技术领域technical field
本发明涉及电力电子技术领域，尤其涉及一种三相PWM整流器BP神经网络PI参数自整定方法。The invention relates to the technical field of power electronics, in particular to a BP neural network PI parameter self-tuning method for a three-phase PWM rectifier.
背景技术Background technique
电动汽车符合当今社会“环保”、“节能”的主题，受到了广泛关注。AC-DC变换器是车载充电系统的重要组成部分，其中，PWM整流器以其能量可双向流动、高功率因数运行、谐波含量少等性能得到广泛应用。PI控制器因其结构简单、实用性强被广泛应用于工业生产过程中。对于PI参数的整定，一般使用试凑法完成，但试凑过程既耗时又耗力，并且当系统的运行状态发生变化时，依靠试凑出的PI参数并不能保证系统的稳定性和暂态性能。三相PWM整流器为典型的非最小相位系统，当整定电压外环PI参数时，由于其控制对象具有右半平面零点，所以为PI参数的整定以及稳定性的判断带来困难，导致无法直接基于传统频域法通过稳定裕度进行整定与判稳。因此，以致稳为目标的PI参数自动整定逐渐成为研究热点。Electric vehicles conform to the themes of "environmental protection" and "energy saving" in today's society, and have received widespread attention. The AC-DC converter is an important part of the vehicle charging system. Among them, the PWM rectifier is widely used because of its bidirectional energy flow, high power factor operation, and low harmonic content. PI controller is widely used in industrial production process because of its simple structure and strong practicability. For the tuning of PI parameters, the trial and error method is generally used to complete, but the trial and error process is time-consuming and labor-intensive, and when the operating state of the system changes, relying on the PI parameters obtained by trial and error cannot guarantee the stability and temporary stability of the system. state performance. The three-phase PWM rectifier is a typical non-minimum phase system. When setting the PI parameters of the voltage outer loop, because its control object has a right-half-plane zero point, it brings difficulties to the setting of the PI parameters and the judgment of stability, which makes it impossible to directly base on The traditional frequency domain method uses the stability margin to adjust and determine the stability. Therefore, the automatic tuning of PI parameters with the goal of achieving stability has gradually become a research hotspot.
对于非最小相位系统右半平面零点的问题，现有解决方法主要包括参数优化设计、补偿控制等。B.Yin等通过忽略某些动态因素，并应用前馈去耦控制器，将多输入多输出的三相PWM整流器非线性非最小相位模型转化为单输入单输出的线性最小相位模型，并设计相应控制器进行控制[B.Yin,R.Oruganti,and S.K.Panda.A simple single-input–single-output(SISO)model for a three-phase PWM rectifier.IEEE Trans.PowerElectron.,Mar.2009,24(3):620-631,]。但该方法仅适用于系统传递函数的穿越频率远小于右半平面零点转折频率的情况，具有一定的局限性。F.A.Villarroel等考虑了短视距时，整流器非最小相位零点可能导致的稳定性问题，提出了一种面向非最小相位三相PWM整流器的预测性最短视距电压控制方法[F.A.Villarroel et al.Apredictive shortest-horizon voltage control algorithm for non-minimum phase three-phaserectifiers.IEEE Access.,2022,10:107598-107615]。但此方法由于增加了三个方程的评估，运算量大。For the right-half-plane zero problem of non-minimum phase systems, the existing solutions mainly include parameter optimization design, compensation control, etc. By ignoring some dynamic factors and applying a feed-forward decoupling controller, B.Yin et al. transformed the nonlinear non-minimum phase model of the three-phase PWM rectifier with multiple inputs and multiple outputs into a linear minimum phase model with single input and single output, and designed The corresponding controller is controlled [B.Yin, R.Oruganti, and S.K.Panda. A simple single-input–single-output (SISO) model for a three-phase PWM rectifier.IEEE Trans.PowerElectron.,Mar.2009,24 (3): 620-631,]. However, this method is only applicable to the case where the crossover frequency of the system transfer function is much smaller than the right-half-plane zero-point corner frequency, and has certain limitations. F.A.Villarroel et al. considered the stability problem that may be caused by the non-minimum phase zero point of the rectifier when the short-sight distance is short, and proposed a predictive shortest-sight voltage control method for non-minimum phase three-phase PWM rectifiers [F.A.Villarroel et al.Apredictive shortest -horizon voltage control algorithm for non-minimum phase three-phase rectifiers.IEEE Access.,2022,10:107598-107615]. However, this method has a large amount of computation due to the addition of the evaluation of three equations.
关于控制器PI参数的自整定方法主要有继电反馈技术、模糊控制理论、智能算法等。W.Stefanutti等将继电反馈技术运用于DC-DC变换器中，在变换器软启动期间引入输出电压扰动，通过迭代方法整定PI参数[W.Stefanutti,P.Mattavelli,andS.Saggini.Autotuning of digitally controlled DC–DC converters based on relayfeedback.IEEE Trans.Power Electron.,Jan.2007,22(1):199-207]。但继电反馈法在进行自整定时需要向系统注入扰动，会降低系统的运行性能，且难以实现在线整定。H.Lin等针对三相三电平中性点钳位有源前端整流器，提出了一种由3个控制环组成的模糊滑模控制策略，复杂度低，且可以抑制抖振现象[H.Lin et al.Fuzzy sliding-mode control forthree-level NPC AFE rectifiers:a chattering alleviation approach.IEEETrans.Power Electron.,Oct.2022,37(10):11704-11715]。但信息简单的模糊处理将导致系统的控制精度降低和动态品质变差；若要提高精度就必然增加量化级数，导致搜索范围扩大，降低决策速度。The self-tuning methods of controller PI parameters mainly include relay feedback technology, fuzzy control theory, intelligent algorithm and so on. W. Stefanutti et al applied the relay feedback technology to the DC-DC converter, introduced the output voltage disturbance during the soft start of the converter, and adjusted the PI parameters by an iterative method [W. Stefanutti, P. Mattavelli, and S. Saggini. Autotuning of Digitally controlled DC–DC converters based on relay feedback. IEEE Trans. Power Electron., Jan. 2007, 22(1): 199-207]. However, the relay feedback method needs to inject disturbance into the system during self-tuning, which will reduce the operating performance of the system, and it is difficult to realize online tuning. H. Lin et al. proposed a fuzzy sliding mode control strategy consisting of three control loops for three-phase three-level neutral point clamped active front-end rectifiers, which has low complexity and can suppress chattering [H. Lin et al. Fuzzy sliding-mode control forthree-level NPC AFE rectifiers: a chattering elevation approach. IEEE Trans. Power Electron., Oct. 2022, 37(10): 11704-11715]. However, the simple fuzzy processing of information will lead to the reduction of the control precision and the deterioration of the dynamic quality of the system; if the precision is to be improved, the number of quantization series must be increased, resulting in the expansion of the search range and the reduction of decision-making speed.
人工神经网络由于其较强的非线性拟合能力和相对简单的学习算法，在工业中有着越来越多的应用。W.Dong提出一种基于人工神经网络(ANN)的DC/DC降压变换器控制方法。ANN经过训练，可以基于近似动态规划(ADP)实现最佳控制。并通过实验证明ANN控制器能够跟踪快速变化的参考命令，在可变负载下保持稳定的输出电压[W.Dong,S.Li,andX.Fu.Control of a buck DC/DC converter using approximate dynamic programmingand artificial neural networks.IEEE Trans.Circuits Syst.,Apr.2021,68(4):1760-1768]。X.Fu等使用循环神经网络对单相并网逆变器进行控制，基于自适应动态规划原理对神经网络进行训练，以达到近似最优控制[X.Fu and S.Li.Control of single-phasegrid-connected converters with LCL filters using recurrent neural network andconventional control methods.IEEE Trans.Power Electron.,Jul.2016,31(7):5354-5364]。M.Mehrasa等针对不同工作变化下的并网九电平封装电池逆变器提出了一种经过训练的人工神经网络(ANN)输入输出反馈线性化(IOFL)控制策略[M.Mehrasa,M.Babaie,andM.Sharifzadeh.An input–output feedback linearization control methodsynthesized by artificial neural network for grid-tied packed E-Cellinverter.IEEE Trans.Ind.Appl.,Jun.2021,57(3):3131-3142]。但以上方法对神经网络整定过程缺乏约束，且神经网络的初始加权系数及初始学习率的选取具有一定的随机性，若选取不当可能导致系统失稳。Due to its strong nonlinear fitting ability and relatively simple learning algorithm, artificial neural network has more and more applications in industry. W.Dong proposed a DC/DC step-down converter control method based on artificial neural network (ANN). The ANN is trained to achieve optimal control based on Approximate Dynamic Programming (ADP). And it is proved by experiments that the ANN controller can track the rapidly changing reference command and maintain a stable output voltage under variable load [W. Dong, S. Li, and X. Fu. Control of a buck DC/DC converter using approximate dynamic programming and artificial neural networks.IEEE Trans.Circuits Syst.,Apr.2021,68(4):1760-1768]. X.Fu et al. used the recurrent neural network to control the single-phase grid-connected inverter, and trained the neural network based on the principle of adaptive dynamic programming to achieve approximate optimal control [X.Fu and S.Li.Control of single- phase grid-connected converters with LCL filters using recurrent neural network and conventional control methods. IEEE Trans. Power Electron., Jul. 2016, 31(7): 5354-5364]. M.Mehrasa et al. proposed a trained artificial neural network (ANN) input-output feedback linearization (IOFL) control strategy for grid-connected nine-level packaged battery inverters under different operating conditions [M.Mehrasa, M. Babaie, and M. Sharifzadeh. An input–output feedback linearization control method synthesized by artificial neural network for grid-tied packed E-Cellinverter. IEEE Trans. Ind. Appl., Jun. 2021, 57(3):3131-3142]. However, the above methods lack constraints on the neural network tuning process, and the selection of the initial weight coefficient and initial learning rate of the neural network has a certain degree of randomness, and improper selection may lead to system instability.
发明内容Contents of the invention
针对现有技术中存在的缺陷，本发明的目的是提出一种三相PWM整流器BP神经网络PI参数自整定方法，通过右半平面零点串联补偿方法将三相PWM整流器补偿为最小相位系统，在此基础上构造以穿越频率、相角裕度为性能指标的稳定性约束条件，使用BP神经网络在稳定性条件约束下根据系统运行状态进行PI参数自整定，保证整流器工作在稳定裕度内，提高动态响应性能。For the defects existing in the prior art, the purpose of the present invention is to propose a three-phase PWM rectifier BP neural network PI parameter self-tuning method, and the three-phase PWM rectifier is compensated as the minimum phase system by the right half-plane zero-point series compensation method. On this basis, the stability constraint conditions with crossover frequency and phase angle margin as performance indicators are constructed, and the BP neural network is used to perform self-tuning of PI parameters according to the system operating state under the constraints of stability conditions, so as to ensure that the rectifier works within the stability margin. Improve dynamic response performance.
为达到以上目的，本发明采用的技术方案是：一种三相PWM整流器BP神经网络PI参数自整定方法，其中，包括以下步骤：For achieving above object, the technical scheme that the present invention adopts is: a kind of three-phase PWM rectifier BP neural network PI parameter self-tuning method, wherein, comprise the following steps:
(1)考虑了三相PWM整流器非最小相位性质，设计右半平面零点串联补偿环节，将非最小相位系统补偿为最小相位系统；(1) Considering the non-minimum phase property of the three-phase PWM rectifier, the right-half-plane zero point series compensation link is designed to compensate the non-minimum phase system to the minimum phase system;
(2)所使用神经网络为反向传播(BP)神经网络，PI参数整定方法为使神经网络输出层神经元的输出对应于PI参数，通过神经网络的自身学习算法，对各层神经元加权系数在线调整，以得到最优控制律下的PI参数；(2) The neural network used is a backpropagation (BP) neural network, and the PI parameter tuning method is to make the output of the neurons in the output layer of the neural network correspond to the PI parameters, and weight the neurons of each layer through the self-learning algorithm of the neural network The coefficients are adjusted online to obtain the PI parameters under the optimal control law;
(3)采用模糊原理对BP神经网络输入层输入进行归一化处理；(3) The fuzzy principle is used to normalize the input of the BP neural network input layer;
(4)在BP神经网络输出层神经元加权系数修正过程中引入系统的穿越频率与相角裕度作为稳定性能指标，以使稳定性能指标在稳定范围内作为约束规则对BP神经网络输出即PI参数进行约束；(4) In the process of correcting the weight coefficients of neurons in the output layer of the BP neural network, the crossover frequency and phase angle margin of the system are introduced as stable performance indicators, so that the stable performance indicators are within the stable range as constraint rules for the output of the BP neural network, that is, PI Parameters are constrained;
(5)由穿越频率、相角裕度与PI参数的关系引入稳定性修正系数对BP神经网络输出层神经元加权系数进行修正，进一步在保证系统稳定的前提下在线整定PI参数。(5) The stability correction coefficient is introduced from the relationship between crossing frequency, phase angle margin and PI parameters to modify the weighting coefficients of neurons in the output layer of BP neural network, and further adjust the PI parameters online under the premise of ensuring system stability.
进一步，右半平面零点补偿环节是根据零幅度误差跟踪技术设计的，补偿结构为串联补偿，所设计串联补偿环节置于电压外环PI控制器之后，用于补偿整流器传递函数中的右半平面零点。Furthermore, the right-half-plane zero point compensation link is designed according to the zero-amplitude error tracking technology, and the compensation structure is series compensation. The designed series compensation link is placed after the voltage outer loop PI controller to compensate the right half-plane in the rectifier transfer function. zero.
进一步，所使用BP神经网络输入层神经元个数M＝4，分别以三相PWM整流器直流母线电压、参考电压、输出电压误差以及参数1作为输入。隐含层设置为一层，其神经元个数n＝4，使用经验公式确定。输出层神经元个数L＝2，以电压环参数Kpu、Kiu作为神经网络输出。Further, the number of neurons in the input layer of the BP neural network used is M=4, and the three-phase PWM rectifier DC bus voltage, reference voltage, output voltage error and parameter 1 are used as inputs. The hidden layer is set to one layer, the number of neurons n=4, using the empirical formula Sure. The number of neurons in the output layer is L=2, and the voltage loop parameters Kpu and Kiu are used as the output of the neural network.
进一步，输入层输入归一化处理方法为“归档”模糊化处理，即根据输入变量模糊子集的隶属函数找出相应隶属度。Further, the input normalization processing method of the input layer is "archive" fuzzy processing, that is, to find out the corresponding degree of membership according to the membership function of the fuzzy subset of the input variables.
进一步，输出层各神经元加权系数为其调整式为(1)，其中η为学习速率，α为惯性系数，Udc(k+1)为直流母线电压，u(k)为PI控制器输出u(k)＝u(k-1)+Kpu[e(k)-e(k-1)]+Kiu[e(k)]，e(k+1)为直流母线电压输出误差，/>为输出层第l个神经元输出，为隐含层第i个神经元输出，sgn为符号函数。稳定性能指标的稳定范围为穿越频率处于10k rad～30k rad，相角裕度处于45°～120°。Further, the weighting coefficient of each neuron in the output layer is The adjustment formula is (1), where η is the learning rate, α is the inertia coefficient, Udc (k+1) is the DC bus voltage, u(k) is the output of the PI controller u(k)=u(k-1 )+Kpu [e(k)-e(k-1)]+Kiu [e(k)], e(k+1) is the DC bus voltage output error, /> is the output of the lth neuron in the output layer, is the output of the i-th neuron in the hidden layer, and sgn is a sign function. The stable range of the stable performance index is that the crossover frequency is 10k rad to 30k rad, and the phase angle margin is 45° to 120°.
进一步，穿越频率及相角裕度与电压环PI参数Kpu、Kiu的关系为(1)，穿越频率与Kpu及Kiu均呈递增关系；相角裕度与Kiu呈递减关系，与Kpu的关系为，当Kiu小于1时呈递减关系，当Kiu大于1时呈递增关系。输出层神经元加权系数修正方法为，当穿越频率小于稳定范围时，增大Kpu，即在(1)中，l＝0时增加m1ωu，当穿越频率大于稳定范围时，减小Kpu，即在(1)中，l＝0时减去m2ωu；当相角裕度小于稳定范围时，增大Kpu，即在(1)中，l＝0时增加当相角裕度大于稳定范围时，增大Kiu，即在(1)中，l＝1时增加/>其中，m1,m2,m3,m4为稳定性修正系数。则考虑稳定性约束的输出层加权系数修正式为(2)。Furthermore, the relationship between the crossover frequency and the phase angle margin and the voltage loop PI parameters Kpu and Kiu is (1), and the crossover frequency and Kpu andK iuare both in an increasing relationship; The relationship with Kpu is a decreasing relationship when Kiu is less than 1, and an increasing relationship when Kiu is greater than 1. The correction method of the weight coefficient of neurons in the output layer is: when the crossing frequency is less than the stable range, increase Kpu , that is, in (1), when l=0, increase m1 ωu , and when the crossing frequency is greater than the stable range, decrease Kpu , that is, in (1), when l=0, subtract m2 ωu ; when the phase angle margin is less than the stable range, increase Kpu , that is, in (1), increase when l=0 When the phase angle margin is greater than the stable range, increase Kiu , that is, increase when l=1 in (1) /> Among them, m1 , m2 , m3 , and m4 are stability correction coefficients. Then the correction formula of the weight coefficient of the output layer considering the stability constraint is (2).
本发明的效果在于：基于零幅度误差跟踪技术设计了三相PWM整流系统右半平面零点的串联补偿环节，将非最小相位系统近似补偿为最小相位系统，降低了右半平面零点对整流器运行性能的影响。且该补偿方法是控制算法上的补偿，无需额外硬件，具有成本低、实用性强、效果好的优点。在此基础上，提出了基于穿越频率与相角裕度的稳定性约束规则与调整方法，对BP神经网络的加权系数进行在线调整，可以用于确定一组较好的神经网络加权系数初始值，同时也可以保证三相PWM整流系统始终在所设置的稳定裕度下运行。综上所述，采用本发明所述方法可以根据所提稳定性能指标可以判断出整流器运行是否稳定，并及时调整使整流器由不稳定状态被调节到稳定状态。此外，还可以有效降低阶跃响应与负载突变时的电压超调与跌落，缩短调节时间，提高动态响应速度与运行稳定性。The effect of the present invention is: based on the zero-amplitude error tracking technology, the series compensation link of the right-half-plane zero point of the three-phase PWM rectification system is designed, and the non-minimum phase system is approximately compensated as the minimum phase system, which reduces the right-half-plane zero point to the operating performance of the rectifier Impact. Moreover, the compensation method is a compensation on a control algorithm, does not require additional hardware, and has the advantages of low cost, strong practicability, and good effect. On this basis, a stability constraint rule and adjustment method based on the crossing frequency and phase angle margin are proposed, and the online adjustment of the weighting coefficient of the BP neural network can be used to determine a set of better initial values of the weighting coefficient of the neural network. , it can also ensure that the three-phase PWM rectification system always operates under the set stability margin. To sum up, using the method of the present invention can judge whether the rectifier is running stably according to the proposed stability performance index, and adjust it in time so that the rectifier is adjusted from an unstable state to a stable state. In addition, it can effectively reduce the voltage overshoot and drop during step response and load mutation, shorten the adjustment time, and improve the dynamic response speed and operation stability.
附图说明Description of drawings
图1是本发明的整体流程图；Fig. 1 is the overall flowchart of the present invention;
图2是本发明使用的三相PWM整流器拓扑；Fig. 2 is the three-phase PWM rectifier topology that the present invention uses;
图3是三相PWM整流器双闭环控制传递函数框图；Fig. 3 is a block diagram of a three-phase PWM rectifier double closed-loop control transfer function;
图4是三相PWM整流器串联补偿结构框图；Fig. 4 is a block diagram of the series compensation structure of the three-phase PWM rectifier;
图5是BP神经网络结构；Fig. 5 is a BP neural network structure;
图6是神经网络PI控制器结构；Fig. 6 is neural network PI controller structure;
图7是穿越频率ωu及相角裕度关于Kpu，Kiu的函数图像；Figure 7 shows the crossover frequency ωu and the phase angle margin About Kpu , function image of Kiu ;
图8是整流器在稳定性约束下由不稳定到稳定状态实验结果；Figure 8 is the experimental result of the rectifier from unstable to steady state under stability constraints;
图9是BP神经网络PI自整定下整流器运行状态变化时的实验结果；Fig. 9 is the experimental result when the operating state of the rectifier changes under the BP neural network PI self-tuning;
图10是BP神经网络PI自整定与传统PI控制各阶段实验结果对比。Figure 10 is a comparison of the experimental results of BP neural network PI self-tuning and traditional PI control at each stage.
具体实施方式Detailed ways
下面结合说明书附图对本发明的具体实施方式作进一步详细的说明。The specific implementation manners of the present invention will be further described in detail below in conjunction with the accompanying drawings.
本发明设计的是一种三相PWM整流器BP神经网络PI参数自整定方法，基于零幅度误差跟踪技术设计串联补偿环节，对整流器传递函数右半平面零点进行补偿。在此基础上推导出穿越频率、相角裕度表达式，构造稳定性约束条件，对BP神经网络加权系数调整过程进行约束，使用BP神经网络实现PI参数自整定。图1是本发明的一个整体流程图。The invention designs a three-phase PWM rectifier BP neural network PI parameter self-tuning method, designs a series compensation link based on the zero amplitude error tracking technology, and compensates the zero point of the right half plane of the rectifier transfer function. On this basis, the crossover frequency and phase angle margin expressions are deduced, and the stability constraints are constructed to constrain the adjustment process of the weight coefficient of the BP neural network, and the PI parameter self-tuning is realized by using the BP neural network. Fig. 1 is an overall flow chart of the present invention.
具体实现步骤如下：The specific implementation steps are as follows:
步骤一，考虑三相PWM整流器非最小相位性质，设计右半平面零点串联补偿环节，将非最小相位系统补偿为最小相位系统。Step 1: Considering the non-minimum phase property of the three-phase PWM rectifier, design the right-half-plane zero point series compensation link, and compensate the non-minimum phase system to the minimum phase system.
图2为三相PWM整流器拓扑，定义开关函数Sk为式(3)。Fig. 2 is the topology of the three-phase PWM rectifier, and the switch function Sk is defined as formula (3).
三相PWM整流器在dq坐标系中的数学模型为式(4)。The mathematical model of the three-phase PWM rectifier in the dq coordinate system is formula (4).
令三相PWM整流器交流侧输出电压的d、q分量分别为vd、vq。Let the d and q components of the output voltage of the AC side of the three-phase PWM rectifier be vd and vq respectively.
vd＝udcSd vq＝udcSq (5)vd = udc Sd vq = udc Sq (5)
使用小信号建模引入拉氏变换得到整流器电压环被控对象即有功电流与直流母线电压的传递函数为式(6)。Using small-signal modeling and introducing Laplace transform, the transfer function of the controlled object of the rectifier voltage loop, that is, the active current and the DC bus voltage, is expressed as formula (6).
结合电流环的传递函数，可以画出双闭环控制传递函数结构框图如图3。则电压外环的传递函数为式(7)：Combined with the transfer function of the current loop, the structural block diagram of the double closed-loop control transfer function can be drawn as shown in Figure 3. Then the transfer function of the voltage outer loop is formula (7):
令式(7)中分子等于0，可发现存在一个右半平面零点z0＝ed/(LIq)。因此，三相PWM整流器的电压环为非最小相位系统。Setting the numerator in formula (7) equal to 0, it can be found that there is a right-half-plane zero point z0 =ed /(LIq ). Therefore, the voltage loop of the three-phase PWM rectifier is a non-minimum phase system.
本文采用三相PWM整流器右半平面零点串联补偿结构框图如图4所示。This paper uses the three-phase PWM rectifier right half-plane zero series compensation structure block diagram shown in Figure 4.
图4中，PI控制器用于控制系统的运行性能，串联补偿环节F(s)用于抵消被补偿环节G(s)即式(6)中存在的右半平面零点。可以得出电压环PI控制器输出Rin与输出电压Udc之间的传递函数为式(8)。In Fig. 4, the PI controller is used to control the operating performance of the system, and the series compensation link F(s) is used to offset the compensated link G(s), which is the right half-plane zero point in equation (6). It can be drawn that the transfer function between the voltage loop PI controller output Rin and the output voltage Udc is formula (8).
若上式中G(s)存在稳定逆，则补偿环节F(s)可以设置为该稳定逆，所以补偿环节F(s)可以表示为式(9)：If G(s) in the above formula has a stable inverse, then the compensation link F(s) can be set as the stable inverse, so the compensation link F(s) can be expressed as formula (9):
其中，P(s)为包含G(s)中所有极点的多项式，Zs(s)为包含所有左半平面零点的多项式，Zu(s)为包含所有右半平面零点的多项式，为Zu(s)的近似值。Zu(s)可以表示为式(10)。where P(s) is a polynomial containing all poles in G(s), Zs (s) is a polynomial containing all left-half-plane zeros, Zu (s) is a polynomial containing all right-half-plane zeros, is an approximate value of Zu (s). Zu (s) can be expressed as formula (10).
Zu(s)＝bunsn+bu(n-1)sn-1+...+bu0s0 (10)Zu (s)＝bun sn +bu(n-1) sn-1 +...+bu0 s0 (10)
确定后，即可完成对G(s)中右半平面零点的补偿。本文中采用零幅度误差跟踪技术来进行右半平面零点的串联补偿。Sure After that, the compensation for the zero point of the right half plane in G(s) can be completed. In this paper, the zero-amplitude error tracking technique is used to perform series compensation of the right-half-plane zero.
由式(6)和式(9)可以得到F(s)中各分量的表达式：The expressions of each component in F(s) can be obtained from formula (6) and formula (9):
令可以得到/>的表达式为式(12)。make can get /> The expression of is formula (12).
于是可以得到整流器右半平面零点补偿环节F(s)为：Therefore, the right half-plane zero point compensation link F(s) of the rectifier can be obtained as:
进一步得到系统整体传递函数为式(14)。The overall transfer function of the system is further obtained as formula (14).
取p＝1，此时系统为最小相位系统，可以通过稳定裕度等判断系统稳定性。Taking p=1, the system is the minimum phase system at this time, and the stability of the system can be judged by the stability margin and so on.
步骤二，选定所使用神经网络为反向传播(BP)神经网络，PI参数整定方法为使神经网络输出层神经元的输出对应于PI参数，通过神经网络的自身学习算法，对各层神经元加权系数在线调整，以得到最优控制律下的PI参数。Step 2, the neural network used is selected as the backpropagation (BP) neural network, and the PI parameter tuning method is to make the output of the neuron in the output layer of the neural network correspond to the PI parameter. Through the self-learning algorithm of the neural network, each layer of neurons The element weighting coefficients are adjusted online to obtain the PI parameters under the optimal control law.
本文所采用的BP神经网络结构如图5所示，本方法中，输入层神经元个数M＝4，将整流器的直流母线电压Udc、参考电压Uref、系统误差e以及常数1作为输入。输出层神经元个数L＝2，将电压环Kpu、Kiu作为输出。隐含层神经元数目根据经验公式(15)设置为4个。即为4-4-2型神经网络。The BP neural network structure used in this paper is shown in Figure 5. In this method, the number of neurons in the input layer is M=4, and the DC bus voltage Udc of the rectifier, the reference voltage Uref , the system error e and the constant 1 are used as inputs . The number of neurons in the output layer is L=2, and the voltage loops Kpu and Kiu are output. The number of hidden layer neurons is set to 4 according to empirical formula (15). It is a 4-4-2 neural network.
基于BP神经网络的PI控制器结构如图6所示，该控制系统由两部分组成：(1)经典PI控制器，直接对被控对象进行闭环控制，其中PI参数由神经网络在线整定；(2)神经网络：根据系统的运行状态，实时调整PI参数，以达到某种性能指标的最优化。即使输出层神经元的输出对应于PI控制器的Kp、Ki参数，通过神经网络的自身学习算法，对加权系数在线调整，从而可以得到最优控制律下的Kp、Ki参数，达到对系统的最优控制。The structure of PI controller based on BP neural network is shown in Fig. 6. The control system consists of two parts: (1) Classical PI controller, which directly performs closed-loop control on the controlled object, in which PI parameters are adjusted online by neural network; ( 2) Neural network: According to the operating state of the system, adjust PI parameters in real time to achieve the optimization of a certain performance index. Even if the output of the neurons in the output layer corresponds to the Kp and Ki parameters of the PI controller, the weighting coefficients can be adjusted online through the self-learning algorithm of the neural network, so that the Kp and Ki parameters under the optimal control law can be obtained. achieve optimal control of the system.
经典增量式数字PI控制器的控制计算式为(16)。The control formula of the classic incremental digital PI controller is (16).
u(k)＝u(k-1)+Kp[e(k)-e(k-1)]+Ki[e(k)] (16)u(k)=u(k-1)+Kp [e(k)-e(k-1)]+Ki [e(k)] (16)
则可以将u(k)看作与Kp、Ki、u(k-1)等有关的非线性函数，BP神经网络算法用于寻找这一最优控制规律。Then u(k) can be regarded as a nonlinear function related to Kp , Ki , u(k-1), etc., and the BP neural network algorithm is used to find this optimal control law.
步骤三，采用模糊原理对BP神经网络输入层输入进行归一化处理。Step 3: normalize the input of the input layer of the BP neural network by using the fuzzy principle.
对于传统的BP神经网络，输入层的激活函数通常使用Sigmoid函数，但当输入过大时，便会使函数输出始终保持为1，此时激活函数对输入的变化不再敏感。本文采用“归档模糊化”对输入层输入进行预处理。For the traditional BP neural network, the activation function of the input layer usually uses the Sigmoid function, but when the input is too large, the function output will always be kept at 1, and the activation function is no longer sensitive to input changes. In this paper, "archive fuzzification" is used to preprocess the input layer input.
此处以直流母线电压输出误差e为例，通过计算e/Uref，将e＝Uref-Udc归一化，将其在闭区间[0,1]分成若干等级，完成“归档”模糊量化。处理公式如式(17)。Here, the DC bus voltage output error e is taken as an example. By calculating e/Uref , normalize e=Uref -Udc , divide it into several levels in the closed interval [0,1], and complete the "archive" fuzzy quantization . The processing formula is as formula (17).
其中，E为整流器输出电压误差的模糊论域，sgn为符号函数，等级划分可以根据实际情况进行调整。将E乘以一个缩减系数调至0-1的数量级，可以将e转化为概念值，送至神经网络。对于本方法中神经网络的其他输入也均按照实际情况进行模糊归一化处理。Among them, E is the fuzzy domain of rectifier output voltage error, sgn is a sign function, and the classification can be adjusted according to the actual situation. By multiplying E by a reduction factor and adjusting it to the order of 0-1, e can be converted into a conceptual value and sent to the neural network. For other inputs of the neural network in this method, fuzzy normalization is also carried out according to the actual situation.
步骤四，在BP神经网络输出层神经元加权系数修正过程中引入系统的穿越频率ωu与相角裕度作为稳定性能指标，以使稳定性能指标在稳定范围内作为约束规则对BP神经网络输出即PI参数进行约束。Step 4, introduce the crossover frequency ωu and the phase angle margin of the system in the correction process of the neuron weight coefficient of the output layer of the BP neural network As a stable performance index, the stable performance index is used as a constraint rule to constrain the output of the BP neural network, that is, the PI parameter within a stable range.
BP神经网络的学习过程可以分为“前向网络计算”和“反向误差传播——加权系数修正”两个部分。The learning process of BP neural network can be divided into two parts: "forward network calculation" and "backward error propagation - weight coefficient correction".
定义以下变量：Define the following variables:
输入层第j个神经元输入：The jth neuron input of the input layer:
输入层第j个神经元输出：The output of the jth neuron in the input layer:
隐含层第i个神经元输入：The i-th neuron input of the hidden layer:
隐含层第i个神经元输出：The output of the i-th neuron in the hidden layer:
输出层第l个神经元输入：The input of the lth neuron in the output layer:
输出层第l个神经元输入：The input of the lth neuron in the output layer:
隐含层神经元加权系数：Hidden layer neuron weighting coefficient:
输出层神经元加权系数：Output layer neuron weighting coefficient:
隐含层激活函数：f[·]＝tanh(x)＝(ex-e-x)/(ex+e-x)。Hidden layer activation function: f[·]=tanh(x)=(ex -e-x )/(ex +e-x ).
下面进行各层神经元输入输出的前向计算。Next, the forward calculation of the input and output of each layer of neurons is performed.
首先计算输入层神经元输出将输入层输入进行归一化处理之后即为其输出/>First calculate the input layer neuron output After the input layer input is normalized, it is its output />
其次计算隐含层神经元的输入式(18)和输出式(19)。Next, calculate the input formula (18) and output formula (19) of hidden layer neurons.
最后计算输出层神经元的输入式(20)和输出式(21)。Finally, the input formula (20) and output formula (21) of the output layer neurons are calculated.
其中，输出层神经元的输出即为电压环的PI参数。上述各式中的上角标(1)、(2)、(3)分别表示输入层、隐含层、输出层。Wherein, the output of the neuron in the output layer is the PI parameter of the voltage loop. The superscripts (1), (2), and (3) in the above formulas represent the input layer, hidden layer, and output layer, respectively.
接下来对神经网络加权系数进行修正。Next, modify the weighting coefficients of the neural network.
首先，取性能指标函数J1为式(22)。First, take the performance index functionJ1 as formula (22).
按J1对加权系数的负梯度方向调整加权系数，并附加一个惯性项使J1快速收敛到全局最小，则输出层加权系数修正式为式(23)，η为学习速率，α为惯性系数。Adjust the weighting coefficient according to the negative gradient direction of the weighting coefficient by J1 , and add an inertia term Make J1 quickly converge to the global minimum, then the output layer weight coefficient correction formula is formula (23), η is the learning rate, α is the inertia coefficient.
由于式(24)中未知，所以近似用符号函数取代，其误差可通过调整η来补偿。由式(16)可以求得/>如式(25)，式中/>Since in formula (24) unknown, so it is approximated by a sign function, and its error can be compensated by adjusting η. From formula (16) can get /> Such as formula (25), where />
则BP神经网络输出层的加权系数修正公式为式(26)。Then the weight coefficient correction formula of the output layer of BP neural network is formula (26).
根据上述推算方法，可以得到隐含层加权系数修正公式为式(27)。其中，f'[·]＝[1-f2(x)]/2。According to the above calculation method, the hidden layer weight coefficient correction formula can be obtained as formula (27). Wherein, f'[·]=[1-f2 (x)]/2.
右半平面零点补偿之后的整流器控制系统传递函数为式(28)。The transfer function of the rectifier control system after right half plane zero point compensation is formula (28).
令s＝jωu，求解以ωu为未知数的方程式(29)，可以得到由Kpu、Kiu、Kpi、Kii、L表示的穿越频率ωu表达式(30)。Let s=jωu , solve the equation (29) with ωu as the unknown, and get the expression (30) of the crossing frequency ωu represented by Kpu , Kiu , Kpi , Kii , L.
ωu＝g(Kpu,Kiu,Kpi,Kii,L) (30)ωu =g(Kpu ,Kiu ,Kpi ,Kii ,L) (30)
将式(30)代入式(31)中，可以得到相角裕度关于Kpu、Kiu、Kpi、Kii、L的表达式(32)：Substituting Equation (30) into Equation (31), the expression (32) of the phase angle margin with respect to Kpu , Kiu , Kpi , Kii , L can be obtained:
在神经网络每次输出PI参数后，由式(30)计算穿越频率，由式(32)计算幅值裕度，当满足穿越频率处于10k rad～30k rad，相角裕度处于45°～120°时，则输出PI参数；否则进行稳定性约束下的加权系数修正。After the neural network outputs PI parameters each time, the crossover frequency is calculated by formula (30), and the amplitude margin is calculated by formula (32). When the crossover frequency is 10k rad to 30k rad, the phase angle margin is 45° to 120 °, the PI parameters are output; otherwise, the weighting coefficient correction under the stability constraint is carried out.
步骤五，由穿越频率、相角裕度与PI参数的关系引入稳定性修正系数对BP神经网络输出层神经元加权系数进行修正，进一步在保证系统稳定的前提下在线整定PI参数。Step 5: The stability correction coefficient is introduced from the relationship between the crossing frequency, phase angle margin and PI parameters to correct the weighting coefficients of neurons in the output layer of the BP neural network, and the PI parameters are further adjusted online under the premise of ensuring system stability.
为了使用穿越频率及相角裕度对神经网络整定的电压环PI参数进行约束并修正输出层加权系数将Kpi、Kii、L给定定值，绘制ωu及/>关于Kpu、Kiu的函数如图7所示，已找到变化规律。In order to use the crossover frequency and phase angle margin to constrain the PI parameters of the voltage loop tuned by the neural network and correct the weighting coefficient of the output layer Given Kpi , Kii , and L as fixed values, draw ωu and /> The functions of Kpu and Kiu are shown in Figure 7, and the changing rules have been found.
结合图7(a)、(b)中ωu、与Kpu、Kiu的关系，得出对BP神经网络PI参数整定的稳定性约束规则及修正方法如下。Combined with ωu , The relationship with Kpu , Kiu , the stability constraint rules and correction methods for BP neural network PI parameter tuning are obtained as follows.
(1)设定穿越频率范围为10k rad～30k rad，当BP神经网络整定的PI参数由式(30)计算后的ωu小于此范围时，由于ωu与Kpu相关性较明显，所以增大Kpu，即在式(26)中，当l＝0时的表达式基础上增加m1ωu；当ωu大于设定范围时，则适当减小Kpu，即在式(26)中，l＝0时表达式上减去m2ωu。m1,m2为穿越频率修正系数，可取一个较小值。当ωu处于设定范围时，则将m1,m2设为0。(1) Set the crossover frequency range as 10k rad to 30k rad. When the PI parameter adjusted by the BP neural network calculated by formula (30) is less than this range, since the correlation between ω uand Kpu is obvious, so Increase Kpu , that is, in formula (26), increase m1 ωu on the basis of the expression when l=0; when ωu is greater than the set range, then decrease Kpu appropriately, that is, in formula (26 ), when l=0, subtract m2 ωu from the expression. m1 and m2 are correction coefficients of crossing frequency, which can take a smaller value. When ωu is in the setting range, m1 and m2 are set to 0.
(2)设定相角裕度范围为45°～120°，当BP神经网络整定的PI参数由式(32)计算后得到的小于此范围时，为避免动态响应速度过慢，保持Kiu不变，适当增大Kpu，即在式(26)中，当l＝0时表达式基础上增加/>当/>大于设定范围时，保持Kpu不变，适当增大Kiu，即在式(26)中，l＝1时表达式上增加/>m3,m4为相角裕度修正系数，可取一个较小值。当/>处于设定范围时，则将m3,m4设为0。(2) Set the phase angle margin range from 45° to 120°, when the PI parameters adjusted by the BP neural network are calculated by formula (32) When it is less than this range, in order to avoid the dynamic response speed being too slow, keep Kiu unchanged, and increase Kpu appropriately, that is, in formula (26), when l=0, increase on the basis of the expression /> when /> When it is larger than the set range, keep Kpu unchanged, and increase Kiu appropriately, that is, in formula (26), when l=1, the expression increases/> m3 and m4 are phase angle margin correction coefficients, which can take a smaller value. when /> When it is within the setting range, set m3 and m4 to 0.
则考虑稳定性约束的输出层加权系数修正表达式为式(33)，m1,m2,m3,m4的取值如上所述。Then the output layer weight coefficient correction expression considering the stability constraint is formula (33), and the values of m1 , m2 , m3 , and m4 are as above.
为了显示本发明的显著效果，本实施例给出一些利用实施例得出的实验结果。三相PWM整流器网侧电压有效值设置为110V，直流侧电压给定为300V,在本方法控制下进行实验。In order to show the remarkable effects of the present invention, this example gives some experimental results obtained by using the examples. The effective value of the voltage on the grid side of the three-phase PWM rectifier is set to 110V, and the voltage on the DC side is set to 300V. Experiments are carried out under the control of this method.
首先，进行稳定性实验验证。通过设置神经网络初始权值，使整流器运行在不稳定状态，不稳定运行一段时间后，施加稳定性约束，在约束规则的调整下，使整流器恢复到稳定运行状态，实验结果如图8所示。0-t1为不控整流阶段，t1-t2阶段为不稳定阶段，在不稳定阶段，直流母线电压Udc没有达到给定值，此时在没有稳定性约束的情况下，神经网络整定的PI值过小，导致无法消除稳态误差，使得调节时间变长，系统不能稳定运行。在此阶段的PI控制下，为180°，ωu只有6rad，均处于稳定裕度范围外，说明在没有稳定性约束的情况下，当初始权值设置不恰当时，BP神经网络整定的PI参数可能使系统处于不稳定状态。t2时刻，施加稳定性约束，此时，在式(33)对输出层神经元加权系数的调节下，电压环PI参数被迅速调整为恰当值，/>与ωu也被迅速调整到设置范围内。调整过程如图8所示，调节时间约为100ms，且此过程网侧电流畸变小，可以实现平滑过渡。此后，直流母线电压被调整为300V。证明了本文所提基于稳定性约束的BP神经网络PI自整定方法，可以根据整流器运行时所表现的稳定性能指标及时做出调整，从而达到致稳的目的。Firstly, the stability experiment is verified. By setting the initial weight of the neural network, the rectifier runs in an unstable state. After a period of unstable operation, a stability constraint is imposed. Under the adjustment of the constraint rules, the rectifier returns to a stable operating state. The experimental results are shown in Figure 8. . 0-t1 is the uncontrolled rectification stage, and the t1 -t2 stage is the unstable stage. In the unstable stage, the DC bus voltage Udc does not reach the given value. At this time, in the absence of stability constraints, the neural network If the set PI value is too small, the steady-state error cannot be eliminated, the adjustment time becomes longer, and the system cannot run stably. Under PI control at this stage, is 180°, and ωu is only 6rad, both of which are outside the stability margin range, indicating that in the absence of stability constraints, when the initial weights are not set properly, the PI parameters tuned by the BP neural network may make the system in an unstable state . At time t2 , the stability constraint is imposed. At this time, under the adjustment of the weight coefficient of the neurons in the output layer by formula (33), the PI parameter of the voltage loop is quickly adjusted to an appropriate value, /> And ωu is also quickly adjusted to the set range. The adjustment process is shown in Figure 8, the adjustment time is about 100ms, and the current distortion on the grid side is small during this process, and a smooth transition can be achieved. Thereafter, the DC bus voltage is adjusted to 300V. It is proved that the BP neural network PI self-tuning method based on stability constraints proposed in this paper can be adjusted in time according to the stable performance indicators of the rectifier during operation, so as to achieve the purpose of stability.
其次，将本方法与传统PI控制实验结果进行对比，整体实验结果如图9所示。图9中0-t1为不控整流阶段，t1-t2进行斜坡启动，t3时刻给定300-330V阶跃信号，t4时刻给定330V-300V阶跃信号，t5时刻将负载由130Ω突变为65Ω，t6时刻由65Ω突变为130Ω。各阶段对比结果如图10所示。图10(a)、(b)为t3时刻300-330V传统PI控制与本方法控制下的阶跃响应过程。本文所提方法使Udc超调量减小了33.3％，调节时间缩短26ms。图10(c)、(d)为t4时刻330-300V传统PI控制与本方法控制下的阶跃响应过程。本文所提方法使Udc跌落量减小了40％，调节时间缩短48ms。以上实验结果分析表明，阶跃响应时，本文所提方法可以减小Udc的超调量或跌落量，并大幅缩短动态响应时间，提高动态响应速度。图10(e)、(f)为t5时刻负载由130Ω突变为65Ω时，传统PI控制与本方法的实验结果对比。本方法使Udc跌落量减少了50％，调节时间缩短20ms。图10(g)、(h)为t6时刻负载由65Ω突变为130Ω时传统PI控制与本方法的实验结果对比。本文所提方法使超调量减少了54.5％，调节时间缩短了47ms。验证了本方法可以根据系统负载状态的变化及时调整PI参数，加快系统在负载扰动下的动态响应速度，提高稳定性能。Secondly, compare this method with the experimental results of traditional PI control, and the overall experimental results are shown in Figure 9. In Figure 9, 0-t1 is the uncontrolled rectification stage,t1 -t2 starts the ramp, a 300-330V step signal is given att3 , a 330V-300V step signal is given att4 , andt5 will be The load changes suddenly from 130Ω to 65Ω, and changes from 65Ω to 130Ω att6 . The comparison results of each stage are shown in Figure 10. Figure 10 (a), (b) is the step response process under the traditional PI control of 300-330V and the control of this method at timet3 . The method proposed in this paper reduces the Udc overshoot by 33.3%, and shortens the adjustment time by 26ms. Figure 10(c), (d) is the step response process under 330-300V traditional PI control and this method control at timet4 . The method proposed in this paper reduces the Udc drop by 40%, and shortens the adjustment time by 48ms. The analysis of the above experimental results shows that the method proposed in this paper can reduce the overshoot or drop of Udc in step response, greatly shorten the dynamic response time and improve the dynamic response speed. Figure 10(e) and (f) show the comparison of experimental results between traditional PI control and this method when the load changes from 130Ω to 65Ω at timet5 . This method reduces the Udc drop by 50%, and shortens the adjustment time by 20ms. Figure 10(g) and (h) are the experimental results comparison between traditional PI control and this method when the load changes from 65Ω to 130Ω at timet6 . The method proposed in this paper reduces the overshoot by 54.5%, and shortens the adjustment time by 47ms. It is verified that this method can adjust PI parameters in time according to the change of system load state, speed up the dynamic response speed of the system under load disturbance, and improve the stability performance.
本发明可以用其它具体形式来实施，而不脱离其精神或本质特征。所描述的实施例在所有方面都被认为仅是说明性的而非限制性的，例如：The present invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive, for example:
1)三相PWM整流器的拓扑不局限于实施例中的配置；1) The topology of the three-phase PWM rectifier is not limited to the configuration in the embodiment;
2)实验时的电压等级不局限于本实施例中设置的电压等级；2) The voltage level during the experiment is not limited to the voltage level set in this embodiment;
3)三相PWM整流器所接负载类型不局限于实施例中所使用的负载；3) The type of load connected to the three-phase PWM rectifier is not limited to the load used in the embodiment;
4)给定电压变化及负载变化形式与幅度不局限于本实施例中所设置的数值。因此，本发明的范围由所附权利要求书而非上述描述来指示。落入权利要求的等效技术方案的意义和范围中的所有变化都包含在其范围之中。4) The form and magnitude of the given voltage change and load change are not limited to the values set in this embodiment. Accordingly, the scope of the invention is indicated by the appended claims rather than the foregoing description. All changes that come within the meaning and range of equivalent technical solutions of the claims are included in the scope thereof.
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| CN202310390924.6ACN116449682A (en) | 2023-04-13 | 2023-04-13 | A BP neural network PI parameter self-tuning method for three-phase PWM rectifier |
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