CN111800057B - Predictive control method and system for permanent magnet synchronous motor - Google Patents
Predictive control method and system for permanent magnet synchronous motor Download PDFInfo
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- CN111800057B CN111800057B CN202010748954.6A CN202010748954A CN111800057B CN 111800057 B CN111800057 B CN 111800057B CN 202010748954 A CN202010748954 A CN 202010748954A CN 111800057 B CN111800057 B CN 111800057B
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- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
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Abstract
The invention discloses a prediction control method for a permanent magnet synchronous motor, which comprises the following steps: calculating a given torque change rate of the next period; estimating a current torque change rate reference coefficient for representing d-axis and q-axis coefficients according to the torque change rate of the motor in the previous two periods, and establishing a torque change rate curve based on a voltage vector angle under a dq coordinate system based on the current torque change rate reference coefficient; solving two reference voltage vectors by using an expression of a torque change rate curve and a given torque change rate in the next period, and screening out three basic voltage vectors by combining the change of the current magnetic flux based on the two reference voltage vectors; and estimating a magnetic flux vector after time delay compensation in the current period, substituting the three basic voltage vectors into a preset value function, determining an optimal voltage vector, and outputting an optimal pulse output signal through the inverter to control the motor. The invention reduces the calculated amount of the prediction control method, does not need to use motor parameters to select the optimal voltage vector, and lightens the dependency on a prediction model.
Description
Technical Field
The invention relates to the technical field of motor control, in particular to a prediction control method and a prediction control system for a permanent magnet synchronous motor.
Background
The permanent magnet motor is widely applied to industry, agriculture, aerospace and household appliances, has the characteristics of simple structure, low loss, high efficiency, small volume, light weight and the like, and along with the wide change of the application occasions of the permanent magnet motor, the control performance requirements of the permanent magnet motor are higher and higher in recent years, and the control technology of the permanent magnet motor is also rapidly developed. The model predictive control has the advantages of simple principle, easy processing of system nonlinear constraint and the like, and is a motor optimization control method which is deeply and widely concerned in the current variable frequency speed control system.
However, the conventional model predictive control method needs to traverse all the open states of the inverter power tubes, and each control period selects a plurality of basic voltage vectors as candidate voltage vectors in the optimization process of the inverter driving signal, so that the problem of large calculation amount occurs in the whole optimization process, and current harmonics and torque ripple are easily caused. In addition, torque prediction is needed when the optimal voltage vector is selected, and in the prior art, a prediction equation containing motor parameters is mostly adopted to predict the torque, so that the dependence of a torque prediction result on a prediction model is strong, but in the actual operation process of the motor, parameters (resistance, inductance and the like) in the motor can be changed under the influence of a working environment, for example: the resistance increases as the temperature at which the motor operates increases. The variation of these parameters affects the result of torque prediction, so that the actual value of the torque is inconsistent with the torque value used for control, and the control effect of the motor is further affected.
Therefore, there is a need in the prior art to provide a new method for controlling a permanent magnet synchronous motor, which reduces the calculation amount of the conventional model prediction method and avoids the influence of motor parameters on torque estimation, thereby improving the operation efficiency and reducing the dependency of the control process on the model.
Disclosure of Invention
In order to solve the technical problem, the present invention provides a predictive control method for a permanent magnet synchronous motor, including: step one, acquiring the electromagnetic torque given by the current period, estimating the electromagnetic torque of the next period, and converting the difference value of the electromagnetic torque and the electromagnetic torque into the torque change rate given by the next period by utilizing the sampling period; estimating a torque change rate reference for respectively representing d-axis and q-axis coefficients in the current period according to the torque change rates of the motor in the previous two periods, and establishing a torque change rate curve based on a voltage vector angle under a dq coordinate system based on the torque change rate reference; thirdly, obtaining two reference voltage vectors according to the given torque change rate of the next period by utilizing a continuous expression corresponding to the torque change rate curve, and screening out three basic voltage vectors from the basic voltage vectors corresponding to all sectors by combining the change of the current magnetic flux on the basis of the two reference voltage vectors; and step four, estimating a magnetic flux vector of the current period after delay compensation, substituting the three basic voltage vectors into a preset cost function to estimate the torque change rate of the next period, and determining an optimal voltage vector based on the torque change rate so as to output an optimal pulse output signal through the inverter to control the motor.
Preferably, the cost function comprises: the given torque change rate term of the next period, the estimated torque change rate term of the next period, the given magnetic flux vector term of the current period and the estimated magnetic flux vector term of the current period after time delay compensation are expressed by the following expressions:
wherein i represents the serial number of the basic voltage vector, k represents the serial number of the current cycle,
indicating a given rate of change of torque for the next cycle,
indicating the estimated torque rate of change, CF, of the next cycle corresponding to the ith base voltage vectoriThe corresponding value of the cost function under the action of the ith basic voltage vector is shown,
represents the given flux vector of the current cycle,
representing the estimated flux vector for two consecutive cycles after the current cycle,
representing the weight coefficients.
Preferably, in the third step, the method comprises: determining a first reference sector in which a first position angle corresponding to the first reference voltage vector is located and a second reference sector in which a second position angle corresponding to the second reference voltage vector is located; and comparing the difference value of the two position angles with a preset sector angle, and selecting the three basic voltage vectors from a plurality of basic voltage vectors on the basis of the comparison result and by referring to the increment or decrement change of the current period magnetic flux vector and the previous period magnetic flux vector and the positions of the first reference sector and the second reference sector.
Preferably, when the difference between the two position angles is greater than or equal to the sector angle, the method includes: when the current magnetic flux change condition is incremental change, determining a reference sector located in the positive direction of a d axis in the first reference sector and the second reference sector, and taking two basic voltage vectors and a zero vector related to the reference sector as the three basic voltage vectors; and when the current magnetic flux change condition is decrement change, determining a reference sector positioned in the negative direction of the d axis in the first reference sector and the second reference sector, and taking two basic voltage vectors and a zero vector related to the reference sector as the three basic voltage vectors.
Preferably, when the difference between the two position angles is smaller than the sector angle, the method includes: if the first reference sector and the second reference sector are the same target sector, determining the current target sector and the sector positioned in the positive direction of the d axis of the current target sector when the current magnetic flux change condition is incremental change, and selecting three basic voltage vectors forming the two sectors; when the current magnetic flux change condition is decrement change, a current target sector and a sector positioned in the negative direction of a d axis of the current target sector are determined, and three basic voltage vectors forming the two sectors are selected.
Preferably, when the difference between the two position angles is smaller than the sector angle, the method further includes: and if the first reference sector and the second reference sector are not in the same target sector, selecting three basic voltage vectors forming the two sectors.
Preferably, the torque change rate is estimated by representing a discretized expression of the torque change rate curve by the following expression:
where k represents the sequence number of the current cycle,
represents the estimated rate of change of torque, θ k-x, for the k-1 th cycle]A voltage vector angle in dq coordinate system representing the k-1 th or k-2 th period, x represents the cycle number after the k moment,
reference coefficient, Δ T, representing estimated rate of change of d-axis torquee[k-1]Indicates the variation of electromagnetic torque, DeltaT, of the k-1 th cyclee[k-2]Represents the variation of electromagnetic torque, T, of the k-2 th cyclesWhich represents the time corresponding to the sampling period,
representing the estimated q-axis torque rate of change reference coefficient.
In another aspect, the present invention further provides a predictive control system for a permanent magnet synchronous motor, including: the torque change rate given value calculation module is used for acquiring the electromagnetic torque given in the current period, estimating the electromagnetic torque of the next period, and converting the difference value of the two into the torque change rate given in the next period by utilizing the sampling period; the torque change rate reference coefficient estimation module is used for estimating torque change rate references which are used for respectively representing d-axis coefficients and q-axis coefficients in the current period according to the torque change rates of the motor in the previous two periods, and based on the torque change rate references, a torque change rate curve based on a voltage vector angle under a dq coordinate system is established; the voltage vector selection module is used for obtaining two reference voltage vectors according to the given torque change rate of the next period by utilizing a continuous expression corresponding to the torque change rate curve, and screening out three basic voltage vectors from basic voltage vectors corresponding to all sectors by combining the change of the current magnetic flux on the basis of the two reference voltage vectors; and the evaluation and prediction control module is used for estimating a magnetic flux vector after time delay compensation in the current period, substituting the three basic voltage vectors into a preset cost function to estimate the torque change rate of the next period, and determining an optimal voltage vector based on the torque change rate so as to output an optimal pulse output signal through the inverter to control the motor.
Preferably, the cost function comprises: the given torque change rate term of the next period, the estimated torque change rate term of the next period, the given magnetic flux vector term of the current period and the estimated magnetic flux vector term of the current period after time delay compensation are expressed by the following expressions:
wherein i represents the serial number of the basic voltage vector, k represents the serial number of the current cycle,
indicating a given rate of change of torque for the next cycle,
indicating the estimated torque rate of change, CF, of the next cycle corresponding to the ith base voltage vectoriThe corresponding value of the cost function under the action of the ith basic voltage vector is shown,
represents the given flux vector of the current cycle,
representing the estimated flux vector for two consecutive cycles after the current cycle,
representing the weight coefficients.
Preferably, the voltage vector selection module includes: a sector positioning unit that determines a first reference sector in which a first position angle corresponding to a first reference voltage vector is located and a second reference sector in which a second position angle corresponding to a second reference voltage vector is located; and a basic voltage vector screening unit which compares the difference value of the two position angles with a preset sector angle, and selects the three basic voltage vectors from a plurality of basic voltage vectors based on the comparison result and by referring to the increment or decrement change of the current period magnetic flux vector and the previous period magnetic flux vector and the positions of the first reference sector and the second reference sector.
Compared with the prior art, one or more embodiments in the above scheme can have the following advantages or beneficial effects:
the invention provides a prediction control method and a prediction control system for a permanent magnet synchronous motor. The method and the system take the torque change rate and the electromagnetic flux parameters which have small influence on the actual running process of the motor as evaluation parameters of a value function for selecting the optimal voltage vector angle. The torque change rate estimation is performed on the voltage vector angle using the torque change rate curve without using the motor parameters, and by using this curve and the magnetic flux command, only three basic voltage vectors having influence on the torque or magnetic flux of the motor operation need be estimated in the cost function, and seven basic voltage vectors need not be estimated. Therefore, the problem of large calculation amount in the traditional model prediction method is solved, the optimal voltage vector angle is selected without using motor parameters, and the dependency on the prediction model is reduced.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
fig. 1 is a step diagram of a predictive control method for a permanent magnet synchronous motor according to an embodiment of the present application.
Fig. 2 is a control principle schematic diagram of a predictive control method for a permanent magnet synchronous motor according to an embodiment of the present application.
Fig. 3 is a flowchart of a vector selection step in the prediction control method for a permanent magnet synchronous motor according to the embodiment of the present application.
Fig. 4 is a schematic diagram illustrating a first case in a vector selection step in the prediction control method for the permanent magnet synchronous motor according to the embodiment of the present application.
Fig. 5 is a schematic diagram illustrating a second case in the vector selection step in the prediction control method for a permanent magnet synchronous motor according to the embodiment of the present application.
Fig. 6 is a schematic diagram illustrating an effect of a change in inductance and load torque of a stator of a motor on a torque change rate in the prediction control method for the permanent magnet synchronous motor according to the embodiment of the present application.
Fig. 7 is a block diagram of a predictive control system for a permanent magnet synchronous motor according to an embodiment of the present application.
Detailed Description
The following detailed description of the embodiments of the present invention will be provided with reference to the drawings and examples, so that how to apply the technical means to solve the technical problems and achieve the technical effects can be fully understood and implemented. It should be noted that, as long as there is no conflict, the embodiments and the features of the embodiments of the present invention may be combined with each other, and the technical solutions formed are within the scope of the present invention.
The permanent magnet motor is widely applied to industry, agriculture, aerospace and household appliances, has the characteristics of simple structure, low loss, high efficiency, small volume, light weight and the like, and along with the wide change of the application occasions of the permanent magnet motor, the control performance requirements of the permanent magnet motor are higher and higher in recent years, and the control technology of the permanent magnet motor is also rapidly developed. The model predictive control has the advantages of simple principle, easy processing of system nonlinear constraint and the like, and is a motor optimization control method which is deeply and widely concerned in the current variable frequency speed control system.
However, the conventional model predictive control method needs to traverse all the open states of the inverter power tubes, and each control period selects a plurality of basic voltage vectors as candidate voltage vectors in the optimization process of the inverter driving signal, so that the problem of large calculation amount occurs in the whole optimization process, and current harmonics and torque ripple are easily caused. In addition, torque prediction is needed when the optimal voltage vector is selected, and in the prior art, a prediction equation containing motor parameters is mostly adopted to predict the torque, so that the dependence of a torque prediction result on a prediction model is strong, but in the actual operation process of the motor, parameters (resistance, inductance and the like) in the motor can be changed under the influence of a working environment, for example: the resistance increases as the temperature at which the motor operates increases. The variation of these parameters affects the result of torque prediction, so that the actual value of the torque is inconsistent with the torque value used for control, and the control effect of the motor is further affected.
Therefore, in order to solve the above technical problems, the present invention proposes a predictive control method for a permanent magnet synchronous motor, which selects a torque change rate and an electromagnetic flux, which have less influence on an actual operation process of the motor, as evaluation parameters for selecting a cost function of an optimum voltage vector angle. Specifically, firstly, a given value of a torque change rate is calculated according to a given value of electromagnetic torque; then, evaluating the torque change rate by establishing a torque change rate curve based on a voltage vector angle under a dq coordinate system, and screening three candidate voltage vectors for evaluating the optimal voltage vector angle from a sector diagram containing a plurality of basic voltage vectors by combining the change condition of the magnetic flux vector estimated value; then, according to a cost function comprising a given torque change rate, a given magnetic flux vector, an estimated magnetic flux vector subjected to time delay compensation processing and a torque change rate estimated by using a torque change rate curve, three candidate voltage vectors are respectively substituted into the cost function, and a voltage vector corresponding to the minimum cost value is used as an optimal voltage vector angle, so that a driving signal for driving the inverter to work is obtained based on the optimal voltage vector angle, and the inverter provides a corresponding three-phase pulse output signal for the permanent magnet synchronous motor through the obtained current driving signal.
Therefore, under the condition of not using motor parameters, the invention carries out torque prediction estimation on the voltage vector angle by using an estimated torque change rate curve, and only three basic voltage vector angles are required to be estimated in a cost function by using the curve and the command without estimating seven basic voltage vector angles, thereby solving the problem of large calculation amount in the traditional model prediction method, selecting the optimal voltage vector angle without using the motor parameters and lightening the dependency on the prediction model.
Fig. 1 is a step diagram of a predictive control method for a permanent magnet synchronous motor according to an embodiment of the present application. Fig. 2 is a control principle schematic diagram of a predictive control method for a permanent magnet synchronous motor according to an embodiment of the present application. The process of the predictive control method according to the invention is described below with reference to fig. 1 and 2. Step S110 obtains the given electromagnetic torque of the current cycle, estimates the electromagnetic torque of the next cycle, and converts the difference between the two (the difference between the given electromagnetic torque of the current cycle and the electromagnetic torque of the next cycle) into the given torque change rate of the next cycle by using the sampling cycle. Then, step S120 establishes a torque change rate curve based on the voltage vector angle in the dq coordinate system, estimates two torque change rate reference coefficients used for respectively representing the number of d-axis and q-axis in the current period according to the torque change rates of the motor in the first two periods (of the current period), obtains an estimated d-axis torque change rate reference coefficient and an estimated q-axis torque change rate reference coefficient corresponding to the current period, and establishes the torque change rate curve based on the estimated torque change rate reference coefficients in the d-axis and the q-axis. Next, step S130 obtains two reference voltage vectors from the torque change rate specified in the next cycle calculated in step S110 by using the serialization expression corresponding to the torque change rate curve established in step S120 based on the real-time torque change rate and the two estimated torque change rate reference coefficients obtained in step S120, and based on this, three basic voltage vectors are selected from the basic voltage vectors corresponding to all sectors in conjunction with the current (estimated) magnetic flux change. Finally, step S140 estimates the flux vector of the current cycle after the delay compensation process, and substitutes the three basic voltage vectors obtained in step S130 into a preset cost function to estimate the torque change rate of the next cycle based on the corresponding voltage vector angle, based on which, the optimal voltage vector angle is determined by combining the torque change rate given by the next cycle and the flux vector given by the current cycle obtained in step S110, so as to output the optimal pulse output signal through the inverter to control the current permanent magnet synchronous motor.
As shown in fig. 2, the control principle of the whole prediction control method is schematically illustrated, and the main purpose is to reduce the number of the optimized basic voltage vectors substituted into the cost function. In particular, a given electromagnetic torque
The estimated electromagnetic torque of the next cycle is passed through each sampling period
Taking the difference and dividing by the sampling period TsConversion to a desired rate of change of torque (given rate of change of torque)
As the expected value of the torque change rate in the cost function (the given value of the torque change rate). Estimated rate of change of torque
On the one hand, the number of basic voltage vectors used for optimizing is reduced, and on the other hand, the estimated electromagnetic torque of the next period is obtained through torque prediction and delay compensation
Given magnetic flux vector
Directly as a desired control quantity on the one hand and by means of an estimated flux vector for each period on the other hand
Making a difference according to the increment
Plus and minus (limiting means are added to limit it too large) further reducing the number of basic voltage vectors that need to be optimized. After such processing, all sectors are pairedThe corresponding 7 basic voltage vectors are reduced to 3.
With continued reference to fig. 1 and 2, the following describes in detail the process of the predictive control method of the present invention.
Specifically, in step S110, it is first necessary to calculate a given electromagnetic torque corresponding to the current cycle (step S1101). Then, a current and a voltage of the inverter driving signal input to the inverter, which are currently collected, and a current and a voltage of an optimal three-phase pulse output signal output by the inverter (which needs to be input to the PMSM) are used to predict and estimate a torque in a current cycle, and a flux linkage (flux vector) in the next two cycles are predicted and estimated, so that an estimated electromagnetic torque corresponding to the current cycle and an estimated flux vector in the next two cycles are obtained (step S1102).
It should be noted that, in the practical application process, because the time corresponding to the calculation period (sampling period) in the predictive control calculation process is short, the time when the predicted and estimated flux linkage (flux vector) actually acts on the permanent magnet synchronous motor (the time when the flux vector is responded by the permanent magnet synchronous motor) corresponding to the current period is often one or two periods after the calculation period. Therefore, in the embodiment of the present invention, in order to improve the accuracy of the estimation of the torque prediction result by the voltage vector angle, it is necessary to perform the delay compensation process on the estimated amount of the magnetic flux vector, that is, it is necessary to use the predicted and estimated flux linkage data of the next two cycles as the flux linkage data actually responded by the motor in the current cycle.
Then, the process proceeds to step S1103. Step S1103 performs predictive estimation on the electromagnetic torque of the next cycle according to the estimated electromagnetic torque corresponding to the current cycle obtained in step S1102 and the estimated torque change rate corresponding to the current cycle (wherein, in the embodiment of the present invention, the torque change rate corresponding to the current cycle is estimated according to the following expression 1), performs delay compensation processing, uses the estimated electromagnetic torque of the next cycle as the electromagnetic torque data to which the motor responds in the current cycle, and then proceeds to step S1104. Step S1104 is to calculate a difference between the estimated electromagnetic torque corresponding to the next cycle obtained in step S1103 and the predetermined electromagnetic torque corresponding to the current cycle obtained in step S1101, convert the current difference into a predetermined torque change rate for the next cycle using the sampling cycle, and then end step S110 and proceed to step S120.
Steps S120 and S130 are processes of reducing the number of basic voltage vectors to be searched by substituting the basic voltage vectors into the cost function, and three voltage vectors corresponding to the current motor operating state are selected for the subsequent torque change rate prediction using the estimated torque change rate curve. Fig. 3 is a flowchart of a vector selection step in the prediction control method for a permanent magnet synchronous motor according to the embodiment of the present application.
As shown in fig. 3, first, step 1201 estimates two torque change rate reference coefficients η for representing the d-axis and q-axis numbers respectively in the current cycle according to the torque change rates of the motor in two adjacent cycles before the current cycle1、η2And further establishing a torque change rate curve based on a voltage vector angle under a dq coordinate system according to the torque change rate reference coefficients of the d axis and the q axis. Thus, in embodiments of the present invention, the constructed torque rate of change curve versus voltage vector angle is used to predict the estimated torque rate of change.
Fig. 6 is a schematic diagram illustrating an effect of a change in inductance and load torque of a stator of a motor on a torque change rate in the prediction control method for the permanent magnet synchronous motor according to the embodiment of the present application. As illustrated in fig. 6, when the motor stator inductance changes, the rate of change of torque will be made to vary significantly. Referring to the following torque variation expression in an ideal state during the actual operation of the motor:
HT＝η1+η2sinθ (0-1)
η2＝(3pλm/2Ls)Vm (0-2)
wherein HTRepresenting the rate of change of torque, η, in real time2Reference coefficient, η, representing the current rate of change of d-axis torque1Representing current q-axis torque variationA conversion rate reference coefficient, theta represents a voltage vector angle under a dq coordinate system, p represents the logarithm of the magnetic poles of the motor, and lambdamRepresenting the current permanent magnetic flux, LsRepresenting the stator inductance, V, of the machinemRepresenting the magnitude of the current voltage vector, RsRepresenting the stator winding resistance, T, of the machineeRepresenting the current electromagnetic torque, ωrWhich is indicative of the current angular frequency of the antenna,
representing the current flux vector and p representing the current load angle.
As can be seen from the above equations (0-1), (0-2) and (0-3), the rate of change of torque and η are found in practical use1、η2Is related to eta1、η2Related to the parameters of the motor. Now discuss eta1，η2Impact on control performance: for η1Although affected by the dc voltage and motor parameters, it varies very slowly compared to the sampling frequency; for η2Its maximum change, albeit influenced by motor parameters and other variables, over several sampling periods, particularly at steady state, is compared to the rate of change of torque HTSo to speak, it is negligible. Because the mechanical time constant of the motor is much larger than the sampling period, its value does not vary much in a short time, although the electromagnetic torque may vary faster than the motor speed, but η, as seen in fig. 62There is no effect on the rate of torque change. In addition, FIG. 6 shows that empty and full loads also have little effect on the rate of change of torque. Furthermore, the motor parameter may be considered to be a constant value over several sampling periods. Therefore, in a short time, the torque change rate is almost constant and changes only with the change in voltage. That is, the motor parameters will not be aligned with η in a short time1And η2Which have a large impact and they can be considered constant over several sampling periods. Thus, according to the above analysis, only η is passed1And η2A torque rate curve may be estimated and used to predict the torque rate for the next sample period. Thus, the d-axis and q-axis torque change rate reference frame which does not relate to motor parameters is designedThe expression of the number is used for establishing a torque change rate discretization expression and a continuity expression which are irrelevant to the motor parameters, so that the influence of the motor parameters on torque prediction is avoided.
Further, a discretized expression of the torque rate curve is represented by the following expression to determine the estimated torque rate per cycle:
where k represents the sequence number of the current cycle,
represents the estimated rate of change of torque, θ k-x, for the k-1 th cycle]Voltage vector angles in dq coordinate systems representing periods k-1 and k-2, x represents the number of periods after the time k,
reference coefficient, Δ T, representing estimated rate of change of d-axis torque at current cyclee[k-1]Indicates the variation of electromagnetic torque, DeltaT, of the k-1 th cyclee[k-2]Represents the variation of electromagnetic torque, T, of the k-2 th cyclesWhich represents the time corresponding to the sampling period,
representing the estimated q-axis torque rate of change reference coefficient for the current cycle.
After the estimated d-axis torque change rate reference coefficient and the q-axis torque change rate reference coefficient are obtained and the establishment of the torque change rate curve is completed, step S120 is ended, and the process proceeds to step S130 to screen the basic voltage vector.
Step S1301 acquires the given torque change rate of the next period obtained in step S110, obtains two reference voltage vectors by using the serialization expression corresponding to the torque change rate curve according to the given torque change rate of the next period, and determines a sector angle corresponding to each reference voltage vector. Wherein the expression of the continuation corresponding to the torque change rate curve is expressed by the following expression:
wherein HTThe torque change rate on the ordinate of the torque change rate curve is represented, and θ represents a voltage vector angle corresponding to a reference voltage vector on the abscissa of the torque change rate curve. Specifically, first, as can be seen from equation (2), the graph of the torque change rate curve is a sine wave with respect to θ (voltage vector angle), and the torque change rate given in the next cycle obtained in step S110 is taken as a transverse curve (i.e., the torque change rate given in the next cycle is taken as the voltage vector angle) of the curve
) Intersects the torque rate curve such that the abscissa of the curve is in the range of 0 to pi to obtain two phase vectors theta1、θ2The two phase vectors theta1、θ2Then, the voltage vector angle θ corresponding to the two reference voltage vectors obtained in step S13011、θ2。
It should be noted that, in an ideal state, the given torque change rate is obtained through (0-1), (0-2) and (0-3) above, but in an actual application process, during the continuous operation of the motor, the influence of the motor parameters on the torque prediction result is large. Therefore, the calculation of the given torque rate of change for the next cycle described in step S110 of the present invention is without motor parameters. Further, the principle of the calculation process of the given torque change rate of the next cycle involved in step S110 is obtained as follows: firstly, discretizing and converting the formula (0-1) to obtain an expression:
HT[k]＝△Te[k]/Ts＝(Te[k+1]-Te[k])/Ts (0-4)
wherein, Delta Te[k]Represents the variation of the electromagnetic torque, T, of the k +1 period from the current periode[k+1]Electromagnetic torque, T, representing the k +1 periode[k]Electromagnetic torque, T, representing the current cyclesRepresenting the sampling period. Secondly, to find the minimum base voltage vector predicting the estimated torque that can be applied to the motor and the torque difference given, T in equation (0-4) ise[k+1]Replacement with a given electromagnetic torque of the current cycle
Will Te[k]Replacement with estimated electromagnetic torque of next cycle
Resulting in a given torque rate of change calculation for the next cycle as described in step S110, which does not involve motor parameters.
Then, using the reference voltage vector calculation formula, according to the voltage vector angle theta corresponding to the two reference voltage vectors1、θ2A first reference voltage vector and a corresponding first sector angle (first position angle) thereof, and a second reference voltage vector and a corresponding second sector angle (second position angle) thereof, which are required in step S1301, are obtained. Wherein the reference voltage vector calculation formula is expressed by the following expression:
wherein v isref1Representing a first reference voltage vector, thetarIndicating the current rotor electrical angle, v, of a permanent magnet synchronous machineref2Representing a second reference voltage vector, σ1Representing a first position angle, σ2Representing a second position angle, VmRepresenting the current voltage vector magnitude, j representing the imaginary sign, and e representing the natural constant. Further, the first sector angle represents an angle between the first reference voltage vector and the first fundamental voltage vector (V1)And the second sector angle represents the angle of the second reference voltage vector with respect to the first base voltage vector (V1).
After determining the sector angles corresponding to the two reference voltage vectors, the process proceeds to step S1302 to screen the basic voltage vectors. For a permanent magnet synchronous motor of a three-phase control power supply, 6 basic voltage vectors form 6 sectors. And since the reference voltage vector is in any one sector, the two adjacent basic voltage vectors forming the sector are the best choice for minimizing the error of the torque change rate, so that at most 5 basic voltage vectors (including 10 vector) are evaluated. However, the actual optimum basic voltage vector selection control requirement also considers the influence of the magnetic flux vector, and the two reference voltages do not necessarily all contribute to the optimum magnetic flux. Since the non-salient PMSM has a flux linkage component in the positive direction of the d axis under the stable operation condition, the influence factor of the flux linkage component needs to be taken into consideration in the optimal basic voltage vector selection process. Thus, after step S1302, a first reference sector in which a first position angle corresponding to the first reference voltage vector is located and a second reference sector in which a second position angle corresponding to the second reference voltage vector is located need to be determined; next, it is necessary to compare the difference between the two position angles with a preset sector angle (for a permanent magnet synchronous motor of a three-phase control power supply, there are 6 sectors each having 60 °, that is, 2 pi/3), and based on the comparison result, with reference to the increment or decrement change of the current period flux vector and the previous period flux vector and the positions of the first reference sector and the second reference sector, select three basic voltage vectors as candidates from a plurality of basic voltage vectors associated with the first reference sector and/or the second reference sector.
Further, referring to fig. 3, step S1302 determines whether the difference between the first position angle and the second position angle is smaller than a preset sector angle, and if the difference between the two position angles is greater than or equal to the sector angle, the process proceeds to step S1303. Fig. 4 is a schematic diagram illustrating a first case in a vector selection step in the prediction control method for the permanent magnet synchronous motor according to the embodiment of the present application. Step S1303 determines a first reference sector (sector I) in which the angle is located according to the first position angle corresponding to the first reference voltage vector, and determines a second reference sector (sector III) in which the angle is located according to the second position angle corresponding to the second reference voltage vector, and then the process proceeds to step S1304. Step S1304 determines whether the change in magnetic flux in the current cycle is an incremental change or a decremental change, by further determining whether the change in magnetic flux in the current cycle is positive or negative (using the difference between the estimated magnetic flux in the current cycle and the estimated magnetic flux in the previous cycle as the change in magnetic flux in the current cycle), and if the change in magnetic flux is an incremental change, the routine proceeds to step S1305. Referring to fig. 4, step S1305 determines a reference sector located in the positive direction of the d-axis of the first reference sector and the second reference sector as a target sector, and then proceeds to step S1306. Step S1306 takes the two basic voltage vectors and the zero vector involved in composing the current target sector as the three basic voltage vectors as candidates. As shown in fig. 4, the salient pole PMSM has a flux linkage component in the positive direction of the d-axis under the steady operation condition, and if the magnetic flux increases, the sector I located in the positive direction of the d-axis is the target sector, and the reference vectors V1, V2, and the zero vector are selected, leaving the voltage vector having no influence on the control of the torque or the magnetic flux.
In step S1304, if the current magnetic flux change is a decrement change, the process proceeds to step S1307. Referring to fig. 4, step S1307 determines a reference sector located in the negative direction of the d-axis of the first reference sector and the second reference sector as a target sector, and then proceeds to step S1308. Step S1308 takes the two basic voltage vectors and the zero vector involved in composing the current target sector as the three basic voltage vectors as candidates. As shown in fig. 4, if the magnetic flux is reduced, the sector III located in the negative direction of the d-axis is the target sector, and the reference vectors V3, V4 and the zero vector are selected, leaving the voltage vector having no influence on the control of the moment or the magnetic flux.
Further, in step S1302, if the difference between the two position angles is smaller than the sector angle, the process proceeds to step S1309. Fig. 5 is a schematic diagram illustrating a second case in the vector selection step in the prediction control method for a permanent magnet synchronous motor according to the embodiment of the present application. Step S1309 determines a first reference sector where the angle is located according to the first position angle corresponding to the first reference voltage vector, and determines a second reference sector where the angle is located according to the second position angle corresponding to the second reference voltage vector, based on which, it is determined whether the first reference sector and the second reference sector are the same sector, if the two sectors are the same sector, the process proceeds to step S1310. Step S1310 is to further determine whether the change of the magnetic flux vector in the current cycle is positive or negative (the difference between the estimated magnetic flux vector corresponding to the current cycle and the estimated magnetic flux vector corresponding to the previous cycle is used as the change of the magnetic flux vector in the current cycle), that is, whether the change of the magnetic flux in the current cycle is an incremental change or a decremental change, and if the change of the magnetic flux in the current cycle is an incremental change, the routine proceeds to step S1311. Step S1311, if the first reference sector and the second reference sector are the same target sector, when the current magnetic flux change condition is incremental change, determines the current target sector and the sector located in the positive direction of the d axis of the current target sector, and selects three basic voltage vectors constituting the two (adjacent) sectors.
Fig. 5a shows a case where the current torque change rate is positive and the first reference sector and the second reference sector when the current magnetic flux change is incremental are both sector II, at which time, V1, V2, and V3 constituting sector II and sector I (the sectors in the positive direction of the d axis of the current target sector) are selected as candidate three basic voltage vectors, and voltage vectors having no influence on the control of the torque or the magnetic flux are discarded. Fig. 5c shows the case when the current torque change rate is negative and the first reference sector and the second reference sector are both the sector V when the current magnetic flux change is incremental, at which time the three basic voltage vectors constituting the sectors V and VI (the sectors in the positive direction of the current target sector d axis) are selected as candidates for V5, V6, and V1.
In step S1310, if the current magnetic flux change is a decrement change, the process proceeds to step S1312. Step S1312, if the first reference sector and the second reference sector are the same target sector, when the current magnetic flux variation condition is a decrement variation, determines the current target sector and the sector located in the negative direction of the d-axis of the current target sector, and selects three basic voltage vectors constituting the two (adjacent) sectors, and discards the voltage vector having no influence on the control of the torque or the magnetic flux.
Fig. 5b shows a case where the current torque change rate is positive and the first reference sector and the second reference sector when the current magnetic flux change is decrement are both sector II, and at this time, three basic voltage vectors constituting sectors II and III (sectors in the direction of the negative axis of the current target sector) V2, V3, and V4 are selected as candidates, and voltage vectors having no influence on the control of the torque or the magnetic flux are discarded. Fig. 5d shows a case where the current torque change rate is negative and the first reference sector and the second reference sector when the current magnetic flux change is decrement are both the sector V, and at this time, V4, V5, and V6 constituting the sector V and the sector IV (the sector in the negative direction of the current target sector d axis) are selected as the three basic voltage vectors of the candidates, and the voltage vectors having no influence on the control of the torque or the magnetic flux are discarded.
Further, in step S1309, if the first reference sector and the second reference sector are not the same sector, the process proceeds to step S1313. In step S1313, if the first reference sector and the second reference sector are not in the same target sector, three basic voltage vectors forming the two (adjacent) sectors are selected. In this way, the basic voltage vector is sorted in steps S1301 to S1313. At this time, voltage vectors irrelevant to the torque or magnetic flux of the motor operation are excluded, and the range from the original 7 basic voltage vectors to 3 basic voltage vectors having an influence on the torque change rate prediction estimation is realized. Thus, the above step S130 is ended, and the process proceeds to step S140 to select an optimum voltage vector angle.
In step S140, first, the estimated magnetic flux vectors corresponding to the next two cycles obtained in step S1102 (that is, the magnetic flux vectors after the delay compensation in the current cycle), the given torque change rate corresponding to the next cycle obtained in step S110, and the given magnetic flux vectors corresponding to the current cycle need to be obtained, the three basic voltage vectors obtained in step S130 are respectively substituted into the torque change rate estimation items in the cost function by using a preset cost function to estimate the torque change rate in the next cycle, so as to obtain torque cost values corresponding to the three basic voltage vectors, and the basic voltage vector corresponding to the lowest torque cost value is used as the optimal voltage vector to transmit the driving signal corresponding to the current optimal voltage vector to the inverter, so that the inverter provides the optimal three-phase pulse output signal to the current permanent magnet synchronous motor. In this way, the error between the predicted value of the torque change rate and the expected value (given value) is minimized, and the torque cost value which minimizes the error between the predicted value of the magnetic flux vector and the expected value (given value) is selected, so that the three-phase voltage of the control motor is obtained to complete the control of the PMSM.
The cost function in the embodiment of the invention comprises the following steps: the magnetic flux vector estimation method comprises a magnetic flux vector estimation term of the next two periods after the current period, a magnetic flux vector given term of the current period, a torque change rate given term of the next period and a torque change rate estimation term of the next period. The torque change rate estimation term of the next cycle needs to be estimated by using the three basic voltage vectors obtained in step S130, so as to obtain 3 torque change rate estimation values, and then obtain 3 cost function output values, so that the basic voltage vector corresponding to the minimum cost function output value is used as the optimal voltage vector, and the control is performed according to the optimal voltage vector. Further, the cost function is expressed by the following expression:
where i denotes the number of the basic voltage vector,
representing a given rate of change of torque for the next cycle,
indicating the estimated torque rate of change, CF, of the next cycle corresponding to the ith base voltage vectoriThe corresponding value of the cost function under the action of the ith basic voltage vector is shown,
represents the given flux vector of the current cycle,
representing the estimated flux vector for two consecutive cycles after the current cycle,
representing the weight coefficients. It should be noted that, in the embodiment of the present invention, the weighting factor is not specifically limited, and those skilled in the art can set the weighting factor according to actual requirements.
On the other hand, the invention also provides a predictive control system for the permanent magnet synchronous motor based on the predictive control method for the permanent magnet synchronous motor. Fig. 7 is a block diagram of a predictive control system for a permanent magnet synchronous motor according to an embodiment of the present application. As shown in fig. 7, the predictive control system according to the present invention includes: a torque rate set point calculation module 71, a torque rate reference coefficient estimation module 72, a voltage vector selection module 73, and an evaluation and prediction control module 74.
The torque change rate set value calculation module 71 is implemented according to the method described in step S110, and is configured to obtain the electromagnetic torque given in the current period, estimate the electromagnetic torque in the next period, and convert the difference between the two into the torque change rate given in the next period by using the sampling period. The torque change rate reference coefficient estimation module 72 is implemented according to the method described in step S120, and is configured to estimate two torque change rate reference coefficients respectively representing the d-axis and q-axis numbers in the current cycle according to the torque change rates of the motor in the previous two cycles, and based on the two torque change rate reference coefficients, establish a torque change rate curve based on the voltage vector angle in the dq coordinate system. The voltage vector selection module 73 is implemented according to the method described in step S130 above, and is configured to obtain two reference voltage vectors from the torque change rate given in the next cycle by using the continuous expression corresponding to the torque change rate curve generated by the torque change rate reference coefficient estimation module 72, and based on this, in combination with the current magnetic flux change, screen out three basic voltage vectors from the basic voltage vectors corresponding to all sectors. The estimation and prediction control module 74 is implemented according to the method described in step S140, and is configured to estimate the magnetic flux vector after the delay compensation in the current period, substitute the three basic voltage vectors output by the voltage vector selection module 73 into a preset cost function to estimate the torque change rate in the next period, and based on this, determine the optimal voltage vector in combination with the torque change rate given in the next period, so as to output the optimal pulse output signal through the inverter to control the current permanent magnet synchronous motor.
Further, in the evaluation and prediction control module 74, the cost function includes: the method comprises the following steps of setting a torque change rate term given in the next period, setting an estimated torque change rate of the next period, setting a magnetic flux vector term given in the current period and setting an estimated magnetic flux vector term after time delay compensation in the current period. Wherein the cost function is represented by the following expression:
where i denotes the number of the basic voltage vector,
representing a given rate of change of torque for the next cycle,
indicating the estimated torque rate of change, CF, of the next cycle corresponding to the ith base voltage vectoriThe corresponding value of the cost function under the action of the ith basic voltage vector is shown,
represents the given flux vector of the current cycle,
representing the estimated flux vector for two consecutive cycles after the current cycle,
representing the weight coefficients.
Further, the voltage vector selection module 73 includes: a sector location unit 731 and a basic voltage vector screening unit 732. The sector locating unit 731 is configured to determine a first reference sector in which a first position angle corresponding to the first reference voltage vector is located, and a second reference sector in which a second position angle corresponding to the second reference voltage vector is located. The basic voltage vector screening unit 732 is configured to compare the difference between the two position angles with a preset sector angle, and select three basic voltage vectors from the plurality of basic voltage vectors based on the comparison result and with reference to the incremental or decremental change of the current-period magnetic flux vector and the previous-period magnetic flux vector.
The invention provides a prediction control method and a prediction control system for a permanent magnet synchronous motor. The method and the system take the torque change rate and the electromagnetic flux parameters which have small influence on the actual running process of the motor as evaluation parameters of a value function for selecting the optimal voltage vector angle. By using the torque change rate curve for torque change rate prediction without using motor parameters and by using this curve and the magnetic flux command, only three basic voltage vectors having influence on the torque or magnetic flux at which the motor operates need to be evaluated in the cost function, and seven basic voltage vectors need not be evaluated. Therefore, the problem of large calculation amount in the traditional model prediction method is solved, the optimal voltage vector angle is selected without using motor parameters, and the dependency on the prediction model is reduced.
The above description is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (4)
1. A predictive control method for a permanent magnet synchronous motor, comprising:
step one, acquiring the electromagnetic torque given by the current period, estimating the electromagnetic torque of the next period, and converting the difference value of the electromagnetic torque and the electromagnetic torque into the torque change rate given by the next period by utilizing the sampling period;
estimating a torque change rate reference which is used for respectively representing d-axis and q-axis coefficients in the current period according to the torque change rates of the motor in the previous two periods, establishing a torque change rate curve based on a voltage vector angle under a dq coordinate system based on the torque change rate reference, and establishing the torque change rate curve by using the following expression:
wherein HTTorque change rate representing the ordinate of the torque change rate curve, theta represents the voltage vector angle corresponding to the reference voltage vector on the abscissa of the torque change rate curve, k represents the sequence number of the current cycle, HT[k-1]Represents the torque change rate of the k-1 th cycle, theta k-1]Represents the voltage vector angle in dq coordinate system of the k-1 th period, theta [ k-2 ]]Represents the voltage vector angle in the dq coordinate system of the k-2 th period,
reference coefficient, Δ T, representing estimated rate of change of d-axis torquee[k-1]Indicates the variation of electromagnetic torque, DeltaT, of the k-1 th cyclee[k-2]Represents the variation of electromagnetic torque, T, of the k-2 th cyclesWhich represents the time corresponding to the sampling period,
representing estimated q-axis torqueA rate of change reference coefficient;
step three, intersecting the torque change rate curve with a curve corresponding to the given torque change rate of the next period to obtain two reference voltage vectors, and screening three basic voltage vectors from the basic voltage vectors corresponding to all sectors in combination with the change of the current magnetic flux on the basis, wherein the three basic voltage vectors are screened in the following way:
determining a first reference sector in which a first position angle corresponding to the first reference voltage vector is located and a second reference sector in which a second position angle corresponding to the second reference voltage vector is located;
comparing the difference value of the two position angles with a preset sector angle, and selecting three basic voltage vectors from a plurality of basic voltage vectors based on the comparison result and by referring to the increment or decrement change of the current period magnetic flux vector and the previous period magnetic flux vector and the positions of the first reference sector and the second reference sector, wherein when the difference value of the two position angles is larger than or equal to the sector angle, the method comprises the following steps:
when the current magnetic flux change condition is incremental change, determining a reference sector located in the positive direction of a d axis in the first reference sector and the second reference sector, and taking two non-zero basic voltage vectors and a zero vector related to the reference sector as the three basic voltage vectors;
when the current magnetic flux change condition is decrement change, determining a reference sector positioned in the negative direction of a d axis in the first reference sector and the second reference sector, and taking two nonzero basic voltage vectors and a zero vector related to the reference sector as the three basic voltage vectors;
when the difference value of the two position angles is smaller than the sector angle, the method comprises the following steps:
if the first reference sector and the second reference sector are the same target sector, when the current magnetic flux change condition is incremental change, determining the current target sector and a sector positioned in the positive direction of the d axis of the current target sector, and selecting three non-zero basic voltage vectors forming the two sectors as the three basic voltage vectors;
when the current magnetic flux change condition is decrement change, determining a current target sector and a sector positioned in the negative direction of a d axis of the current target sector, and selecting three non-zero basic voltage vectors forming the two sectors as the three basic voltage vectors;
if the first reference sector and the second reference sector are not in the same target sector, selecting three non-zero basic voltage vectors forming the two sectors as the three basic voltage vectors;
and step four, estimating a magnetic flux vector of the current period after delay compensation, substituting the three basic voltage vectors into a continuous expression corresponding to the torque change rate curve to estimate the torque change rate of the next period, and then determining an optimal voltage vector by using a preset cost function according to the torque change rate given by the next period, the estimated torque change rate of the next period, the magnetic flux vector given by the current period and the estimated magnetic flux vector of the current period after delay compensation to output an optimal pulse output signal through an inverter to control the motor.
2. The predictive control method of claim 1, wherein the cost function comprises: the given torque change rate term of the next period, the estimated torque change rate term of the next period, the given magnetic flux vector term of the current period and the estimated magnetic flux vector term of the current period after time delay compensation are expressed by the following expressions:
where i denotes the number of the basic voltage vector,
indicating a given rate of change of torque for the next cycle,
indicating the estimated torque rate of change, CF, of the next cycle corresponding to the ith base voltage vectoriThe corresponding value of the cost function under the action of the ith basic voltage vector is shown,
represents the given flux vector of the current cycle,
representing the estimated flux vector for two consecutive cycles after the current cycle,
representing the weight coefficients.
3. A predictive control system for a permanent magnet synchronous machine, comprising:
the torque change rate given value calculation module is used for acquiring the electromagnetic torque given in the current period, estimating the electromagnetic torque of the next period, and converting the difference value of the two into the torque change rate given in the next period by utilizing the sampling period;
a torque change rate reference coefficient estimation module which estimates a torque change rate reference for respectively representing coefficients of a d axis and a q axis in a current period according to the torque change rates of the motor in the previous two periods, and establishes a torque change rate curve based on a voltage vector angle in a dq coordinate system based on the torque change rate reference, wherein the torque change rate curve is established by using the following expression:
wherein HTTorque change rate representing the ordinate of the torque change rate curve, theta represents the voltage vector angle corresponding to the reference voltage vector on the abscissa of the torque change rate curve, k represents the sequence number of the current cycle, HT[k-1]Represents the torque change rate of the k-1 th cycle, theta k-1]Represents the voltage vector angle in dq coordinate system of the k-1 th period, theta [ k-2 ]]Represents the voltage vector angle in the dq coordinate system of the k-2 th period,
reference coefficient, Δ T, representing estimated rate of change of d-axis torquee[k-1]Indicates the variation of electromagnetic torque, DeltaT, of the k-1 th cyclee[k-2]Represents the variation of electromagnetic torque, T, of the k-2 th cyclesWhich represents the time corresponding to the sampling period,
representing an estimated q-axis torque rate of change reference coefficient;
and the voltage vector selection module is used for intersecting the torque change rate curve with a curve corresponding to the given torque change rate in the next period to obtain two reference voltage vectors, and screening three basic voltage vectors from basic voltage vectors corresponding to all sectors in combination with the change of the current magnetic flux on the basis, wherein the three basic voltage vectors are screened in the following way:
determining a first reference sector in which a first position angle corresponding to the first reference voltage vector is located and a second reference sector in which a second position angle corresponding to the second reference voltage vector is located;
comparing the difference value of the two position angles with a preset sector angle, and selecting three basic voltage vectors from a plurality of basic voltage vectors based on the comparison result and by referring to the increment or decrement change of the current period magnetic flux vector and the previous period magnetic flux vector and the positions of the first reference sector and the second reference sector, wherein when the difference value of the two position angles is larger than or equal to the sector angle, the method comprises the following steps:
when the current magnetic flux change condition is incremental change, determining a reference sector located in the positive direction of a d axis in the first reference sector and the second reference sector, and taking two non-zero basic voltage vectors and a zero vector related to the reference sector as the three basic voltage vectors;
and when the current magnetic flux change condition is decrement change, determining a reference sector positioned in the negative direction of the d axis in the first reference sector and the second reference sector, and taking two non-zero basic voltage vectors and a zero vector related to the reference sector as the three basic voltage vectors.
When the difference value of the two position angles is smaller than the sector angle, the method comprises the following steps:
if the first reference sector and the second reference sector are the same target sector, when the current magnetic flux change condition is incremental change, determining the current target sector and a sector positioned in the positive direction of the d axis of the current target sector, and selecting three non-zero basic voltage vectors forming the two sectors as the three basic voltage vectors;
when the current magnetic flux change condition is decrement change, determining a current target sector and a sector positioned in the negative direction of a d axis of the current target sector, and selecting three non-zero basic voltage vectors forming the two sectors as the three basic voltage vectors;
if the first reference sector and the second reference sector are not in the same target sector, selecting three non-zero basic voltage vectors forming the two sectors as the three basic voltage vectors;
and the evaluation and prediction control module is used for estimating a magnetic flux vector after the current period is subjected to delay compensation, substituting the three basic voltage vectors into a continuous expression corresponding to the torque change rate curve to estimate the torque change rate of the next period, and determining an optimal voltage vector by using a preset value function according to the torque change rate given by the next period, the estimated torque change rate of the next period, the magnetic flux vector given by the current period and the estimated magnetic flux vector after the current period is subjected to delay compensation so as to output an optimal pulse output signal through the inverter to control the motor.
4. The predictive control system of claim 3, wherein the cost function comprises: the given torque change rate term of the next period, the estimated torque change rate term of the next period, the given magnetic flux vector term of the current period and the estimated magnetic flux vector term of the current period after time delay compensation are expressed by the following expressions:
where i denotes the number of the basic voltage vector,
indicating a given rate of change of torque for the next cycle,
indicating the estimated torque rate of change, CF, of the next cycle corresponding to the ith base voltage vectoriThe corresponding value of the cost function under the action of the ith basic voltage vector is shown,
represents the given flux vector of the current cycle,
representing the estimated flux vector for two consecutive cycles after the current cycle,
representing the weight coefficients.
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