CN117691909A - Linear induction motor three-level dual-vector model predictive thrust control method and system - Google Patents
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- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
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- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
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- 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
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- H02P25/062—Linear motors of the induction type
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- H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
- H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
- H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using DC to AC converters or inverters
- H02P27/08—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using DC to AC converters or inverters with pulse width modulation
- H02P27/12—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using DC to AC converters or inverters with pulse width modulation pulsing by guiding the flux vector, current vector or voltage vector on a circle or a closed curve, e.g. for direct torque control
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Abstract
Description
技术领域Technical field
本发明属于直线电机控制技术领域,更具体地,涉及一种直线感应电机三电平双矢量模型预测推力控制方法及系统。The invention belongs to the technical field of linear motor control, and more specifically, relates to a linear induction motor three-level dual vector model predictive thrust control method and system.
背景技术Background technique
与旋转感应电机驱动轨道交通系统相比,直线感应电机无需齿轮箱等传动机构可直接产生直线运动,具有爬坡能力更强、转弯半径更小和截面积更小等优点,高度契合错综复杂的轨道交通网络发展需求。同时,随着轨道交通客流量的不断增加,新建线路多采用直流1500V供电方式,以满足更高功率等级的牵引电机需要。与两电平拓扑相比,三电平逆变器拓扑(以NPC型三电平逆变器拓扑应用最为广泛)具有输出电压正弦度高、单个功率器件电压应力小、输出电流畸变率小等优点。因此,三电平变频驱动的直线感应电机牵引系统在轨道交通中具有广阔应用前景。Compared with rotary induction motor-driven rail transit systems, linear induction motors can directly produce linear motion without the need for transmission mechanisms such as gearboxes. They have the advantages of stronger climbing ability, smaller turning radius and smaller cross-sectional area, and are highly suitable for intricate tracks. transportation network development needs. At the same time, as the passenger flow of rail transit continues to increase, newly built lines mostly adopt the DC 1500V power supply method to meet the needs of higher power level traction motors. Compared with the two-level topology, the three-level inverter topology (NPC three-level inverter topology is the most widely used) has the characteristics of high output voltage sinusoidality, small voltage stress of a single power device, and small output current distortion rate, etc. advantage. Therefore, the three-level variable frequency drive linear induction motor traction system has broad application prospects in rail transit.
然而,因初级铁芯开断,直线感应电机面临严重端部效应,使得电机运行中互感变化剧烈并造成高速运行时推力衰减严重。模型预测推力控制将直接推力控制与模型预测控制相结合,以推力和初级磁链为控制目标,采用在线寻优的方式确定拟作用电压矢量,易于处理多目标约束条件,能有效缓解端部效应造成的推力衰减,同时保持直接推力控制所具有的快速动态响应能力,在直线感应电机驱动系统中具有巨大发展潜力。However, due to the disconnection of the primary iron core, the linear induction motor faces severe end effects, which causes the mutual inductance to change drastically during motor operation and causes severe thrust attenuation during high-speed operation. Model predictive thrust control combines direct thrust control with model predictive control, takes thrust and primary flux as control targets, and uses online optimization to determine the pseudo-acting voltage vector. It is easy to handle multi-objective constraints and can effectively alleviate end effects. The resulting thrust attenuation, while maintaining the fast dynamic response capability of direct thrust control, has great potential for development in linear induction motor drive systems.
由于在整个控制周期仅作用一个电压矢量,传统单矢量模型预测推力控制存在较大的推力波动和电流谐波。为进一步提升稳态性能,通常采用在每个控制周期内作用两个电压矢量的方式,即双矢量模型预测推力控制,实现在少量增加开关频率的情况下显著降低推力波动,相关方法已在两电平逆变器驱动的直线感应电机系统中得到应用。但上述方法直接应用于三电平逆变器时仍存在一定的困难。首先,三电平逆变器明显增加的离散电压矢量使得电压矢量组合的数量急剧增加。在不考虑简化的情况下,两电平逆变器仅存在49种双矢量组合,而三电平逆变器存在729种双矢量组合,难以采用已有方法确定最优电压矢量组合。其次,现有方法难以考虑三电平逆变器拓扑带来的固有控制要求,如中性点电压平衡和开关的平稳过渡。因此,尽管双矢量模型预测推力控制的核心思想是通用的,但现有方法难以有效扩展至三电平变频驱动的直线感应电机系统以实现稳态性能的提升。Since only one voltage vector acts during the entire control cycle, the traditional single vector model predicts the existence of large thrust fluctuations and current harmonics in thrust control. In order to further improve the steady-state performance, a method of applying two voltage vectors in each control cycle, that is, dual-vector model predictive thrust control, is usually used to significantly reduce thrust fluctuations with a small increase in switching frequency. Related methods have been used in two It is applied in linear induction motor system driven by level inverter. However, there are still certain difficulties when the above method is directly applied to three-level inverters. First, the significantly increased discrete voltage vectors of the three-level inverter dramatically increase the number of voltage vector combinations. Without considering simplification, there are only 49 dual-vector combinations for two-level inverters, while there are 729 dual-vector combinations for three-level inverters. It is difficult to determine the optimal voltage vector combination using existing methods. Secondly, it is difficult for existing methods to consider the inherent control requirements brought by the three-level inverter topology, such as neutral point voltage balance and smooth transition of switches. Therefore, although the core idea of dual-vector model predictive thrust control is universal, existing methods are difficult to effectively extend to three-level variable frequency driven linear induction motor systems to achieve steady-state performance improvement.
发明内容Contents of the invention
针对现有技术的缺陷,本发明的目的在于提供一种考虑电压矢量优化的直线感应电机三电平双矢量模型预测推力控制方法及系统,旨在解决现有双矢量模型预测推力控制应用于三电平变频驱动的直线感应电机系统时存在的算法复杂、三电平逆变器固有控制要求难以有效考虑等问题。In view of the shortcomings of the existing technology, the purpose of the present invention is to provide a linear induction motor three-level dual-vector model predictive thrust control method and system that considers voltage vector optimization, aiming to solve the problem of existing dual-vector model predictive thrust control applied to three-level systems. The linear induction motor system driven by level variable frequency has problems such as complex algorithm and difficulty in effectively considering the inherent control requirements of the three-level inverter.
为实现上述目的,本发明提供了一种直线感应电机三电平双矢量模型预测推力控制方法,包括以下步骤:In order to achieve the above objectives, the present invention provides a linear induction motor three-level dual-vector model predictive thrust control method, which includes the following steps:
S1:实时采集中点箝位(Neutral-Point-Clamped,NPC)NPC型三电平逆变器驱动的直线感应电机控制系统的状态参数,包括电机相电流、速度和逆变器中点电压;根据采样结果利用推力和磁链观测器计算当前时刻的电机推力和初级磁链;S1: Real-time collection of the status parameters of the linear induction motor control system driven by the Neutral-Point-Clamped (NPC) NPC three-level inverter, including motor phase current, speed and inverter midpoint voltage; Use the thrust and flux observer to calculate the motor thrust and primary flux at the current moment based on the sampling results;
S2:将速度控制器产生的推力参考值、初级磁链幅值参考值、当前时刻的电机推力、电机速度和初级磁链输入参考初级磁链矢量发生器,经参考初级磁链矢量发生器运算输出参考初级磁链矢量;S2: Input the thrust reference value generated by the speed controller, the primary flux amplitude reference value, the motor thrust at the current moment, the motor speed and the primary flux vector generator into the reference primary flux vector generator, and then calculate it through the reference primary flux vector generator Output reference primary flux vector;
S3:根据参考初级磁链矢量求解参考电压矢量,根据参考电压矢量位置确定候选电压矢量组合,计算各候选电压矢量组合对应的占空比;将各候选电压矢量组合及其占空比代入所定义的价值函数,确定最优电压矢量组合;S3: Solve the reference voltage vector based on the reference primary flux vector, determine the candidate voltage vector combinations based on the reference voltage vector position, and calculate the duty cycle corresponding to each candidate voltage vector combination; substitute each candidate voltage vector combination and its duty cycle into the defined value function to determine the optimal voltage vector combination;
S4:根据最优电压矢量组合及其占空比产生各桥臂开关脉冲,作用于三电平逆变器,实现对直线感应电机的控制。S4: Generate switching pulses for each bridge arm based on the optimal voltage vector combination and its duty cycle, which act on the three-level inverter to control the linear induction motor.
进一步优选地,根据参考电压矢量位置确定候选电压矢量组合的方法,包括以下步骤:Further preferably, the method for determining candidate voltage vector combinations based on reference voltage vector positions includes the following steps:
将NPC型三电平逆变器可产生的全部离散电压矢量按照幅值大小分为大矢量、中矢量、小矢量和零矢量;其中,大矢量幅值为2/3倍的udc;中矢量幅值为倍的udc;小矢量幅值为1/3倍的udc;udc为直流母线电压;All discrete voltage vectors that can be generated by the NPC three-level inverter are divided into large vectors, medium vectors, small vectors and zero vectors according to their amplitudes; among them, the large vector amplitude is 2/3 times u dc ; medium The vector magnitude is times u dc ; the small vector amplitude is 1/3 times u dc ; u dc is the DC bus voltage;
以6个中矢量为分界线,将逆变器输出电压平面划分为6个大扇区I~VI;其中,扇区I的角平分线方向定义为α轴方向,扇区II和扇区III的分界线方向定义为β轴方向;Using the six median vectors as dividing lines, the inverter output voltage plane is divided into six large sectors I to VI; among them, the angular bisector direction of sector I is defined as the α-axis direction, sector II and sector III The dividing line direction of is defined as the β axis direction;
以第I扇区为例,以u1α=udc/3和u1β=0为分界线,将第I扇区进一步划分为4个小区域:R1~R4;根据参考电压矢量的具体大小结合表1确定候选电压矢量组合,并计算各候选电压矢量组合对应的占空比;对于参考电压矢量处于其他扇区的情况,先通过坐标变换将其旋转至第I扇区,然后采用第I扇区中的条件判断所处区域,进而确定各自对应的候选电压矢量组合;Taking sector I as an example, using u 1α = u dc /3 and u 1β = 0 as the dividing line, sector I is further divided into four small areas: R1 ~ R4; combined according to the specific size of the reference voltage vector Table 1 determines the candidate voltage vector combinations, and calculates the duty cycle corresponding to each candidate voltage vector combination; for the case where the reference voltage vector is in other sectors, first rotate it to the I-th sector through coordinate transformation, and then use the I-th sector The conditions in the area are used to determine the area, and then the corresponding candidate voltage vector combinations are determined;
表1Table 1
将各候选电压矢量组合及其占空比代入所定义的价值函数,确定最优电压矢量组合;Substitute each candidate voltage vector combination and its duty cycle into the defined value function to determine the optimal voltage vector combination;
进一步优选地,针对候选电压矢量组合(ui,uj),综合推力、初级磁链、中点电压及开关状态切换约束的控制目标,所设计的价值函数形式为:Further preferably, for the candidate voltage vector combination (u i , u j ), the value function designed is in the form of:
其中,ku为权重系数,为考虑延时补偿后的中点电压预测值,dopt为候选电压矢量组合(ui,uj)对应的占空比,表达式为:Among them, k u is the weight coefficient, In order to consider the midpoint voltage prediction value after delay compensation, d opt is the duty cycle corresponding to the candidate voltage vector combination (u i , u j ), and the expression is:
Hm为根据开关状态避免P、N状态直接切换的约束条件,表达式为:H m is the constraint to avoid direct switching of P and N states according to the switch state. The expression is:
其中,Sx(x将分别为a、b和c)表示x相的开关状态,分别用数字“1”、“0”和“-1”表示开关状态P、O和N;k和k+1分别代表k和k+1时刻。Among them, S x (x will be a, b and c respectively) represents the switching state of the 1 represents time k and k+1 respectively.
另一方面,本发明提供了一种直线感应电机三电平双矢量模型预测推力控制系统,包括:On the other hand, the present invention provides a linear induction motor three-level dual-vector model predictive thrust control system, including:
推力及初级磁链观测模块,用于根据电机相电流、速度和上一时刻计算的初级磁链,利用推力和磁链观测器计算电机当前时刻推力及初级磁链;The thrust and primary flux observation module is used to calculate the current thrust and primary flux of the motor using the thrust and flux observer based on the motor phase current, speed and the primary flux calculated at the previous moment;
参考量转换模块,用于将速度控制器产生的推力参考值、初级磁链幅值参考值、当前时刻的电机推力、电机速度和初级磁链输入参考初级磁链矢量发生器,经运算输出参考初级磁链矢量,并进一步根据最优参考磁链矢量求解参考电压矢量;The reference conversion module is used to input the thrust reference value generated by the speed controller, the primary flux amplitude reference value, the motor thrust at the current moment, the motor speed and the primary flux into the reference primary flux vector generator, and then output the reference value after calculation Primary flux linkage vector, and further solve the reference voltage vector based on the optimal reference flux linkage vector;
最优电压矢量组合选择模块,用于根据参考电压矢量的位置确定候选电压矢量组合,并计算各组合对应的占空比,将候选电压矢量组合及其占空比分别代入所定义的价值函数,选择使价值函数最小的候选电压矢量组合作为最优电压矢量组合;The optimal voltage vector combination selection module is used to determine candidate voltage vector combinations based on the position of the reference voltage vector, calculate the duty cycle corresponding to each combination, and substitute the candidate voltage vector combination and its duty cycle into the defined value function, Select the candidate voltage vector combination that minimizes the value function as the optimal voltage vector combination;
脉冲序列控制模块,用于根据最优电压矢量组合及其占空比产生三相桥臂脉冲并作用于NPC型三电平逆变器相应桥臂,实现对直线感应电机的控制。The pulse sequence control module is used to generate three-phase bridge arm pulses based on the optimal voltage vector combination and its duty cycle and act on the corresponding bridge arm of the NPC three-level inverter to control the linear induction motor.
总体而言,通过本发明所构思的以上技术方案与现有技术相比,具有以下有益效果:Generally speaking, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:
(1)本发明提供的直线感应电机三电平双矢量模型预测推力控制方法及系统,针对三电平逆变器提出新的电压矢量平面扇区划分方法及相应的简化搜索方法,能极大减少所需评价的电压矢量组合数量,有效降低双矢量模型预测推力控制在三电平变频驱动的直线感应电机系统中的实施复杂度;(1) The linear induction motor three-level dual vector model predictive thrust control method and system provided by the present invention proposes a new voltage vector plane sector division method and corresponding simplified search method for the three-level inverter, which can greatly Reduces the number of voltage vector combinations that need to be evaluated, and effectively reduces the implementation complexity of dual-vector model predictive thrust control in a three-level variable frequency drive linear induction motor system;
(2)本发明提供的直线感应电机三电平双矢量模型预测推力控制方法及系统,通过分析不同电压矢量组合下的开关次数,利用冗余小矢量特点优化待评价电压矢量组合,有效降低了开关频率;并通过分析及数学推导,将中点电压平衡及电压矢量平滑切换等三电平逆变器固有控制需求包含在价值函数中,保证了系统的控制性能。(2) The linear induction motor three-level dual-vector model predictive thrust control method and system provided by the present invention analyzes the switching times under different voltage vector combinations and uses the characteristics of redundant small vectors to optimize the voltage vector combination to be evaluated, effectively reducing switching frequency; and through analysis and mathematical derivation, the inherent control requirements of the three-level inverter such as mid-point voltage balance and voltage vector smooth switching are included in the value function to ensure the control performance of the system.
附图说明Description of the drawings
图1是本发明提供的直线感应电机三电平双矢量模型预测推力控制方法流程图;Figure 1 is a flow chart of the linear induction motor three-level dual vector model predictive thrust control method provided by the present invention;
图2是本发明提供的直线感应电机T型等效电路图;Figure 2 is a T-shaped equivalent circuit diagram of the linear induction motor provided by the present invention;
图3是本发明提供的参考初级磁链矢量发生器结构图;Figure 3 is a structural diagram of the reference primary flux vector generator provided by the present invention;
图4是本发明提供的NPC型三电平逆变器拓扑及其电压矢量分布图,(a)NPC型三电平逆变器拓扑,(b)NPC型三电平逆变器离散电压矢量分布图;Figure 4 is an NPC type three-level inverter topology and its voltage vector distribution diagram provided by the present invention, (a) NPC type three-level inverter topology, (b) NPC type three-level inverter discrete voltage vector Distribution;
图5是本发明提供的电压矢量扇区划分示意图,(a)R1区域具体位置,(b)R2区域具体位置;Figure 5 is a schematic diagram of the voltage vector sector division provided by the present invention, (a) the specific location of the R1 area, (b) the specific location of the R2 area;
图6是本发明提供的不同电压矢量组合开关脉冲图,(a)(u13,u25)电压矢量组合开关脉冲图,(b)(u14,u25)电压矢量组合开关脉冲图;Figure 6 is a switching pulse diagram of different voltage vector combinations provided by the present invention, (a) (u 13 , u 25 ) voltage vector combination switching pulse diagram, (b) (u 14 , u 25 ) voltage vector combination switching pulse diagram;
图7是本发明提供的直线感应电机三电平双矢量模型预测推力控制系统的架构图;Figure 7 is an architectural diagram of the linear induction motor three-level dual vector model predictive thrust control system provided by the present invention;
图8是本发明实施例提供的是否考虑P、N状态直接切换的效果对比图,(a)不考虑P、N状态直接切换效果,(b)考虑P、N状态直接切换效果;Figure 8 is a comparison diagram of the effect of direct switching whether to consider P and N states according to an embodiment of the present invention. (a) The effect of direct switching is not considered to be P and N states. (b) The effect of direct switching is considered to be P and N states;
图9是本发明实施例提供的相同开关频率下各模型预测推力控制方法电压电流波形及谐波分析图,(a)传统单矢量模型预测推力控制,(b)不含电压矢量优化的双矢量模型预测推力控制,(c)本发明方法。Figure 9 is a voltage, current waveform and harmonic analysis diagram of each model predictive thrust control method under the same switching frequency provided by the embodiment of the present invention, (a) traditional single vector model predictive thrust control, (b) dual vector without voltage vector optimization Model predictive thrust control, (c) method of the invention.
具体实施方式Detailed ways
为了使本发明的目的、技术方案及优点更加清楚明白,以下结合附图及实施例,对本发明进行进一步详细说明。应当理解,此处所描述的具体实施例仅仅用以解释本发明,并不用于限定本发明。此外,下面所描述的本发明各个实施方式中所涉及到的技术特征只要彼此之间不构成冲突就可以相互组合。In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.
本发明提供的直线感应电机三电平双矢量模型预测推力控制方法流程图,如图1所示,具体包括以下步骤:The flow chart of the linear induction motor three-level dual-vector model predictive thrust control method provided by the present invention is shown in Figure 1, and specifically includes the following steps:
S1:利用电流传感器和速度传感器分别采样电机相电流和速度信号;根据采样结果分别利用推力和磁链观测器计算当前时刻的电机推力和初级磁链;S1: Use the current sensor and speed sensor to sample the motor phase current and speed signals respectively; use the thrust and flux observers to calculate the motor thrust and primary flux at the current moment based on the sampling results;
具体地,直线感应电机的T型等效电路如图2所示,相比旋转感应电机,由于初级铁芯开断结构,产生边端效应,导致电机运行中励磁电感发生变化,为了定量描述这种互感变化,定义函数f(Q):Specifically, the T-shaped equivalent circuit of the linear induction motor is shown in Figure 2. Compared with the rotary induction motor, due to the primary core breaking structure, the edge effect occurs, resulting in changes in the excitation inductance during motor operation. In order to quantitatively describe this Mutual inductance changes, define function f(Q):
其中:Q=lR2/v2(Lm0+Ll2);l为电机初始长度;v2为电机线速度;R2为电机次级电阻;Ll2为电机次级漏电感;Lm0为电机静止时励磁电感;Among them: Q=lR 2 /v 2 (L m0 +L l2 ); l is the initial length of the motor; v 2 is the linear speed of the motor; R 2 is the secondary resistance of the motor; L l2 is the secondary leakage inductance of the motor; L m0 is Excitation inductance when the motor is stationary;
根据图2所示等效电路,直线感应电机数学模型可表示为:According to the equivalent circuit shown in Figure 2, the mathematical model of the linear induction motor can be expressed as:
其中,u1=u1α+ju1β和u2=u2α+ju2β分别为初级和次级电压矢量;i1=i1α+ji1β和i2=i2α+ji2β为初级和次级电流矢量;ψ1=ψ1α+jψ1β和ψ2=ψ2α+jψ2β为初级和次级磁链矢量;L1=Lmeq+Ll1和L2=Lmeq+Ll2为初级和次级电感;R1和R2为电机初级和次级电阻;p为微分算子,ω2为次级角速度,ω2=v2π/τ,τ为电机极距;Lmeq为考虑边端效应后的等效励磁电感,可表示为:Among them, u 1 =u 1α +ju 1β and u 2 =u 2α +ju 2β are the primary and secondary voltage vectors respectively; i 1 =i 1α +ji 1β and i 2 =i 2α +ji 2β are the primary and secondary voltage vectors respectively. Current vector; ψ 1 =ψ 1α +jψ 1β and ψ 2 =ψ 2α +jψ 2β are the primary and secondary flux linkage vectors; L 1 =L meq +L l1 and L 2 =L meq +L l2 are the primary and secondary flux vectors. Primary inductance; R 1 and R 2 are the primary and secondary resistances of the motor; p is the differential operator, ω 2 is the secondary angular velocity, ω 2 =v 2 π/τ, τ is the motor pole pitch; L meq is the edge considered The equivalent magnetizing inductance after the effect can be expressed as:
Lmeq=Lm0(1-f(Q)) (3)L meq =L m0 (1-f(Q)) (3)
进一步具体地,基于公式(2)中的数学模型可建立推力和磁链观测器如下:Further specifically, based on the mathematical model in formula (2), the thrust and flux observer can be established as follows:
其中,k和k-1分别代表k和k-1时刻的电机状态变量,上标“^”代表观测量,为漏磁系数,Fe为电磁推力,Ts为控制周期。Among them, k and k-1 represent the motor state variables at time k and k-1 respectively, and the superscript "^" represents the observation quantity. is the magnetic leakage coefficient, F e is the electromagnetic thrust, and T s is the control period.
S2:将速度控制器产生的推力参考值、初级磁链幅值参考值、当前时刻的电机推力、电机速度和初级磁链输入参考初级磁链矢量发生器,经参考初级磁链矢量发生器运算输出参考初级磁链矢量;S2: Input the thrust reference value generated by the speed controller, the primary flux amplitude reference value, the motor thrust at the current moment, the motor speed and the primary flux vector generator into the reference primary flux vector generator, and then calculate it through the reference primary flux vector generator Output reference primary flux vector;
参考初级磁链发生器的结构如图3所示,为了清楚地解释参考初级磁链发生器的工作原理,首先将直线感应电机的推力表达式简化为:The structure of the reference primary flux generator is shown in Figure 3. In order to clearly explain the working principle of the reference primary flux generator, first the thrust expression of the linear induction motor is simplified as:
其中,ω1为初级磁链的旋转角速度,即同步角速度,τc=σL2/R2。对式(6)进行拉普拉斯变换可得:Among them, ω 1 is the rotation angular speed of the primary magnetic link, that is, the synchronous angular speed, τ c =σL 2 /R 2 . Apply Laplace transform to equation (6) to get:
其中,ωs为滑差角速度。Among them, ω s is the slip angular velocity.
由式(7)可以看出,以滑差角速度为输入的推力传递函数等价于一个一阶系统。因此,可以采用PI控制器来实现良好的推力跟踪性能,并由此将推力误差转换为等效滑差角速度ωs。初级磁链的位置变化角Δθ1由等效滑差角速度和次级角速度计算。参考初级磁链矢量的相角可进一步根据当前时刻的初级磁链相位角θ1和位置变化角Δθ1计算。在式(5)估计出当前时刻的初级磁链矢量后,其相位角θ1由其α-β分量计算:It can be seen from equation (7) that the thrust transfer function with slip angular velocity as input is equivalent to a first-order system. Therefore, a PI controller can be used to achieve good thrust tracking performance, and thereby convert the thrust error into equivalent slip angular velocity ω s . The position change angle Δθ 1 of the primary flux linkage is calculated from the equivalent slip angular velocity and the secondary angular velocity. The phase angle of the reference primary flux vector can be further calculated based on the primary flux phase angle θ 1 and the position change angle Δθ 1 at the current moment. After estimating the primary flux linkage vector at the current moment in equation (5), its phase angle θ 1 is calculated from its α-β component:
最后,由初级磁链幅值参考值和相角参考值得到参考初级磁链矢量,将其作为新的控制目标。其中,推力控制目标体现在其相角中,磁链控制目标体现在其幅值中。通过引入参考初级磁链发生器,可以避免使用两个不同量纲的参考值(推力和磁链)来计算参考电压矢量。Finally, the reference primary flux vector is obtained from the primary flux amplitude reference value and phase angle reference value, which is used as a new control target. Among them, the thrust control target is reflected in its phase angle, and the flux control target is reflected in its amplitude. By introducing a reference primary flux generator, it is possible to avoid using two reference values of different dimensions (thrust and flux) to calculate the reference voltage vector.
S3:根据参考初级磁链矢量求解参考电压矢量,根据参考电压矢量位置确定候选电压矢量组合,计算各候选电压矢量组合对应的占空比;将各候选电压矢量组合及其占空比代入所定义的价值函数,确定最优电压矢量组合;S3: Solve the reference voltage vector based on the reference primary flux vector, determine the candidate voltage vector combinations based on the reference voltage vector position, and calculate the duty cycle corresponding to each candidate voltage vector combination; substitute each candidate voltage vector combination and its duty cycle into the defined value function to determine the optimal voltage vector combination;
具体地,针对实际控制系统计算时间导致的延迟,首先需要进一步结合电机数学模型预测来补偿延迟的影响,从而提高控制器的控制精度。通过当前k时刻的采样和观测值,对k+1时刻进行预测,预测表达式为:Specifically, for the delay caused by the calculation time of the actual control system, it is first necessary to further combine the motor mathematical model prediction to compensate for the impact of the delay, thereby improving the control accuracy of the controller. Based on the sampling and observation values at the current k time, the k+1 time is predicted. The prediction expression is:
其中,上标k+1代表k+1时刻的电机状态变量,uopt为上一时刻作用于逆变器的等效初级电压。Among them, the superscript k+1 represents the motor state variable at time k+1, u opt is the equivalent primary voltage acting on the inverter at the last moment.
基于无差拍原理,参考电压矢量可以通过让k+2时刻的初级磁链预测值等于其参考值来计算:Based on the deadbeat principle, the reference voltage vector can be calculated by making the predicted value of the primary flux linkage at time k+2 equal to its reference value:
图4中的(a)为NPC型三电平逆变器拓扑图,在不同的开关状态下,电机的每一相都可以连接到直流母线的正极(P)、负极(N)或中性点(O);因此,三相相互组合可以产生27个待评价电压矢量,按其幅值大小分为四类:大矢量{u1,u3,...u11},中矢量{u2,u4,...u12},小矢量{u13,u14,...u24},零矢量{u25,u26,u27},各电压矢量的具体分布如图4中的(b)所示。在图4中的(b)中,双矢量实际能够合成的点在图中用实线表示,而距离参考电压矢量距离最近的点将使价值函数的值最小,进而产生最优的控制效果;因此,基于参考电压矢量指导最优电压矢量组合的选择,可以有效避免将每个电压矢量组合代入价值函数反复计算和比较,有效降低算法复杂度。(a) in Figure 4 is the topology diagram of the NPC three-level inverter. In different switching states, each phase of the motor can be connected to the positive pole (P), negative pole (N) or neutral of the DC bus. point (O); therefore, the three-phase combination can produce 27 voltage vectors to be evaluated, which are divided into four categories according to their amplitudes: large vectors {u 1 , u 3 ,...u 11 }, medium vectors {u 2 ,u 4 ,...u 12 }, small vector {u 13 ,u 14 ,...u 24 }, zero vector {u 25 ,u 26 ,u 27 }, the specific distribution of each voltage vector is shown in Figure 4 As shown in (b). In (b) of Figure 4, the points where the two vectors can actually be synthesized are represented by solid lines in the figure, and the points closest to the reference voltage vector will minimize the value of the value function, thereby producing the optimal control effect; Therefore, based on the reference voltage vector to guide the selection of the optimal voltage vector combination, it can effectively avoid substituting each voltage vector combination into the value function for repeated calculation and comparison, and effectively reduce the complexity of the algorithm.
进一步地,为了方便根据参考电压矢量排除尽可能多的电压矢量组合,以6个中矢量为分界线,将逆变器输出电压范围划分为6个大扇区I~VI。以第I扇区为例,每条边界线对应1到2个电压矢量组合:(u13,u25),(u14,u25),(u14,u15),(u13,u16),(u1,u13),(u1,u14),(u2,u13),(u2,u14),(u1,u2),(u13,u24),(u14,u23),(u1,u12),(u12,u13),(u12,u14)。为进一步减少需要评价的电压矢量组合数量,以u1α=udc/3和u1β=0为分界线,将第I扇区进一步划分为4个小区域:R1~R4,如图5所示,并进一步考虑开关动作次数对电压矢量组合进行优化。例如,(u13,u25)和(u14,u25)对于推力和磁链控制具有完全相同的效果,然而前者比后者多产生2次开关动作,如图6所示,故仅保留(u14,u25)作为候选电压矢量组合。Furthermore, in order to facilitate the elimination of as many voltage vector combinations as possible based on the reference voltage vector, the inverter output voltage range is divided into six large sectors I to VI using the six mid-vectors as dividing lines. Taking sector I as an example, each boundary line corresponds to 1 to 2 voltage vector combinations: (u 13 ,u 25 ), (u 14 ,u 25 ), (u 14 ,u 15 ), (u 13 ,u 16 ), (u 1 ,u 13 ), (u 1 ,u 14 ), (u 2 ,u 13 ), (u 2 ,u 14 ), (u 1 ,u 2 ), (u 13 ,u 24 ) , (u 14 ,u 23 ), (u 1 ,u 12 ), (u 12 ,u 13 ), (u 12 ,u 14 ). In order to further reduce the number of voltage vector combinations that need to be evaluated, using u 1α = u dc /3 and u 1β = 0 as the dividing line, sector I is further divided into four small areas: R1 ~ R4, as shown in Figure 5 , and further consider the number of switching actions to optimize the voltage vector combination. For example, (u 13 , u 25 ) and (u 14 , u 25 ) have exactly the same effect on thrust and flux control. However, the former produces two more switching actions than the latter, as shown in Figure 6, so only (u 14 , u 25 ) as candidate voltage vector combinations.
当参考电压矢量处于第I扇区时,根据参考电压矢量所处的具体区域,并考虑对开关次数进行优化,可得不同情况下的候选电压矢量组合如表1所示,其中和/>分别为参考电压矢量的α轴和β轴分量。When the reference voltage vector is in the I-th sector, according to the specific area where the reference voltage vector is located and considering the optimization of the number of switches, the candidate voltage vector combinations under different situations are shown in Table 1, where and/> are the α-axis and β-axis components of the reference voltage vector respectively.
表1Table 1
当参考电压处于其他扇区n时,可通过坐标变换首先将其旋转至第I扇区,之后参考表1确定其具体区域,进而确定各自对应的候选电压矢量组合。坐标变换公式为:When the reference voltage is in other sectors n, it can first be rotated to the I-th sector through coordinate transformation, and then refer to Table 1 to determine its specific area, and then determine the corresponding candidate voltage vector combinations. The coordinate transformation formula is:
进一步地,在确定候选电压矢量组合后需要进一步确定两个电压矢量各自作用时间,即占空比。当参考电压矢量为时,对于电压矢量组合(ui,uj),ui的占空比dopt可表示为:Furthermore, after determining the candidate voltage vector combination, it is necessary to further determine the respective action time of the two voltage vectors, that is, the duty cycle. When the reference voltage vector is When , for the voltage vector combination (u i , u j ), the duty cycle d opt of u i can be expressed as:
其中,·表示两个矢量的点乘,||ui-uj||表示矢量(ui-uj)的幅值。相应地,uj的占空比为(1-dopt)。式(12)所计算的占空比需进一步约束在[0,1]区间内。Among them, · represents the dot product of two vectors, ||u i -u j || represents the amplitude of the vector (u i -u j ). Correspondingly, the duty cycle of u j is (1-d opt ). The duty cycle calculated by Equation (12) needs to be further constrained to the range [0,1].
另一方面,和两电平逆变器相比,NPC型三电平逆变器由于中性点引出,在电机运行过程中随着流过中性点电流的变化,逆变器中点电压会发生变化,较大的逆变器中点电压偏移会引起电流和推力的波动,因此为保证电机驱动系统的控制性能,需要对中点电压进行控制,逆变器中点电压定义为:On the other hand, compared with the two-level inverter, the NPC three-level inverter has a neutral point lead. As the current flowing through the neutral point changes during the operation of the motor, the mid-point voltage of the inverter changes. Changes will occur. A large offset in the inverter midpoint voltage will cause fluctuations in current and thrust. Therefore, in order to ensure the control performance of the motor drive system, the midpoint voltage needs to be controlled. The inverter midpoint voltage is defined as:
ΔUc12=Udc1-Udc2 (13)ΔU c12 =U dc1 -U dc2 (13)
其中,Udc1和Udc2分别为电容C1和C2上的电压。基于基尔霍夫电流定律和图4所示的电路拓扑,k+1时刻的中点电压可根据当前时刻电机相电流、电容电压和将作用的开关状态进行预测:Among them, U dc1 and U dc2 are the voltages on the capacitors C 1 and C 2 respectively. Based on Kirchhoff's current law and the circuit topology shown in Figure 4, the midpoint voltage at k+1 moment can be predicted based on the motor phase current, capacitor voltage and the switching state that will act at the current moment:
其中,为电压矢量ui在k时刻各相桥臂的开关状态矩阵,分别用数字“1”、“0”和“-1”表示开关状态P、O和N,/>为三相电流矩阵,C=C1=C2。in, is the switching state matrix of each phase bridge arm of the voltage vector u i at time k. The numbers "1", "0" and "-1" are used to represent the switching states P, O and N respectively,/> is the three-phase current matrix, C=C 1 =C 2 .
在式(14)的基础上,当存在电压矢量组合(ui,uj)同时作用于一个控制周期时,k+1时刻的中点电压预测表达式为:On the basis of equation (14), when there is a combination of voltage vectors (u i , u j ) acting simultaneously on a control period, the prediction expression of the midpoint voltage at time k+1 is:
同时,当某一相的开关状态直接在P和N之间切换时,相电压会出现高电压跳变,造成电机电流畸变甚至在状态切换过程中导致IGBT直通,因此需要采取措施避免P、N状态间的直接切换。应当注意到,在图6所示的开关脉冲模式下,只有两种情况(不考虑先后顺序)可发生P和N的直接切换,如表2所示。At the same time, when the switching state of a certain phase is directly switched between P and N, the phase voltage will undergo a high voltage jump, causing motor current distortion and even causing IGBT shoot-through during the state switching process. Therefore, measures need to be taken to avoid P and N Direct switching between states. It should be noted that in the switching pulse mode shown in Figure 6, there are only two situations (regardless of the order) in which direct switching of P and N can occur, as shown in Table 2.
表2Table 2
根据表2给出的开关状态关系,定义约束条件Hm来避免P、N状态间的直接切换,具体表示为:According to the switch state relationship given in Table 2, the constraint condition H m is defined to avoid direct switching between P and N states, which is specifically expressed as:
其中,x将分别为a、b和c。综合推力、初级磁链、中点电压及开关状态切换约束的控制目标,所设计的价值函数为:where x will be a, b and c respectively. Combining the control objectives of thrust, primary flux linkage, midpoint voltage and switch state switching constraints, the designed value function is:
其中,为根据式(15)进一步考虑延时补偿的中点电压,ku为权重系数。将各候选电压矢量组合及其占空比依次代入式(17)计算价值函数,选择价值函数值最小的候选电压矢量组合作为最优电压矢量组合。in, In order to further consider the midpoint voltage of delay compensation according to equation (15), k u is the weight coefficient. Substituting each candidate voltage vector combination and its duty cycle into equation (17) in turn to calculate the value function, select the candidate voltage vector combination with the smallest value function as the optimal voltage vector combination.
S4:根据最优电压矢量组合及其占空比产生各桥臂开关脉冲,作用于三电平逆变器,实现对直线感应电机的控制。S4: Generate switching pulses for each bridge arm based on the optimal voltage vector combination and its duty cycle, which act on the three-level inverter to control the linear induction motor.
具体地,在确定最优电压矢量组合后,可根据组合中两个电压矢量的开关状态及其占空比合成各桥臂的开关脉冲,直接作用到NPC型三电平逆变器的12个IGBT上,完成对直线感应电机的控制。Specifically, after determining the optimal voltage vector combination, the switching pulses of each bridge arm can be synthesized according to the switching states and their duty cycles of the two voltage vectors in the combination, and directly applied to the 12 NPC three-level inverters. On the IGBT, the control of the linear induction motor is completed.
图7是本发明提供的直线感应电机三电平双矢量模型预测推力控制系统架构图,包括推力及初级磁链观测模块100、参考量转换模块200、最优电压矢量组合选择模块300和脉冲序列控制模块400,其中,Figure 7 is an architecture diagram of the linear induction motor three-level dual vector model predictive thrust control system provided by the present invention, including a thrust and primary flux observation module 100, a reference conversion module 200, an optimal voltage vector combination selection module 300 and a pulse sequence. control module 400, wherein,
推力及初级磁链观测模块100,用于根据电机相电流、速度和上一时刻计算的初级磁链,利用推力和磁链观测器计算电机当前时刻推力及初级磁链;The thrust and primary flux observation module 100 is used to calculate the thrust and primary flux of the motor at the current moment by using the thrust and flux observer based on the motor phase current, speed and the primary flux calculated at the previous moment;
参考量转换模块200,用于将速度控制器产生的推力参考值、初级磁链幅值参考值、当前时刻的电机推力、电机速度和初级磁链输入参考初级磁链矢量发生器,经运算输出参考初级磁链矢量,并进一步根据最优参考磁链矢量求解参考电压矢量;The reference conversion module 200 is used to input the thrust reference value generated by the speed controller, the primary flux amplitude reference value, the motor thrust at the current moment, the motor speed and the primary flux into the reference primary flux vector generator, and output it after calculation Refer to the primary flux vector, and further solve the reference voltage vector based on the optimal reference flux vector;
最优电压矢量组合选择模块300,用于根据参考电压矢量的位置确定候选电压矢量组合,并计算各组合对应的占空比,将候选电压矢量组合及其占空比分别代入所定义的价值函数,选择使价值函数最小的候选电压矢量组合作为最优电压矢量组合;The optimal voltage vector combination selection module 300 is used to determine candidate voltage vector combinations based on the position of the reference voltage vector, calculate the duty cycle corresponding to each combination, and substitute the candidate voltage vector combination and its duty cycle into the defined value function. , select the candidate voltage vector combination that minimizes the value function as the optimal voltage vector combination;
脉冲序列控制模块400,用于根据最优电压矢量组合及其占空比产生三相桥臂脉冲并作用于NPC型三电平逆变器相应桥臂,实现对直线感应电机的控制。The pulse sequence control module 400 is used to generate three-phase bridge arm pulses based on the optimal voltage vector combination and its duty cycle and act on the corresponding bridge arm of the NPC three-level inverter to control the linear induction motor.
本发明所提出双矢量模型预测推力控制方法与传统不含电压矢量优化的双矢量模型预测推力控制的实验效果如图8所示,其中电机速度11m/s、负载50N,状态State表示是否存在P、N之间的直接切换,State=1表示某相存在直接切换,State=0表示不存在直接切换。从实施效果来看,传统方法有时会出现P、N状态的直接切换,从而导致线电压和相电流出现较大的畸变,从而影响电机的控制性能。所提出方法通过表2分析并在价值函数中引入了约束,有效防止了P、N状态间的直接切换。The experimental results of the dual-vector model predictive thrust control method proposed by the present invention and the traditional dual-vector model predictive thrust control without voltage vector optimization are shown in Figure 8, where the motor speed is 11m/s, the load is 50N, and the state indicates whether there is P , direct switching between N, State=1 means there is direct switching in a certain phase, State=0 means there is no direct switching. Judging from the implementation effect, the traditional method sometimes causes direct switching between P and N states, which causes large distortions in line voltage and phase current, thus affecting the control performance of the motor. The proposed method is analyzed in Table 2 and introduces constraints in the value function, which effectively prevents direct switching between P and N states.
为了进一步验证所提出控制方法对直线感应电机驱动系统稳态性能的提升效果,分别对比了两种已有文献中的模型预测推力控制方法在相同开关频率(1.23kHz)下的稳态性能,图9中的(a)为传统的单矢量模型预测推力控制,(b)为不含电压矢量优化的双矢量模型预测推力控制,(c)为本发明提出的方法。图9给出了三种方法在电机速度11m/s、负载180N下的线电压、相电流及其谐波分析。可以看出,所提出方法通过引入双矢量控制并考虑电压矢量优化,在相同的开关频率下展示出更好的稳态性能。In order to further verify the improvement effect of the proposed control method on the steady-state performance of the linear induction motor drive system, the steady-state performance of two model-predicted thrust control methods in the existing literature were compared at the same switching frequency (1.23kHz), as shown in Figure (a) in 9 is the traditional single vector model predictive thrust control, (b) is the dual vector model predictive thrust control without voltage vector optimization, and (c) is the method proposed by the present invention. Figure 9 shows the line voltage, phase current and harmonic analysis of the three methods at a motor speed of 11m/s and a load of 180N. It can be seen that the proposed method exhibits better steady-state performance at the same switching frequency by introducing dual vector control and considering voltage vector optimization.
本领域的技术人员容易理解,以上所述仅为本发明的较佳实施例而已,并不用以限制本发明,凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等,均应包含在本发明的保护范围之内。It is easy for those skilled in the art to understand that the above descriptions are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements, etc., made within the spirit and principles of the present invention, All should be included in the protection scope of the present invention.
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