO 2022100371A1
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sliding mode
current
load
controller
permanent magnet
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PCT/CN2021/124411
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English (en)
French (fr)
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彭思齐
蒋雨函
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湘潭大学
佛山湘潭大学绿色智造研究院
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Publication of WO2022100371A1 publication Critical patent/WO2022100371A1/zh
Priority to US17/829,094 priority Critical patent/US11522480B2/en

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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—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
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/05—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation specially adapted for damping motor oscillations, e.g. for reducing hunting
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/20—Estimation of torque
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/22—Current control, e.g. using a current control loop
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/24—Vector control not involving the use of rotor position or rotor speed sensors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation

Definitions

  • the invention belongs to the field of permanent magnet synchronous motor control, and relates to a sensorless composite control method of a novel dual sliding mode observer, in particular to a novel dual sliding mode observer composite control method which is simple, easy to implement and excellent in effect.
  • SPMSM Surface mount permanent magnet synchronous motor
  • SPMSM surface mount permanent magnet synchronous motor
  • IPMSM built-in permanent magnet synchronous motor
  • DTC Torque Control
  • Vector control commonly uses PI controller to realize double closed-loop control. By measuring the stator current vector of permanent magnet synchronous motor, and then through coordinate transformation, the current vector is decomposed into excitation current and torque current, and the flux linkage and torque of permanent magnet synchronous motor are indirectly controlled. It has the characteristics of high precision and good dynamic and steady performance.
  • Direct torque control is commonly used in bang-bang control, which directly controls the flux linkage and torque of the permanent magnet synchronous motor, eliminating the need for coordinate transformation and current control in vector control, and has better rapidity.
  • the sliding mode observer method has more significant advantages and more mature development in the sensorless control system.
  • the traditional sliding mode observer has the problem of serious chattering and poor load capacity, resulting in poor control performance of the entire system. Therefore, the proposed sliding mode observer control algorithm with better dynamic and steady performance, less chattering phenomenon and stronger load capacity has wider practical application value.
  • the invention solves the problems of poor tracking performance of speed loop and current loop PI controller, difficulty in parameter adjustment and chattering and poor load capacity of traditional sliding mode observer in the double closed-loop vector control process of permanent magnet synchronous motor.
  • the invention provides a novel exponential segmented sliding mode function to replace the switching function in the traditional sliding mode observer, the outer speed loop provides a segmented PI controller, and a sliding mode load observer is designed to observe the load torque pair.
  • the segmented PI controller performs parameter fine-tuning, and at the same time introduces the observed load torque into the q-axis for feedforward compensation.
  • the q-axis current inner loop provides a second-order sliding mode controller with a super-twisting algorithm.
  • the present invention has an overshoot. Small amount, small chattering phenomenon, excellent dynamic and steady performance and good load capacity.
  • the invention provides a sensorless composite control method of a novel dual sliding mode observer, the purpose of which is to weaken the chattering phenomenon and improve the dynamic and steady-state performance and load capacity of the system, which includes:
  • a new exponential piecewise sliding mode function is proposed to observe the back EMF.
  • the expression of the new exponential piecewise sliding mode function is as follows:
  • ⁇ is the thickness of the boundary layer and s ⁇ is the sliding mode surface.
  • This function has the saturation characteristics of the switching function outside the boundary layer, and a small part of the step characteristics at the boundary layer, which can speed up the speed of the system approaching the sliding mode surface without passing through the sliding mode surface.
  • the interior has the characteristics of exponential approach law and continuity. The closer it is to the sliding surface, the slower the approach is, and it is not easy to pass through the sliding surface, which avoids multiple up and down fluctuations along the sliding surface during the system convergence process, so it can be very fast. Good attenuating the chattering phenomenon. Its stability is analyzed using the Lyapunov stability criterion:
  • the current error state equation is obtained by subtracting the mathematical model of the permanent magnet synchronous motor from the reconstructed current state equation:
  • K is the sliding mode gain
  • R s , L s are the stator resistance and inductance, respectively
  • i ⁇ , i ⁇ , u ⁇ , u ⁇ are the stator current and voltage in the stationary coordinate system, respectively
  • e ⁇ , e ⁇ are the inverse The components of the electromotive force on the ⁇ and ⁇ axes, we e is the electrical angular velocity, ⁇ f is the permanent magnet flux linkage, and ⁇ e is the electrical angle.
  • the stability analysis of the novel exponential segmented sliding mode observer proposed in the present invention is carried out, and the Lyapunov function is selected. If the conditions are met The system is asymptotically stable on the sliding surface and the sliding mode exists, so there are:
  • the new exponential segmented sliding mode observer designed by selecting a more accurate sliding mode gain K by trial and error satisfies the Lyapunov stability criterion and has asymptotic stability.
  • the invention designs a segmented PI controller, and takes the presence or absence of load torque as a judgment condition to realize the fine-tuning of the PI controller parameters.
  • the present invention designs a sliding mode observer to observe the load torque in real time, so as to realize the fine-tuning and feed-forward compensation of the segmented PI parameters.
  • the design of the loaded sliding mode observer and the Lyapunov stability analysis are as follows:
  • Load torque error is the estimated mechanical angular velocity
  • J is the moment of inertia
  • T e is the electromagnetic torque
  • l is the control parameter.
  • control parameters a 1 , a 2 , and the tuning process of l are analyzed as follows:
  • the designed load sliding mode observer can reach and stabilize on the sliding mode surface.
  • the control range of control parameters a 1 and a 2 is a 2 ⁇ 0, after fine-tuning according to the trial and error method, select the correct a 1 , a 2 .
  • c is a constant, when l ⁇ 0, the load torque error converges to 0 at an exponential approach speed, that is, the observed load torque can track the actual load torque in real time.
  • the estimated mechanical angular velocity will be and q-axis feedback current i q is input into the designed load sliding mode observer, and according to the setting range of the required control parameters l ⁇ 0, a 2 ⁇ 0, and then adjust the correct control parameters according to the trial and error method, so as to realize the real-time observation of the load torque.
  • the problem of large torque ripple in the double closed-loop vector control process of the permanent magnet synchronous motor is considered.
  • the electromagnetic torque calculation formula Te 1.5p n ⁇ f i q
  • the q-axis current i q and the electromagnetic torque Te exhibit a linear relationship.
  • the invention designs a second-order sliding mode controller on the q-axis to improve the tracking performance of the q-axis current, and indirectly reduces the torque ripple.
  • the present invention sets the quadrature-axis current sliding mode surface as According to the specific expression of the second-order sliding mode controller of the super-twisting algorithm, the q-axis current controller can be designed as: Among them, K p and K i are design parameters, and sign( ) is a switching function.
  • a novel dual sliding mode observer SPMSM sensorless composite control method uses a permanent magnet synchronous motor model to perform Matlab/simulink simulation verification.
  • the present invention has the following technical features:
  • a new exponential piecewise sliding mode function is provided, which weakens the chattering phenomenon, is more conducive to the observation of back electromotive force, and improves the stability of the system.
  • a segmented PI controller is provided in the outer speed loop, and a sliding mode observer is designed to observe the load torque to fine-tune the parameters of the segmented PI controller, so that it can adapt to two different working conditions of no-load operation and sudden load. At the same time, the load torque is introduced into the q-axis for feedforward compensation, which improves the load capacity of the system.
  • the inner loop of the q-axis current provides a second-order sliding mode control of a super-twisting algorithm, which improves the tracking performance of the q-axis current and reduces the torque ripple.
  • Fig. 1 is the principle block diagram of the PMSM composite control method of the novel dual sliding mode observer proposed by the present invention.
  • Fig. 2 is the novel exponential type piecewise sliding mode function proposed by the present invention.
  • FIG. 3 and FIG. 3 are the principle block diagrams of the novel exponential segmented sliding mode observer proposed by the present invention.
  • FIG. 4 and FIG. 4 are flowcharts of the segmented PI controller proposed by the present invention.
  • FIG. 5 and FIG. 5(a) are the rotational speed diagrams of the novel dual sliding mode observer SPMSM sensorless composite control method proposed by the present invention.
  • Figure 5(b) is the rotational speed diagram of the traditional sliding mode observer SPMSM sensorless control method.
  • Fig. 6 Fig. 6 (a) is the rotational speed error diagram of the novel dual sliding mode observer SPMSM sensorless composite control method proposed by the present invention.
  • Fig. 6(b) is the rotational speed error diagram of the traditional sliding mode observer SPMSM sensorless control method.
  • FIG. 7 and FIG. 7(a) are electromagnetic torque diagrams of the novel dual sliding mode observer SPMSM sensorless composite control method proposed by the present invention.
  • FIG. 7(b) is the electromagnetic torque diagram of the traditional sliding mode observer SPMSM sensorless control method.
  • FIG. 8 and FIG. 8 are the rotor position diagrams of the novel dual sliding mode observer SPMSM sensorless composite control method proposed by the present invention.
  • FIG. 9 and FIG. 9 are load torque diagrams estimated by the load sliding mode observer proposed in the present invention.
  • FIG. 10 and FIG. 10 are load torque error diagrams between the load torque estimated by the load sliding mode observer proposed in the present invention and the actual load torque.
  • the estimated back electromotive force is obtained by filtering out the high-order harmonics through the sliding mode gain K and filtering out the high-order harmonics by the low-pass filter.
  • the estimated electrical angular velocity is obtained by dividing the permanent magnet flux linkage ⁇ f by the divider Use the estimated electrical angle value and the estimated electrical angular velocity Realize the double closed-loop vector control strategy of permanent magnet synchronous motor.
  • the present invention will estimate the electrical angular velocity Converted to estimated mechanical angular velocity Then, together with the feedback q-axis current i q , it is input into the load sliding mode observer designed by the present invention to obtain the estimated load torque will estimate the load torque As a judgment condition, fine-tuning of the PI parameters of the outer ring of the speed is carried out.
  • the specific implementation process is as follows:
  • the current error value is obtained by subtracting the actual current i q of the q-axis in the synchronous rotating coordinate system of the feedback
  • the current error value Input into the second-order sliding mode controller proposed in the present invention to obtain the estimated q-axis voltage
  • a novel dual sliding mode observer composite control method realizes sensorless control of a permanent magnet synchronous motor in a medium and high speed domain.
  • a novel exponential piecewise sliding mode function is designed, which has the saturation characteristic of switching function outside the boundary layer, a small part of the step characteristic at the boundary layer, and the characteristics of continuity and exponential reaching law in the boundary layer.
  • the observed back EMF is more accurate.
  • the estimated rotor position angle is obtained by estimating the rotor position by the arc tangent function and estimated electrical angular velocity
  • the chattering phenomenon is weakened and the accuracy is improved.
  • the estimated load torque is output to fine-tune the parameters of the segmented PI controller, and at the same time, the estimated load torque is introduced into the estimated q-axis current of the q-axis for feedforward compensation, so that the system can Adapt to two working conditions of no-load operation and sudden load, and improve the system's anti-load capability.
  • the current inner loop is designed with a second-order sliding mode controller to improve the q-axis current tracking performance, indirectly control the electromagnetic torque, and reduce torque ripple.
  • the present invention is smoother than the traditional sliding mode observer's rotational speed graph, the present invention can well weaken the chattering phenomenon, and suddenly add 5N at 0.2s
  • the load is M
  • the present invention has smaller speed drop, faster speed recovery, and better load capacity
  • the rotational speed estimation error of the present invention is smaller than that of the traditional sliding mode observer, and the rotational speed estimation error is close to 0;
  • the electromagnetic torque ripple of the mode observer is smaller; it can be seen from Fig. 9 and Fig.
  • the load sliding mode observer designed by the present invention can observe the actual load torque in real time, the observation effect is accurate, and the response is fast; analyze the estimated load in Fig. 10 and Fig. 10 The error between the torque and the actual load torque is close to zero. It can be seen from this set of simulation diagrams that the novel dual sliding mode observer SPMSM sensorless composite control method proposed in the present invention can weaken the chattering phenomenon, and has better dynamic and steady-state performance and load capacity, thus proving that the present invention correctness and validity.

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

Abstract

本发明提供了一种新型双滑模观测器的永磁同步电机无传感器复合控制方法，本发明设计了两种滑模观测器，其一提供了一种新型指数型分段滑模函数对反电动势进行观测。其二设计了一种滑模观测器观测负载转矩对分段PI控制器进行参数微调，同时将估计负载转矩引入q轴进行前馈补偿。在q轴电流内环设计了二阶滑模控制器，提高了q轴电流的跟踪性能，间接控制电磁转矩。本发明所提供的新型指数型分段滑模函数，更有利于反电动势观测，削弱了***抖振现象；负载滑模观测器观测负载转矩对分段PI控制器进行参数微调同时进行前馈补偿，提高***带负载能力；二阶滑模控制器减小了转矩脉动。本发明在永磁同步电机的中高速域无传感器控制中具有优良的动稳态性能和广泛的应用价值。

Description

一种新型双滑模观测器SPMSM无传感器复合控制方法 技术领域
本发明属于永磁同步电机控制领域，涉及一种新型双滑模观测器的无传感器复合控制方法，具体涉及一种简单，易行，效果优良的新型双滑模观测器复合控制方法在永磁同步电机中高速域实现无传感器控制的***模型。
背景技术
表贴式永磁同步电机(Permanent Magnet Synchronous Motor，SPMSM)，主要分为表贴式永磁同步电机(SPMSM)和内置永磁同步电机(IPMSM)。具有结构简单、体积小、高功率密度、高效率、易于维护的特点，并且其优越的调速性能使其在众多领域得到广泛应用，例如工业制造、智能机器人、新能源汽车等。随着永磁同步电机应用场合越来越广，对其控制性能的要求也越来越高。当前的众多学者主要集中研究电机的结构设计和电机的控制性能两个方面，良好的控制算法能够大大提高***的性能，目前永磁同步电机常用的控制方法主要有矢量控制(FOC)和直接转矩控制(DTC)。矢量控制常用PI控制器实现双闭环控制，通过测量永磁同步电机定子电流矢量，再通过坐标变换，将电流矢量分解为励磁电流和转矩电流，间接控制永磁同步电机磁链和转矩，具有精度高，动稳态性能好的特点。直接转矩控制则常用bang-bang控制，直接控制永磁同步电机的磁链和转矩，省去了矢量控制中的坐标变换和电流控制，具有更好的快速性。
为实现永磁同步电机高性能双闭环矢量控制，其目的是获得实时的、精确的转速信息和转子位置信息，大多数是安装机械式传感器，如光电编码器。但是机械式传感器存在成本较高，易损坏，***对其依赖性过高，工作环境恶劣性能差等问题。因此为了解决机械式传感器带来的诸多问题，通过算法估计转子位置和速度代替机械式传感器实现永磁同步电机双闭环矢量控制策略。因此永磁同步电机无传感器控制算法的研究成为了当代热潮。
要实现永磁同步电机无传感器，常通过两种方法：一种是基于信号注入，原理是利用电机的凸极率来估计转子位置，常用的有：脉振电压注入法、旋转高频电压注入法；另一种是用观测器观测动态模型中的反电动势来提取转子位置信息。根据永磁同步电机数学模型，可知反电动势与电角速度有关，因此只有在中高速时，反电动势才较为明显，有利于观测和提取，因此中高速域下常采用基于观测器的方法，目前成熟、常用的有滑模观测器法、模型参考自适应、卡尔曼滤波器等。相较于其他两种方法，滑模观测器法在无传感器控制***中具有更显著的优势且发展更加成熟。然而传统滑模观测器存在抖振现象严重，带负载能力差的问题，导致整个***控制性能不佳。因此提出动稳态性能更加优良，抖振现象更加小，带载能力更强的滑模观测器控制算法具有更加广泛的实际应用价值。
发明内容
本发明为解决永磁同步电机双闭环矢量控制过程中转速环和电流环PI控制器跟踪性能差，参数调节困难和传统滑模观测器存在抖振，带负载能力差的问题。
本发明提供了一种新型指数型分段滑模函数代替传统滑模观测器中的开关函数， 转速外环提供了一种分段PI控制器，设计了滑模负载观测器观测负载转矩对分段PI控制器进行参数微调，同时将观测的负载转矩引入q轴进行前馈补偿，q轴电流内环提供了一种super-twisting算法的二阶滑模控制器，本发明具有超调量小，抖振现象小，动稳态性能优越和具有良好的带载能力。
为解决以上技术问题所采用的技术方案是：
本发明提供了一种新型双滑模观测器的无传感器复合控制方法，其目的是削弱抖振现象，提高***动稳态性能和带负载能力，其包括：
提出了一种新型指数型分段滑模函数对反电动势进行观测，新型指数型分段滑模函数表达式如下：
Figure PCTCN2021124411-appb-000001
其中σ为边界层厚度，s αβ为滑模面。
该函数在边界层以外具有开关函数的饱和特性，在边界层处有小部分的阶跃特性，能够在保证不穿过滑模面的前提下加快***趋近滑模面的速度，在边界层内部具有指数趋近律、连续性的特性，越接近滑模面时，趋近越缓慢，不易穿过滑模面，避免了***收敛过程中沿着滑模面多次上下波动，因此能够很好的削弱抖振现象。采用李雅普诺夫稳定性判据对其进行稳定性分析：
设置滑模面为
Figure PCTCN2021124411-appb-000002
重构永磁同步电机电流状态方程：
Figure PCTCN2021124411-appb-000003
将永磁同步电机数学模型与重构后的电流状态方程相减得到电流误差状态方程：
Figure PCTCN2021124411-appb-000004
Figure PCTCN2021124411-appb-000005
其中K为滑模增益；R s，L s分别为定子电阻和电感；i α,i β，u α,u β分别为静止坐标系下 的定子电流和电压；e α,e β分别为反电动势在α，β轴上的分量，w e为电角速度，ψ f为永磁体磁链,θ e为电角度。
当
Figure PCTCN2021124411-appb-000006
时，即估计电流和实际电流相等时，反电动势可用新型指数型分段滑模函数进行观测，即：
Figure PCTCN2021124411-appb-000007
根据Lyapunov稳定性判据对本发明所提的新型指数型分段滑模观测器进行稳定性分析，选取Lyapunov函数
Figure PCTCN2021124411-appb-000008
若满足条件
Figure PCTCN2021124411-appb-000009
***渐近稳定在滑模面上且滑动模态存在，故有：
Figure PCTCN2021124411-appb-000010
其中
Figure PCTCN2021124411-appb-000011
为负定矩阵，电感矩阵
Figure PCTCN2021124411-appb-000012
反电动势矩阵
Figure PCTCN2021124411-appb-000013
因为
Figure PCTCN2021124411-appb-000014
若要满足
Figure PCTCN2021124411-appb-000015
只需满足
Figure PCTCN2021124411-appb-000016
求得只需满足滑模增益K＞max(|e α,e β|)即可。通过试错法选取较为准确的滑模增益K所设计的新型指数型分段滑模观测器满足Lyapunov稳定性判据，具有渐近稳定性。
考虑电机带负载运行过程中温度会升高，电感参数会随之减小，因此转速外环PI控制器的参数整定上会发生变化，为***能够更好的适应空载运行和带载运行，本发明设计分段PI控制器，以有无负载转矩作为判断条件，实现PI控制器参数微调。考虑实际应用过程中考虑负载的不可测性，本发明设计一种滑模观测器对负载转矩进行实时观测，实现分段PI参数微调和前馈补偿。负载滑模观测器的设计和Lyapunov稳定性分析如下：
根据永磁同步电机转矩动力状态方程进行重构，利用滑模观测器观测负载转矩，设计的滑模观测器方程：
Figure PCTCN2021124411-appb-000017
其中滑模控制律为U＝-a 1sign(s w)-a 2s w；a 1，a 2为控制参数。
将永磁同步电机转矩动力状态方程和滑模观测器方程相减，得到转矩动力误差状态方程：
Figure PCTCN2021124411-appb-000018
其中滑模面设置为机械角速度误差
Figure PCTCN2021124411-appb-000019
负载转矩误差
Figure PCTCN2021124411-appb-000020
为 估计机械角速度；J为转动惯量；T e为电磁转矩；
Figure PCTCN2021124411-appb-000021
为估计负载转矩；l为控制参数。根据Lyapunov稳定性判据，选取Lyapunov函数
Figure PCTCN2021124411-appb-000022
***需满足稳定性条件
Figure PCTCN2021124411-appb-000023
可得：
Figure PCTCN2021124411-appb-000024
其中控制参数a 1，a 2，l整定过程分析如下：
(1)当机械角速度误差e 1＞0时，只需满足
Figure PCTCN2021124411-appb-000025
可满足Lyapunov稳定性判据。
①当e 2＞0时，只需满足
Figure PCTCN2021124411-appb-000026
a 2≥0。
②当e 2＜0时，只需满足
Figure PCTCN2021124411-appb-000027
a 2≥0。
(2)当机械角速度误差e 1＜0时，只需满足
Figure PCTCN2021124411-appb-000028
可满足Lyapunov稳定性判据。
①当e 2＞0时，只需满足
Figure PCTCN2021124411-appb-000029
a 2≥0。
②当e 2＜0时，只需满足
Figure PCTCN2021124411-appb-000030
a 2≥0。
因此设计的负载滑模观测器能够到达并稳定在滑模面上，根据等效控制原理即
Figure PCTCN2021124411-appb-000031
时，控制参数a 1，a 2的控制范围为
Figure PCTCN2021124411-appb-000032
a 2≥0，在根据试错法进行微调，选取正确的a 1，a 2。稳定在滑模面后有
Figure PCTCN2021124411-appb-000033
求解后可得
Figure PCTCN2021124411-appb-000034
其中c为常数，当满足l＜0时，负载转矩误差以指数趋近速度收敛到0，即观测的负载转矩能够实时跟踪实际负载转矩。
综上所述，将估计的机械角速度
Figure PCTCN2021124411-appb-000035
和q轴反馈电流i q输入到设计的负载滑模观测器中，且根据所求控制参数的设置范围l＜0，
Figure PCTCN2021124411-appb-000036
a 2≥0，再根据试错法调试正确的控制参数，从而实现对负载转矩的实时观测。
考虑PI控制器跟踪性能差，导致永磁同步电机双闭环矢量控制过程中转矩脉动大的问题。根据电磁转矩计算公式T e＝1.5p nψ fi q，q轴电流i q和电磁转矩T e呈现线性关系。本发明在q轴设计二阶滑模控制器提高对q轴电流的跟踪性能，间接减小转矩脉动。本发明设置交轴电流滑模面为
Figure PCTCN2021124411-appb-000037
根据super-twisting算法的二阶滑模控制器的具体表达式，可设计q轴电流控制器为：
Figure PCTCN2021124411-appb-000038
其中K p，K i为设计参数，sign()为开关函 数。
本发明提供的一种新型双滑模观测器SPMSM无传感器复合控制方法以一台永磁同步电机模型进行Matlab/simulink仿真验证，所述永磁同步电机参数为定子电阻R s＝2.875Ω，定子电感L s＝0.0085H，永磁体磁链ψ f＝0.175，极对数p＝4，转动惯量J＝0.001N·M，且在0.2s时突加5N·M负载进行分析。
本发明有这样一些技术特征：
1、所述新型指数型分段滑模函数边界层厚度σ＝0.002，滑模增益系数K＝200。
2、所述负载滑模观测器参数设置a 1＝10000，a 2＝500。
3、所述super-twisting算法的二阶滑模控制器参数设置：K p＝180，K i＝20。
本发明的新型双滑模观测器的无传感器复合控制***模型具有的有益效果：
1、提供了一种新型指数型分段滑模函数，削弱了抖振现象，更有利于反电动势的观测，提高了***稳定性。
2、在转速外环提供了一种分段PI控制器，设计滑模观测器观测负载转矩对分段PI控制器进行参数微调，使其适应空载运行和突加负载两种不同的工况，同时将负载转矩引入q轴进行前馈补偿，提高了***的带负载能力。
3、q轴电流内环提供了一种super-twisting算法的二阶滑模控制，提高了q轴电流跟踪性能，减小了转矩脉动。
附图说明
下面结合附图和实施例对本发明进一步说明。
图1图1是本发明所提的新型双滑模观测器的PMSM复合控制方法原理框图。
图2图2是本发明所提的新型指数型分段滑模函数。
图3图3是本发明所提的新型指数型分段滑模观测器原理框图。
图4图4是本发明所提的分段PI控制器流程图。
图5图5(a)是本发明所提的新型双滑模观测器SPMSM无传感器复合控制方法的转速图。
图5图5(b)是传统滑模观测器SPMSM无传感器控制方法的转速图。
图6图6(a)是本发明所提的新型双滑模观测器SPMSM无传感器复合控制方法的转速误差图。
图6图6(b)是传统滑模观测器SPMSM无传感器控制方法的转速误差图。
图7图7(a)是本发明所提的新型双滑模观测器SPMSM无传感器复合控制方法的电磁转矩图。
图7图7(b)是传统滑模观测器SPMSM无传感器控制方法的电磁转矩图。
图8图8是本发明所提的新型双滑模观测器SPMSM无传感器复合控制方法的转子位置图。
图9图9是本发明所提的负载滑模观测器估计的负载转矩图
图10图10是本发明所提的负载滑模观测器估计的负载转矩和实际的负载转矩之间的负载转矩误差图。
具体实施方式
采样三相电流i abc、电压u abc，通过Clark变换得到静止坐标系下的电流i αβ，电压u αβ，对重构的电流状态方程进行积分运算后得到估计的电流值
Figure PCTCN2021124411-appb-000039
再与实际采样电流i αβ相减，得到电流误差值
Figure PCTCN2021124411-appb-000040
作为本发明所提新型指数型分段滑模函数的输入再经过滑模增益K，通过低通滤波器滤除高次谐波得到估计的反电动势
Figure PCTCN2021124411-appb-000041
此时
Figure PCTCN2021124411-appb-000042
Figure PCTCN2021124411-appb-000043
和
Figure PCTCN2021124411-appb-000044
输入到除法器中进行除法运算得到估计的电角度
Figure PCTCN2021124411-appb-000045
的正切值，再经过反正切函数运算得到估计的电角度值
Figure PCTCN2021124411-appb-000046
将
Figure PCTCN2021124411-appb-000047
和
Figure PCTCN2021124411-appb-000048
先求平方和再求平方根得到
Figure PCTCN2021124411-appb-000049
通过除法器除以永磁体磁链ψ f得到估计的电角速度
Figure PCTCN2021124411-appb-000050
用估计的电角度值
Figure PCTCN2021124411-appb-000051
和估计的电角速度
Figure PCTCN2021124411-appb-000052
实现永磁同步电机双闭环矢量控制策略。
电机带负载运行过程中，电机温度会升高，电机电感参数会有很大的变化，单一的PI控制器很难使其适应空载和负载两种工况。本发明将估计的电角速度
Figure PCTCN2021124411-appb-000053
转化为估计的机械角速度
Figure PCTCN2021124411-appb-000054
后和反馈的q轴电流i q一起输入到本发明所设计的负载滑模观测器中得到估计的负载转矩
Figure PCTCN2021124411-appb-000055
将估计的负载转矩
Figure PCTCN2021124411-appb-000056
作为判断条件进行转速外环分段PI参数微调，具体实施流程如下：
(1)当估计的负载转矩
Figure PCTCN2021124411-appb-000057
小于所设误差容限ε时，采用空载运行的转速外环PI参数。
(2)当估计的负载转矩
Figure PCTCN2021124411-appb-000058
大于所设误差容限ε时，采用带载运行的转速外环PI参数。同时将估计的负载转矩
Figure PCTCN2021124411-appb-000059
输入的q轴进行前馈补偿。使其***在突加负载的时候，转速突变小，响应快。提高了***的抗负载能力。
通过转速外环分段PI控制器得到的估计q轴电流
Figure PCTCN2021124411-appb-000060
与反馈的同步旋转坐标系下q轴实际电流i q相减得到电流误差值
Figure PCTCN2021124411-appb-000061
将电流误差值
Figure PCTCN2021124411-appb-000062
输入到本发明所提二阶滑模控制器中得到估计的q轴电压
Figure PCTCN2021124411-appb-000063
综上所述，本发明实施例，一种新型双滑模观测器复合控制方法在中高速域实现永磁同步电机无传感器控制。设计了一种新型指数型分段滑模函数，其具有边界层外具有开关函数的饱和特性，边界层处具有小部分阶跃特性，边界层内具有连续性和指数趋近律的特性，避免了在滑模面处多次上下波动，观测的反电动势更加精准。将估计的反电动势
Figure PCTCN2021124411-appb-000064
通过反正切函数进行转子位置估计得到估计转子位置角
Figure PCTCN2021124411-appb-000065
和估计电角速度
Figure PCTCN2021124411-appb-000066
削弱了抖振现象，提高了精度。再将估计电角速度
Figure PCTCN2021124411-appb-000067
作为负载滑模观测器的输入，输出估计的负载转矩对分段PI控制器进行参数微调，同时将估计的负载转矩引入q轴估计的q轴电流中 进行前馈补偿，使其***能够适应空载运行和突加负载两种工况，提高了***抗负载能力。电流内环设计二阶滑模控制器提高q轴电流跟踪性能，间接控制电磁转矩，减小转矩脉动。
下面结合Matlab/simulink仿真图对本发明的应用效果作详细的描述：
对比图5图5(a)和图5图5(b)，本发明相对于传统滑模观测器转速图更加平滑，本发明能够很好的削弱抖振现象，在0.2s时突加5N·M负载时，本发明相对于传统滑模观测器，转速突降更小，且转速恢复更快，具有更好的带负载能力；对比图6图6(a)和图6图6(b)本发明的转速估计误差比传统滑模观测器的转速估计误差小，且转速估计误差近乎接近于0；对比图7图7(a)和图7图7(b)，本发明相对于传统滑模观测器电磁转矩脉动更小；图9图9可以看出本发明设计的负载滑模观测器能够实时的观测实际负载转矩，观测效果准确，响应快；分析图10图10估计的负载转矩和实际的负载转矩误差接近于0。由这组仿真图可以看出，本发明所提的新型双滑模观测器SPMSM无传感器复合控制方法能够削弱抖振现象，具有更好的动稳态性能和带负载能力，从而证明了本发明的正确性和有效性。

Claims (4)

  1. 一种新型双滑模观测器复合控制方法在中高速域实现永磁同步电机无传感器控制，其特征在于，包括以下步骤：
    (1)采样三相电流i abc，电压u abc，经过Clark坐标变换得到静止坐标系下的电流i αβ，电压u αβ，以重构的永磁同步电机电流状态方程为依据积分后得到估计静止坐标系电流值
    Figure PCTCN2021124411-appb-100001
    将估计静止坐标系电流值
    Figure PCTCN2021124411-appb-100002
    与实际静止坐标系电流值i αβ进行差值运算得到电流的误差值
    Figure PCTCN2021124411-appb-100003
    将电流误差值
    Figure PCTCN2021124411-appb-100004
    设为滑模面s αβ，最后根据新型指数型分段滑模函数z(s αβ)对反电动势进行观测。
    (2)设计了负载滑模观测器观测负载转矩，以机械角速度
    Figure PCTCN2021124411-appb-100005
    和反馈的q轴电流作为输入，输出估计的负载转矩
    Figure PCTCN2021124411-appb-100006
    以
    Figure PCTCN2021124411-appb-100007
    的大小作为判断条件对转速外环分段PI控制器进行参数切换，同时将估计的负载转矩
    Figure PCTCN2021124411-appb-100008
    加入到q轴估计电流
    Figure PCTCN2021124411-appb-100009
    中进行前馈补偿。
    (3)以q轴电流误差值
    Figure PCTCN2021124411-appb-100010
    作为滑模面，设计二阶滑模控制器，间接控制电磁转矩。
  2. 根据权利要求1所述的一种新型双滑模观测器复合控制方法在中高速域实现永磁同步电机无传感器控制，其特征是在于提出了一种新型指数型分段滑模函数，其特性更有利于反电动势的观测，削弱了抖振现象，其中新型指数型分段滑模函数表达式：
    Figure PCTCN2021124411-appb-100011
    其中σ为边界层厚度，s αβ为滑模面。
  3. 根据权力要求书1所述的一种新型双滑模观测器复合控制方法在中高速域实现永磁同步电机无传感器控制，其特征是在于设计负载滑模观测器观测负载转矩对分段PI控制器进行参数微调，同时将估计的负载转矩加入q轴进行前馈补偿。
  4. 根据权力要求书1所述的一种新型双滑模观测器复合控制方法在中高速域实现永磁同步电机无传感器控制，其特征是在于交轴电流内环使用super-twisting算法的二阶滑模控制器。设计q轴电流误差为滑模面
    Figure PCTCN2021124411-appb-100012
    设计q轴电流控制器：
    Figure PCTCN2021124411-appb-100013
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