WO2022048100A1 - 一种提高大范围调速响应能力的超高速电动空压机变电压扩稳控制系统及方法 - Google Patents
一种提高大范围调速响应能力的超高速电动空压机变电压扩稳控制系统及方法 Download PDFInfo
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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
- H02P21/22—Current control, e.g. using a current control loop
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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
- H02P21/05—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
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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
- H02P21/12—Stator flux based control involving the use of rotor position or rotor speed sensors
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- the invention belongs to the field of stability expansion control of ultra-high-speed electric air compressors, and in particular relates to an ultra-high-speed electric air compressor variable voltage stability expansion control system and method for improving wide-range speed regulation response capability.
- the ultra-high-speed electric air compressor is an essential core component of the fuel cell system, providing sufficient air for the fuel cell system and ensuring the power output of the fuel cell system.
- the rapid speed change of the ultra-high-speed electric air compressor when the speed of the ultra-high-speed electric air compressor is rapidly adjusted in a large range leads to a sharp increase in the internal flow of the centrifugal turbocharger, and the instability of the outlet gas flow increases.
- the amplitude and frequency of the excitation rise rapidly.
- the amplitude and frequency of the load excitation of the ultra-high-speed electric air compressor surge, which gradually erodes its stability domain under the combined action of electromagnetic excitation, and induces the ultra-high-speed electric air compressor to eventually lose its stability, causing the speed of the ultra-high-speed electric air compressor to vibrate. and vibration noise is extremely serious.
- the Chinese patent (CN110069033A) provides a flow control method for a fuel cell air compressor. Through the predicted vehicle speed, the power required by the fuel cell and the air flow required by the air compressor at the corresponding vehicle speed are calculated, and based on the output The goal is to control the speed of the air compressor to adapt to changes in working conditions.
- the problem with this patent is that the speed control is simply based on the power demand, and the speed vibration generated by the ultra-high-speed air compressor under the influence of the load excitation is not considered in the speed control, resulting in high vibration noise and long response time.
- the Chinese patent (CN110729503A) provides a method for switching the mode of a hydrogen fuel cell air compressor. According to the speed and required power of the air compressor, according to the current switching method, the switching of the closed-loop or open-loop control of the air compressor can be realized. Improve the air flow control accuracy and control responsiveness, and ensure the stability of the air control system in low-speed and small-load areas.
- This method pays attention to the response of the speed control of the ultra-high-speed air compressor, but there are still the following problems: when the ultra-high-speed electric air compressor performs a large-scale rapid speed regulation in the ultra-high-speed range, the mode switching has been unable to control the load excitation caused by The high speed vibration can only ensure stable operation in the low speed and small load area.
- the present invention provides a variable voltage stability expansion control system and method for an ultra-high-speed electric air compressor that improves the wide-range speed regulation response capability, and introduces dynamic theory to the stability of the ultra-high-speed electric air compressor. Analysis is carried out to realize the expansion and stability control of the ultra-high-speed electric air compressor, which can significantly compress the response time of the ultra-high-speed electric air compressor, reduce vibration and noise, and improve stability.
- the present invention achieves the above technical purpose through the following technical means.
- An ultra-high-speed electric air compressor variable voltage stability expansion control system that improves the response capability of large-scale speed regulation, comprising a variable voltage stability expansion control module, and the variable voltage stability expansion control module includes d and q axis voltage stability range solving subsystems , the track positioning control subsystem and the track migration control subsystem, the d, q axis voltage stability range solving subsystem outputs the d, q axis voltage stability range to the track positioning controller according to the input real-time speed and d, q axis current.
- the orbit positioning control subsystem calculates the target convergence region and transmits it to the orbit migration control subsystem, and the orbit migration control subsystem obtains the d and q axis voltage commands according to the target convergence region and the d and q axis decoupling voltages, As the output of the variable voltage expansion stability control module.
- a variable voltage stability expansion control method for an ultra-high-speed electric air compressor that improves the wide-range speed regulation response capability comprising the steps of:
- Step (1) the d, q axis voltage stability range solving subsystem receives the real-time rotational speed signal, the real-time d-axis current signal and the real-time q-axis current signal, and the track migration control subsystem receives the d, q-axis decoupling voltage signals; d, q
- the shaft voltage stability range solving subsystem uses the load excitation matrix value function to identify the current load excitation
- step (2) the d and q axis voltage stability range solving subsystem uses the preset motor electromagnetic and mechanical parameters and the identified current load excitation to obtain the d and q axis voltage stability ranges under the current load conditions
- Step (3) according to the stable range of the d and q axis voltages under the current load conditions, the track positioning control subsystem and the track migration control subsystem correct the input d and q axis decoupling voltage signals, and output d and q axis voltage commands value.
- the acquisition process of the load excitation matrix value function is as follows: using the meshless method to reconstruct the load excitation time domain response matrix using the finite element simulation technology, using the penalty function to impose the boundary conditions of the finite element mesh, and time-step iteration.
- the direct inversion method is used to realize the identification of the value function of the load excitation matrix, and the load excitation matrix value function is obtained.
- the stable ranges of the d- and q-axis voltages under the current load conditions are determined by the identified load excitation, the three-parameter coupling bifurcation set of the d-axis voltage and the q-axis voltage.
- the three-parameter coupled bifurcation set is obtained by solving the critical conditions of the Fold bifurcation and the Hopf bifurcation.
- the acquisition of the d and q-axis voltage stability ranges requires the calculation of the balance point of the system, specifically: establishing a high-dimensional, multi-scale nonlinear dynamic model of the ultra-high-speed electric air compressor, and using the chaotic optimization method to search for the balance point the global optimal solution, take the global optimal solution of the equilibrium point obtained by each chaotic optimization method as the initial search value, the local accurate solution of the equilibrium point obtained by the previous conjugate gradient method and the local accurate solution of the equilibrium point obtained by this chaotic optimization method
- the distance of the global optimal solution of the balance point is the radius, and the conjugate gradient method is used to search for the exact solution of the balance point.
- the stable numerical range of the d and q axis voltages is taken as the convergence region C, and the maximum value of the sum of the squares of the d and q axis voltages is taken as the desired control target g, the desired control target g ⁇ C, the system state variable will automatically tend to g, Complete the expansion control of ultra-high-speed electric air compressors with direct intervention of bifurcation parameters.
- the present invention starts from the goal of resisting strong load excitation, and embeds the variable voltage expansion control module after the voltage decoupling control module, and the variable voltage expansion control module accurately estimates the load excitation, and the calculation guarantees
- the numerical range of d and q axis voltages for the safe and stable operation of the system, the d and q axis voltage commands obtained by applying control are used as the output of the variable voltage expansion stability control module, so that the ultra-high-speed electric air compressor can resist strong load excitation.
- the invention fundamentally solves the problem of rotational speed excitation of an ultra-high-speed electric air compressor and reduces vibration noise; the reduction of rotational speed excitation enables smooth transition of rotational speed, avoids additional overshoot processing, and further compresses response time.
- the invention can adapt to the change of load, especially to the extreme working conditions brought by the full power fuel cell system.
- Fig. 1 is the structure diagram of the variable voltage stability expansion control system of the high-speed electric air compressor according to the present invention
- FIG. 2 is a schematic diagram of the variable voltage stabilization control of the high-speed electric air compressor according to the present invention.
- an ultra-high-speed electric air compressor variable voltage stability expansion control system that improves the response capability of large-scale speed regulation
- the variable voltage stability expansion control module is embedded after the voltage decoupling control module, and the load excitation is accurately performed. Estimate and calculate the numerical range of d and q axis voltages to ensure the safe and stable operation of the system, and apply control to obtain d and q axis voltage commands and As the output of the variable voltage expansion control module, the ultra-high-speed electric air compressor can resist strong load excitation.
- the variable voltage expansion stability control module receives the d and q axis decoupling voltage signals sent by the voltage decoupling module and At the same time, relying on the current loop and the speed loop to receive the required signals for real-time identification of the load excitation, and output the d and q axis voltage commands, the coordinate conversion module converts the d and q axis voltage commands into U ⁇ and U ⁇ , and the SVPWM module outputs six The pulse IGBT control signal; at the same time, the angular velocity calculation module and the position detection module detect the rotor position and the sampling value of the electrical angular velocity in real time, which are used to complete the air compressor control.
- the variable voltage stability expansion control module includes a d, q axis voltage stability range solution subsystem, a track positioning control subsystem, and a track migration control subsystem.
- the d, q axis voltage stability range solving subsystem outputs the d and q axis voltage stability ranges to the track positioning control subsystem according to the input real-time rotational speed ⁇ r and the d and q axis currents id and i q ;
- the system calculates the target convergence region and transmits it to the orbit migration control subsystem; the orbit migration control subsystem calculates the target convergence region and the d and q axis decoupling voltages and Complete the stability expansion control of ultra-high-speed electric air compressors with direct intervention of bifurcation parameters.
- a variable voltage stability expansion control method for an ultra-high-speed electric air compressor that improves the wide-range speed regulation response capability specifically comprising the following steps:
- the d and q-axis voltage stability range solving subsystem receives the real-time rotational speed signal ⁇ r , the real-time d-axis current signal id and the real-time q-axis current signal i q , and the track migration control subsystem receives the d and q-axis decoupling voltage signal d.
- the q-axis voltage stability range solving subsystem uses the load excitation matrix value function to identify the current load excitation.
- the acquisition process of the load excitation matrix value function is as follows: using the meshless method finite element simulation technology to reconstruct the load excitation time domain response matrix, the flow field term and the pressure term are processed separately when space discretization is performed. After space discretization, the function expression between the flow field quantity and the pressure quantity on the meshless node is as follows:
- ⁇ ij is the flow field at node ij
- ⁇ L and ⁇ R are the flow field at the left and right ends of node ij, respectively
- m ij is the mass of node ij
- P ij is the pressure at node ij
- k is an optional parameter
- ⁇ i is the flow field of node i
- ⁇ j is the flow field of node j
- S i and S j are the limiter functions
- the speed, torque, inlet pressure, outlet pressure, air flow, inlet temperature, outlet temperature and other test data of the ultra-high-speed electric air compressor are obtained, and the penalty function is used to impose the boundary conditions of the finite element mesh:
- ⁇ is the boundary penalty factor, is the flow field at the boundary nodes of the finite element mesh, S N is the boundary area, and ⁇ is the magnification system;
- f( ⁇ 1 , ⁇ 2 ,..., ⁇ n ) is the load excitation of the ultra-high-speed electric air compressor
- y a is the response of the measuring point at time a obtained from the actual test
- Y p is the past row space
- Y f is the future row space
- Orthogonal triangular decomposition is used to reduce the Hankel matrix, and the orthogonal projection matrix of Y f on Y p is obtained.
- the singular value decomposition of the orthogonal projection matrix is used to construct the time-domain response state equation of the ultra-high-speed electric air compressor load excitation. for:
- a is the Hankel matrix with only one block row
- W a and V a are the residuals
- B and D are the time-domain state matrix and the time-domain output matrix, respectively, is the Kalman filter matrix
- ⁇ is the eigenvector matrix
- the direct inversion method is used to realize the identification of the load excitation matrix value function.
- the complex time-varying load excitation matrix value function of the ultra-high-speed electric air compressor is expressed as:
- H( ⁇ ) + is the inverse matrix of the load excitation frequency response function matrix
- X( ⁇ ) is the load excitation time domain response matrix
- step (2) the d and q axis voltage stability range solving subsystem uses the preset motor electromagnetic and mechanical parameters and the identified current load excitation to obtain the d and q axis voltage stability ranges under the current load conditions
- f e is the electromagnetic excitation
- ⁇ e is the rotor electrical angular velocity
- ⁇ 1 is a small parameter ( ⁇ 1 ⁇ 0)
- relative to the formula (9 ) is a nearly constant slow variable
- ⁇ is the electrical angular velocity
- ud is the d -axis voltage
- ⁇ is the permanent magnet flux linkage
- u q is the q-axis voltage
- ⁇ is the electromagnetic torque coefficient
- T L is the motor load torque
- F( ⁇ 1 , ⁇ 2 ,... ⁇ n ) represents the load excitation
- the objective function of the chaotic optimization method is defined as:
- i' d is the optimal solution of the d-axis current
- i' q is the optimal solution of the q-axis current
- ⁇ ' is the optimal solution of the motor speed
- the distance is the radius, and the exact solution of the equilibrium point is searched by the conjugate gradient method.
- the search radius of the conjugate gradient method can be calculated by the following formula:
- ⁇ is the difference between the local accurate solution of the equilibrium point obtained by the previous conjugate gradient method and the global optimal solution of the equilibrium point obtained by the chaotic optimization method this time;
- ⁇ is the characteristic root corresponding to the Jacobian matrix of the linear dynamic model, and a 1 , a 2 , and a 3 are coefficients;
- Step (3) according to the stable range of the d and q axis voltages under the current load conditions, the track positioning control subsystem and the track migration control subsystem correct the input d and q axis decoupling voltage signals, and output d and q axis voltage commands value
- the layered control mode is adopted, and the upper layer control uses the orbital positioning control, which is based on the stable numerical range of the d and q axis voltages of the ultra-high-speed electric air compressor;
- the lower layer of the controller uses orbital migration control to implement corresponding control means for the desired control target.
- the orbit positioning control subsystem requires the existence of a convergence domain C in the phase space, so that the adjacent orbits converge with each other, and the d and q-axis voltage stability numerical ranges obtained by the solution are taken as the convergence domain C, and the bifurcation parameters directly intervene in the ultra-high-speed electrodynamic space.
- the controlled form of the compressor expansion control can be expressed as:
- the maximum value of the sum of the squares of the d and q axis voltages is taken as the desired control target:
- the orbit migration control subsystem transfers the system into the target domain, the desired control target g ⁇ C, the system state variables and the desired control target are
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Abstract
提供了一种提高大范围调速响应能力的超高速电动空压机变电压扩稳控制系统及方法，将变电压扩稳控制模块嵌入在电压解耦控制模块之后，d、q轴电压稳定范围求解子系统接收实时转速信号、实时d轴和q轴电流信号，利用负载激励矩阵值函数辨识当前的负载激励，d、q轴电压稳定范围求解子系统利用预设的电机电磁、机械参数以及辨识的当前负载激励，获得当前负载条件下d、q轴电压稳定范围，依据当前负载条件下d、q轴电压稳定范围，轨道定位控制子系统、轨道迁移控制子系统对输入的d、q轴解耦电压信号进行修正，输出d、q轴电压指令值。由此使得超高速电动空压机有效抵抗负载激励影响，从而减弱转速激振，降低振动噪声，缩短响应时间。
Description
本发明属于超高速电动空压机扩稳控制领域，尤其涉及一种提高大范围调速响应能力的超高速电动空压机变电压扩稳控制系统及方法。
超高速电动空压机是燃料电池系统必不可少的核心部件，为燃料电池系统提供充足的空气，保证燃料电池系统的功率输出。然而，超高速电动空压机大范围快速调速时转速突变，引发离心式涡轮增压装置内部流量陡增、出口气体流动不稳定性加强，提高离心式涡轮增压装置内部气体流速，使得负载激励的幅值和频率快速上升。超高速电动空压机负载激励的幅值和频率激增，与电磁激励共同作用下逐渐侵蚀其稳定域，并诱发超高速电动空压机最终失去稳定性，使得超高速电动空压机转速激振和振动噪声异常严重。
中国专利(CN110069033A)提供了一种燃料电池空压机流量控制方法，通过预测得到的车速，计算对应车速下燃料电池所需提供的功率和空压机所需输出的空气流量，并基于该输出目标进行空压机的转速控制，适应工况的变化。该专利存在的问题在于：简单地依靠功率需求进行转速控制，在转速控制时没有考量超高速空压机在负载激励影响下产生的转速激振，振动噪声大，响应时间长。
中国专利(CN110729503A)提供了用于切换氢燃料电池空压机模式的方法，依据空压机转速和需求功率，根据当前执行的切换方式，实现空压机的闭环或开环控制的切换，能够提高空气流量控制精度和控制响应性，在低转速、小负荷区域也能够保证空气控制系统的稳定。这种方法重视了超高速空压机转速控制的响应问题，但仍存在下述问题：超高速电动空压机在超高速区间内进行大范围快速调速时，模式切换已经无法调控负载激励引起的转速激振，只能确保在低转速、小负荷区域的稳定运行。
当前，随着燃料电池系统技术的发展，超高速电动空压机的稳定性问题已经突出地摆在了研究人员的面前，从负载激励入手，提出一种有效解决超高速电动空压机稳定性问题的扩稳控制方法具有极高的现实意义。
发明内容
针对现有技术中存在不足，本发明提供了一种提高大范围调速响应能力的超高速电动空压机变电压扩稳控制系统及方法，引入动力学理论对超高速电动空压机稳定性进行分析，实现超高速电动空压机的扩稳控制，能够显著压缩超高速电动空压机的响应时间，降低振动噪 声，提升稳定性。
本发明是通过以下技术手段实现上述技术目的的。
一种提高大范围调速响应能力的超高速电动空压机变电压扩稳控制系统，包括变电压扩稳控制模块，所述变电压扩稳控制模块包括d、q轴电压稳定范围求解子系统、轨道定位控制子系统和轨道迁移控制子系统，所述d、q轴电压稳定范围求解子系统根据输入的实时转速和d、q轴电流，输出d、q轴电压稳定范围给轨道定位控制子系统，所述轨道定位控制子系统计算出目标收敛域，传递给轨道迁移控制子系统，所述轨道迁移控制子系统根据目标收敛域及d、q轴解耦电压获取d、q轴电压指令，作为变电压扩稳控制模块的输出。
一种提高大范围调速响应能力的超高速电动空压机变电压扩稳控制方法，包括步骤：
步骤(1)，d、q轴电压稳定范围求解子系统接收实时转速信号、实时d轴电流信号和实时q轴电流信号，轨道迁移控制子系统接收d、q轴解耦电压信号；d、q轴电压稳定范围求解子系统利用负载激励矩阵值函数辨识当前的负载激励
步骤(2)，d、q轴电压稳定范围求解子系统利用预设的电机电磁、机械参数以及辨识的当前负载激励，获得当前负载条件下d、q轴电压稳定范围
步骤(3)，依据当前负载条件下d、q轴电压稳定范围，轨道定位控制子系统、轨道迁移控制子系统对输入的d、q轴解耦电压信号进行修正，输出d、q轴电压指令值。
进一步地，所述负载激励矩阵值函数为F(ω)＝H(ω)
+X(ω)，其中H(ω)
+为负载激励频响函数矩阵的逆矩阵，X(ω)为负载激励时域响应矩阵。
进一步地，所述负载激励矩阵值函数的获取过程为：利用无网格法进行有限元仿真技术重构生成负载激励时域响应矩阵，采用罚函数施加有限元网格的边界条件，时间步迭代得到超高速电动空压机负载激励时域响应矩阵；将所述负载激励时域响应矩阵重构为Hankel矩阵，采用正交三角分解及特征值分解，得到超高速电动空压机的负载激励频响函数矩阵，利用直接求逆法实现负载激励矩阵值函数的辨识，得到所述负载激励矩阵值函数。
进一步地，所述当前负载条件下d、q轴电压稳定范围，通过辨识的负载激励、d轴电压与q轴电压的三参数耦合分岔集确定。
进一步地，所述三参数耦合分岔集由求解Fold分岔和Hopf分岔临界条件获取。
进一步地，所述d、q轴电压稳定范围的获取，需要计算系统的平衡点，具体为：建立超高速电动空压机高维度、多尺度非线性动力学模型，使用混沌寻优法搜索平衡点全局最优解，以每次混沌寻优法得到的平衡点全局最优解为搜索初值，以上一次共轭梯度法求得的平衡点局部精确解和本次混沌寻优法求得的平衡点全局最优解的距离为半径，利用共轭梯度法搜索 平衡点精确解。
进一步地，所述d、q轴电压稳定数值范围作为收敛域C，d、q轴电压平方之和最大值作为期望控制目标g，期望控制目标g∈C，系统状态变量将自动趋向于g，完成分岔参数直接干预的超高速电动空压机扩稳控制。
本发明的有益效果为：本发明从抵抗较强负载激励的目标着手，将变电压扩稳控制模块嵌入在电压解耦控制模块之后，变电压扩稳控制模块对负载激励进行准确估计，计算保证系统安全稳定运行的d、q轴电压数值范围，施加控制得到d、q轴电压指令作为变电压扩稳控制模块的输出，使得超高速电动空压机能够抵抗较强负载激励。本发明从根本上解决了超高速电动空压机产生转速激振的问题，降低了振动噪声；转速激振的减少使得转速平滑过渡，免于进行额外的超调处理，响应时间被进一步压缩。本发明能够自适应负载的变化，尤其适应全功率燃料电池系统带来的极端工况。
图1为本发明所述高速电动空压机变电压扩稳控制系统架构图；
图2为本发明所述高速电动空压机变电压扩稳控制原理图。
下面结合附图以及具体实施例对本发明作进一步的说明，但本发明的保护范围并不限于此。
如图1所示，一种提高大范围调速响应能力的超高速电动空压机变电压扩稳控制系统，将变电压扩稳控制模块嵌入在电压解耦控制模块之后，对负载激励进行准确估计，计算保证系统安全稳定运行的d、q轴电压数值范围，施加控制得到d、q轴电压指令
和
作为变电压扩稳控制模块的输出，使得超高速电动空压机能够抵抗较强负载激励。
所述变电压扩稳控制模块接收电压解耦模块发送的d、q轴解耦电压信号
和
同时依靠电流环、转速环接收用于负载激励实时辨识所需信号，输出d、q轴电压指令，坐标转换模块将d、q轴电压指令转换为U
α和U
β，并由SVPWM模块输出六脉IGBT控制信号；与此同时，角速度计算模块、位置检测模块实时检测转子位置及电角速度采样值，用于完成空压机控制。
所述变电压扩稳控制模块包括d、q轴电压稳定范围求解子系统、轨道定位控制子系统、轨道迁移控制子系统。所述d、q轴电压稳定范围求解子系统根据输入的实时转速ω
r以及d、q轴电流i
d和i
q，输出d、q轴电压稳定范围给轨道定位控制子系统；轨道定位控制子系统计 算出目标收敛域，传递给轨道迁移控制子系统；轨道迁移控制子系统根据目标收敛域及d、q轴解耦电压
和
完成分岔参数直接干预的超高速电动空压机扩稳控制。
一种提高大范围调速响应能力的超高速电动空压机变电压扩稳控制方法，具体包括如下步骤：
步骤(1)，d、q轴电压稳定范围求解子系统接收实时转速信号ω
r、实时d轴电流信号i
d和实时q轴电流信号i
q，轨道迁移控制子系统接收d、q轴解耦电压信号
d、q轴电压稳定范围求解子系统利用负载激励矩阵值函数辨识当前的负载激励，负载激励矩阵值函数的获取过程具体为：使用无网格法有限元仿真技术重构生成负载激励时域响应矩阵，进行空间离散时对流场项和压力项分开处理，空间离散后无网格节点上流场量与压力量之间的函数表达形式为：
式中：φ
ij为节点ij的流场量，φ
L和φ
R分别为节点ij左右两端的流场量，m
ij为节点ij的质量，P
ij为节点ij的压力量；
为了精确地捕捉引起负载激励的压力脉动，需构造无振荡的高阶格式，使用线性网格分布函数代替常值网格分布函数，重构后得到空间离散后无网格节点上流场量为：
式中：
和
分别为向前和向后的差分因子，k为可供选择的参数，φ
i为节点i的流量场，φ
j为节点j的流量场，S
i、S
j为限制器函数；
根据台架试验获取超高速电动空压机的转速、转矩、进口压力、出口压力、空气流量、进口温度、出口温度等试验数据，采用罚函数施加有限元网格的边界条件：
式中：α为边界罚因子，
为有限元网格边界节点的流场量，S
N为边界区域，δ为放大系；
在完成空间离散、流场量重构及边界条件获取后，进行时间步迭代，得到超高速电动空压机负载激励时域响应矩阵为：
式中：f(ω
1,ω
2,···,ω
n)为超高速电动空压机负载激励；
将超高速电动空压机负载激励时域响应矩阵重构为Hankel矩阵：
式中：y
a为实际测试所得的a时刻测点的响应，Y
p为过去行空间，Y
f为将来行空间；
采用正交三角分解对Hankel矩阵进行缩减处理，得到Y
f在Y
p上的正交投影矩阵，对正交投影矩阵进行奇异值分解，构建超高速电动空压机负载激励的时域响应状态方程为：
式中：Y
a|a为只有一个块行的Hankel矩阵，W
a、V
a为残差，B和D分别为时域状态矩阵与时域输出矩阵，
为卡尔曼滤波矩阵；
将时域状态矩阵B进行特征值分解，求得超高速电动空压机负载激励频响函数矩阵：
H(ω)＝κ
-1Bκ+Dκ (7)
式中：κ为特征矢量矩阵；
采用直接求逆法实现负载激励矩阵值函数辨识，超高速电动空压机复杂时变负载激励矩阵值函数表示为：
F(ω)＝H(ω)
+X(ω) (8)
式中：H(ω)
+为负载激励频响函数矩阵的逆矩阵，X(ω)为负载激励时域响应矩阵。
步骤(2)，d、q轴电压稳定范围求解子系统利用预设的电机电磁、机械参数以及辨识的当前负载激励，获得当前负载条件下d、q轴电压稳定范围
d、q轴电压稳定范围获取时需要计算系统的平衡点，首先建立超高速电动空压机高维度、多尺度非线性动力学模型：
式中：w＝f
e(cosω
et,ε)表示电磁激励项，f
e为电磁激励，ω
e为转子电角速度，ε
1为小参量(ε
1＜＜0)，相对于式(9)是一个近乎恒定的慢变量；ω为电角速度，u
d为d轴电压，γ为永磁体磁链，u
q为q轴电压，σ为电磁转矩系数，T
L为电机负载转矩，F(ω
1,ω
2,…ω
n)表示负载激励；
使用混沌寻优法搜索平衡点全局最优解，混沌寻优法的目标函数定义为：
min f(i′
d,i′
q,ω′)＝|i′
d|+|i′
q|+|ω′| (10)
式中：i′
d为d轴电流最优解，i′
q为q轴电流最优解，ω′为电机转速最优解；
以每次混沌寻优法得到的平衡点全局最优解为搜索初值，以上一次共轭梯度法求得的平衡点局部精确解与本次混沌寻优法求得的平衡点全局最优解的距离为半径，利用共轭梯度法搜索平衡点精确解，共轭梯度法搜索半径可由下式计算得到：
其中，Δ为上一次共轭梯度法求得的平衡点局部精确解和本次混沌寻优法求得的平衡点全局最优解之间的差值；
式(9)所示的超高速电动空压机高维度、多尺度非线性动力学模型的雅可比矩阵对应特征方程可以表示为：
det＝λ
3+a
1λ
2+a
2λ+a
3 (12)
式中：λ为所述线性动力学模型的雅可比矩阵对应的特征根，a
1、a
2、a
3为系数；
系统平衡点产生Fold分岔的临界条件为：
若式(12)存在一对纯虚特征根和负实特征根，会导致系统平衡点全部失去稳定性产生Hopf分岔，设负实特征根λ
1＝-υ(κ)、一对纯虚特征根
则产生Hopf分岔需要满足下列条件：
式中：
为系统产生Hopf分岔时变量
的参数值，R
e为稳定域，υ为实特征根，τ为特征根实部，ζ为特征根虚部；
Fold分岔和Hopf分岔临界条件给出辨识的负载激励、d轴电压与q轴电压的三参数耦合分岔集，从而确定了该负载条件下能够保证超高速电动空压机稳定运行的d、q轴电压范围。
步骤(3)，依据当前负载条件下d、q轴电压稳定范围，轨道定位控制子系统、轨道迁移控制子系统对输入的d、q轴解耦电压信号进行修正，输出d、q轴电压指令值
如图2所示，在进行d、q轴解耦电压修正时，采用分层控制模式，上层控制使用轨道定位控制，以超高速电动空压机d、q轴电压稳定数值范围为基础；控制器下层使用轨道迁移控制，对期望控制目标实施相应控制手段。
轨道定位控制子系统要求在相空间中存在收敛域C，使得在其邻近轨道相互收敛，将求解得到的d、q轴电压稳定数值范围作为收敛域C，分岔参数直接干预的超高速电动空压机扩稳控制的受控形式可以表示为：
式中：g为期望控制目标，S(t)为控制开关。
考虑到极限压缩超高速电动空压机调速时间的需要，将d、q轴电压平方之和最大值作为期望控制目标：
在完成目标域构建后，轨道迁移控制子系统将系统转入目标域内，期望控制目标g∈C，系统状态变量和期望控制目标有||x(t)-g||<ε
2(ε
2为小参量，ε
2＜＜0)，系统状态变量将自动趋向于g，完成分岔参数直接干预的超高速电动空压机扩稳控制。
所述实施例为本发明的优选的实施方式，但本发明并不限于上述实施方式，在不背离本发明的实质内容的情况下，本领域技术人员能够做出的任何显而易见的改进、替换或变型均属于本发明的保护范围。
Claims (8)
- 一种提高大范围调速响应能力的超高速电动空压机变电压扩稳控制系统，其特征在于，包括变电压扩稳控制模块，所述变电压扩稳控制模块包括d、q轴电压稳定范围求解子系统、轨道定位控制子系统和轨道迁移控制子系统，所述d、q轴电压稳定范围求解子系统根据输入的实时转速和d、q轴电流，输出d、q轴电压稳定范围给轨道定位控制子系统，所述轨道定位控制子系统计算出目标收敛域，传递给轨道迁移控制子系统，所述轨道迁移控制子系统根据目标收敛域及d、q轴解耦电压获取d、q轴电压指令，作为变电压扩稳控制模块的输出。
- 一种根据权利要求1所述的提高大范围调速响应能力的超高速电动空压机变电压扩稳控制系统的控制方法，其特征在于，包括步骤：步骤(1)，d、q轴电压稳定范围求解子系统接收实时转速信号、实时d轴电流信号和实时q轴电流信号，轨道迁移控制子系统接收d、q轴解耦电压信号；d、q轴电压稳定范围求解子系统利用负载激励矩阵值函数辨识当前的负载激励；步骤(2)，d、q轴电压稳定范围求解子系统利用预设的电机电磁、机械参数以及辨识的当前负载激励，获得当前负载条件下d、q轴电压稳定范围；步骤(3)，依据当前负载条件下d、q轴电压稳定范围，轨道定位控制子系统、轨道迁移控制子系统对输入的d、q轴解耦电压信号进行修正，输出d、q轴电压指令值。
- 根据权利要求2所述的超高速电动空压机变电压扩稳控制方法，其特征在于，所述负载激励矩阵值函数为F(ω)＝H(ω) +X(ω)，其中H(ω) +为负载激励频响函数矩阵的逆矩阵，X(ω)为负载激励时域响应矩阵。
- 根据权利要求3所述的超高速电动空压机变电压扩稳控制方法，其特征在于，所述负载激励矩阵值函数的获取过程为：利用无网格法进行有限元仿真技术重构生成负载激励时域响应矩阵，采用罚函数施加有限元网格的边界条件，时间步迭代得到超高速电动空压机负载激励时域响应矩阵；将所述负载激励时域响应矩阵重构为Hankel矩阵，采用正交三角分解及特征值分解，得到超高速电动空压机的负载激励频响函数矩阵，利用直接求逆法实现负载激励矩阵值函数的辨识，得到所述负载激励矩阵值函数。
- 根据权利要求2所述的超高速电动空压机变电压扩稳控制方法，其特征在于，所述当前负载条件下d、q轴电压稳定范围，通过辨识的负载激励、d轴电压与q轴电压的三参数耦合分岔集确定。
- 根据权利要求2所述的超高速电动空压机变电压扩稳控制方法，其特征在于，所述三参数耦合分岔集由求解Fold分岔和Hopf分岔临界条件获取。
- 根据权利要求2所述的超高速电动空压机变电压扩稳控制方法，其特征在于，所述d、 q轴电压稳定范围的获取，需要计算系统的平衡点，具体为：建立超高速电动空压机高维度、多尺度非线性动力学模型，使用混沌寻优法搜索平衡点全局最优解，以每次混沌寻优法得到的平衡点全局最优解为搜索初值，以上一次共轭梯度法求得的平衡点局部精确解和本次混沌寻优法求得的平衡点全局最优解的距离为半径，利用共轭梯度法搜索平衡点精确解。
- 根据权利要求2所述的超高速电动空压机变电压扩稳控制方法，其特征在于，所述d、q轴电压稳定数值范围作为收敛域C，d、q轴电压平方之和最大值作为期望控制目标g，期望控制目标g∈C，系统状态变量将自动趋向于g，完成分岔参数直接干预的超高速电动空压机扩稳控制。
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