CN111049449B - Permanent magnet synchronous motor prediction flux linkage control method based on variable control period - Google Patents
Permanent magnet synchronous motor prediction flux linkage control method based on variable control period Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
- H02P21/141—Flux estimation
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/05—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation specially adapted for damping motor oscillations, e.g. for reducing hunting
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/24—Vector control not involving the use of rotor position or rotor speed sensors
- H02P21/28—Stator flux based control
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
- H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
- H02P25/022—Synchronous motors
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
- H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation
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Abstract
The invention discloses a permanent magnet synchronous motor prediction flux linkage control method based on a variable control period, which comprises the following steps: acquiring an actual stator flux linkage vector according to the rotor flux linkage vector and the stator current vector; acquiring a reference stator flux linkage vector according to the electromagnetic torque, the rotor flux linkage amplitude, the stator flux linkage amplitude and the electrical angular frequency; obtaining a cost function which does not contain a weighting factor according to a control error between the reference stator flux linkage vector and the predicted stator flux linkage vector; determining an optimal effective voltage vector and an optimal acting time thereof and an optimal acting time of a zero voltage vector by minimizing a cost function in two steps; the optimal effective voltage vector and the optimal action time of the zero voltage vector form a variable control period. The control period after each cycle is different; the present invention provides additional degrees of control freedom that significantly reduces torque ripple and stator current harmonics without increasing switching losses.
Description
Technical Field
The invention relates to the field of permanent magnet synchronous motor control, in particular to a permanent magnet synchronous motor prediction flux linkage control method based on a variable control period.
Background
The permanent magnet synchronous motor has the advantages of compact structure, high efficiency, good dynamic performance and the like [1] Therefore, the method is widely applied to the industrial applications such as electric automobiles, robots, wind power generation systems and the like [2] . Permanent magnet synchronous motor control strategies have become one of the focus of research in this area. Traditional high performance control strategies mainly include: magnetic field orientation control and direct torque control [3] . Magnetic field orientation control with excellent steady state performanceThe decoupling control of the stator flux linkage and the electromagnetic torque can be realized. But its dynamic response is not satisfactory due to limitations in control principles and controller parameters. Different from the magnetic field directional control, the basic principle of the direct torque control is to determine the optimal voltage vector from the switching table based on the control errors of the electromagnetic torque and the stator flux linkage, and the direct torque control has a simple control structure and quick dynamic response. But the torque ripple of direct torque control is higher compared to field oriented control [4] 。
In recent years, finite set model predictive control has been widely used in motor drive systems as an optimized control strategy. Compared with magnetic field directional control and direct torque control, the finite set model predictive control has the advantages of simple principle, fast dynamic performance, easy processing of nonlinear constraint of the system and the like [5] . The method can directly predict the variation trend of controlled variables such as electromagnetic torque, stator flux linkage and the like. In the case of a control error between the predicted controlled variable and the reference controlled variable being at a minimum, an optimal voltage vector is selected by evaluating a cost function associated with the controlled variable, the selected voltage vector being more accurate than the voltage vector in direct torque control [6] . However, the variation of the controlled variable is related to the optimal voltage vector and the control period thereof. For a limited set model predictive torque control or flux linkage control based on a single voltage vector, the time of action of the optimal voltage vector is the sampling period. The time of action is fixed, which limits the control freedom, resulting in high torque ripple. In addition, only one optimal voltage vector is applied over the sampling period without changing the switching state, which does not satisfy high-precision torque control [7] 。
To solve this problem, a finite set model prediction based on an extended voltage vector is proposed, which achieves better torque performance but causes a larger computational burden. Furthermore, researchers have proposed predicting torque control or flux linkage control based on a finite set model of fixed control periods and dual voltage vectors [8] . The principle is to divide the control period into two parts, and apply a zero voltage vector after the candidate effective voltage vector (i.e. the non-zero voltage vector). Time of action of effective voltage vectorThe time of application of the zero voltage vector is the remaining time of application of the control period, calculated by methods such as cost function minimization. This strategy can slightly suppress torque ripple compared to limited set model predictive control based on single voltage vectors [9] . The control period is still fixed to the sampling period resulting in limited control freedom and torque control accuracy. To further reduce the torque ripple, a higher switching frequency is required, but this increases the computational burden and switching losses [10] 。
In a permanent magnet synchronous motor predictive control system, a limited set of model predictive controls based on single voltage vectors and on dual voltage vectors have a fixed control period and limited degrees of control freedom, which can result in large torque ripple. Increasing the sampling frequency may enhance the torque ripple rejection capability, but may greatly increase switching losses. Conventional strategies have significant drawbacks in terms of steady state performance and switching losses.
Reference to the literature
[1]G.S.Buja and M.P.Kazmierkowski,“Direct torque control of PWM inverter-fed AC motors-a survey,”IEEE Transactions on Industrial Electronics,2004,51(4):744–757.
[2]X.Liu,H.Chen,J.Zhao,and A.Belahcen,“Research on the performances and parameters of interior PMSM used for electric vehicles,”IEEE Transactions on Industrial Electronics,2016,63(6):3533–3545.
[3]M.H.Vafaie,B.Mirzaeian Dehkordi,P.Moallem,and A.Kiyoumarsi,“A new predictive direct torque control method for improving bothsteady-state and transient-state operations ofthe PMSM,”IEEE Transactions on Power Electronics,2016,31(5):3738–3753.
[4]Lixin Tang,Limin Zhong,M.F.Rahman,and Y.Hu,“A novel direct torque controlled interior permanent magnet synchronous machine drive with low ripple in flux and torque and fixed switching frequency,”IEEE Transactions on Power Electronics,2004,19(2):346–354.
[5]H.Miranda,P.Cortes,J.I.Yuz,and J.Rodriguez,“Predictive torque control ofinduction machines based on state-space models,”IEEE Transactions on Industrial Electronics,2009,56(6):1916–1924.
[6]T.Geyer,G.Papafotiou,and M.Morari,“Model predictive direct torque control part I:Concept,algorithm,and analysis,”IEEE Transactions on Industrial Electronics,2009,56(6):1894–1905.
[7]Z.Zhou,C.Xia,Y.Yan,Z.Wang,and T.Shi,“Torque ripple minimization ofpredictive torque control for PMSM with extended control set,”IEEE Transactions on Industrial Electronics,2017,64(9):6930–6939.
[8]S.A.Davari,D.A.Khaburi,and R.Kennel,“An improved FCS-MPC algorithm for an induction motor with an imposed optimized weighting factor,”IEEE Transactions on Power Electronics,2012,27(3):1540–1551.
[9]Y.Zhang and H.Yang,“Model predictive torque control of induction motor drives with optimal duty cycle control,”IEEE Transactions on Power Electronics,2014,29(12):6593–6603.
[10]P.Karamanakos,P.Stolze,R.M.Kennel,S.Manias,and H.du Toit Mouton,“Variable switching point predictive torque control of induction machines,”IEEE Journal of Emerging and Selected Topics in Power Electronics,2014,2(2):285–295.
Disclosure of Invention
The invention provides a permanent magnet synchronous motor prediction flux linkage control method based on a variable control period and double voltage vectors, which obtains an optimal effective voltage vector, the action time of the optimal effective voltage vector and the action time of a zero voltage vector through two-step cost function minimization; the total acting time of the two components forms a variable control period, provides additional control degrees of freedom, can reduce torque pulsation and stator current harmonic waves of the permanent magnet synchronous motor under the condition of not increasing switching loss, and improves the steady-state performance of a control system of the permanent magnet synchronous motor, and is described in detail below:
a permanent magnet synchronous motor predictive flux linkage control method based on a variable control period, the method comprising:
acquiring an actual stator flux linkage vector according to the rotor flux linkage vector and the stator current vector; acquiring a reference stator flux linkage vector according to the electromagnetic torque, the rotor flux linkage amplitude, the stator flux linkage amplitude and the electrical angular frequency;
obtaining a cost function which does not contain a weighting factor according to a control error between the reference stator flux linkage vector and the predicted stator flux linkage vector; determining an optimal effective voltage vector and an optimal acting time thereof and an optimal acting time of a zero voltage vector by minimizing a cost function in two steps;
the optimal effective voltage vector and the optimal action time of the zero voltage vector form a variable control period.
The method further comprises the steps of:
and according to the sector where the actual stator flux linkage vector is located, candidate effective voltage vectors which reduce the stator flux linkage control error are screened out by judging the actual stator flux linkage vector amplitude and the reference stator flux linkage vector amplitude, and the number of the candidate effective voltage vectors is simplified.
Wherein the control period is no longer fixed, providing an additional degree of control freedom.
The optimal effective voltage vector and the optimal action time thereof are determined through two-step minimization of the cost function, and the optimal action time of the zero voltage vector is specifically as follows:
acquiring the acting time of the double voltage vectors, and calculating the corresponding optimal acting time by substituting each candidate effective voltage vector and zero voltage vector into a cost function;
substituting each candidate effective voltage vector, zero voltage vector and corresponding optimal action time into a cost function for calculation.
The technical scheme provided by the invention has the beneficial effects that:
1. compared with the predictive flux linkage control based on a fixed control period and a double voltage vector, the control period of the invention is obtained by minimizing a cost function, and the control period after each cycle is different; the control freedom degree of the invention is higher than that of the traditional method, namely, the extra control freedom degree is provided, and the torque pulsation and stator current harmonic waves are obviously reduced under the condition of not increasing the switching loss;
2. the invention provides a candidate effective voltage vector simplification algorithm based on stator flux linkage control errors, which reduces the number of candidate effective voltage vectors by half, and effectively reduces the calculation burden;
3. the invention provides a corresponding digital realization principle based on different control modes, has simple design process and reduces the complexity of duty ratio updating caused by variable control period.
Drawings
FIG. 1 is a trace diagram of a stator flux linkage vector;
in the figure, u 1 、u 2 、u 3 、u 4 、u 5 And u 6 Is a candidate effective voltage vector, u 0,7 Is a zero voltage vector, ψ s,ref Is a reference to the stator flux linkage vector,
is the predicted stator flux linkage vector, Δψ s Is the control error of the reference stator flux linkage vector and the predicted stator flux linkage vector, assuming u 2 Is the optimal effective voltage vector, t a,opt Is u 2 T b,opt Is the optimal time of action for the zero voltage vector.
FIG. 2 is a simplified diagram of candidate voltage vectors;
in the figure, ψ s,1 And psi is s,2 Is the actual stator flux linkage vector, θ 1 、θ 2 And theta 3 Respectively is psi s,1 And u 1 、u 2 、u 6 Included angle theta 4 、θ 5 And theta 6 Respectively is psi s,2 And u 5 、u 6 、u 1 An included angle between the two.
FIG. 3 is T s <t a,opt ≤2T s And t is b,opt >T s –t 2 (k) A voltage vector switching schematic diagram at the time;
in the figure, S a 、S b And S is c The switching states of the a phase, the B phase and the C phase, respectively.
FIG. 4 is t a,opt >2T s A voltage vector switching schematic diagram at the time;
FIG. 5 is t a,opt <T s And T is s <t a,opt +t b,opt <2T s A voltage vector switching schematic diagram at the time;
FIG. 6 is t a,opt <T s And T is s <t a,opt +t b,opt >2T s A voltage vector switching schematic diagram at the time;
FIG. 7 is a control block diagram;
in the figure omega e，ref Is the reference value of the electrical angular frequency, T e，ref Is the reference electromagnetic torque, i a,b,c Is the stator three-phase current.
FIG. 8 is a steady-state waveform diagram when the reference torque is 15 N.m and the rotational speed is 150 r/min;
wherein, the graph (a) is a steady-state waveform graph when predictive flux linkage control based on a fixed control period is employed, and the graph (b) is a steady-state waveform graph when predictive flux linkage control based on a variable control period is employed.
FIG. 9 is a steady-state waveform diagram when the reference torque is 15 N.m and the rotational speed is 300 r/min;
wherein, the graph (a) is a steady-state waveform graph when predictive flux linkage control based on a fixed control period is employed, and the graph (b) is a steady-state waveform graph when predictive flux linkage control based on a variable control period is employed.
FIG. 10 is a histogram of torque performance when the reference torque is varied from 5 N.m to 15 N.m and the rotational speed is varied from 150r/min to 600 r/min;
wherein, the graph (a) is a torque peak-to-peak value when predictive linkage control based on a fixed control period is employed, the graph (b) is a torque peak-to-peak value when predictive linkage control based on a variable control period is employed, the graph (c) is a torque standard deviation when predictive linkage control based on a fixed control period is employed, and the graph (d) is a torque standard deviation when predictive linkage control based on a variable control period is employed.
FIG. 11 is a dynamic waveform diagram when the reference torque is stepped from 10 N.m to 15 N.m and the rotational speed is 150 r/min;
wherein, the graph (a) is a dynamic waveform graph when the predictive flux linkage control based on the fixed control period is adopted, the graph (b) is a dynamic waveform graph when the predictive flux linkage control based on the variable control period is adopted, and the graph (c) is a corresponding dynamic process enlarged graph.
FIG. 12 is a graph of rise time line when the reference torque is stepped from 10 N.m to 15 N.m at a rotational speed of 150 r/min;
FIG. 13 is a dynamic waveform diagram of a rotational speed step from 100r/min to 200 r/min.
Wherein, the graph (a) is a dynamic waveform graph when predictive flux linkage control based on a fixed control period is employed, and the graph (b) is a dynamic waveform graph when predictive flux linkage control based on a variable control period is employed.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in further detail below.
Example 1
The embodiment of the invention provides a permanent magnet synchronous motor prediction flux linkage control method based on a variable control period and double voltage vectors, which is used for obtaining an optimal effective voltage vector and optimal action time thereof and optimal action time of a zero voltage vector through two-step cost function minimization, thereby effectively reducing torque pulsation and stator current harmonic waves.
In the modeling process of the permanent magnet synchronous motor system, the actual, reference and predicted stator flux linkage vectors are deduced; in the construction process of the cost function, a cost function only comprising stator flux linkage control errors is designed; considering the calculation burden of the algorithm, a simplified algorithm for reducing the number of candidate effective voltage vectors is provided; in the process of realizing the digitization, a digitization realization algorithm is provided based on different control modes, and the technical scheme is described as follows:
101: acquiring an actual stator flux linkage vector according to the rotor flux linkage vector and the stator current vector; acquiring a reference stator flux linkage vector according to the electromagnetic torque, the rotor flux linkage amplitude, the stator flux linkage amplitude and the electrical angular frequency; in addition, a predicted stator flux linkage vector is also derived;
102: obtaining a cost function which does not contain a weighting factor according to a control error between the reference stator flux linkage vector and the predicted stator flux linkage vector; obtaining the acting time of each candidate effective voltage vector and the acting time of the zero voltage vector through minimizing the cost function (first step); determining an optimal effective voltage vector and its optimal acting time from the candidate effective voltage vectors and an optimal acting time of the zero voltage vector by further minimizing the cost function (second step);
103: the optimal effective voltage vector and the optimal action time of the zero voltage vector are combined to form a variable control period.
Since the optimal time of action of the optimal voltage vector and the optimal time of action of the zero voltage vector are different in each cycle, the control period is no longer fixed to be a sampling period, and the voltage vector is no longer switched at each sampling moment. Therefore, based on different control modes, the action time and the control mode of the next sampling period are updated by judging the action time of the voltage vector so as to realize the digital updating process.
In particular, in order to reduce the amount of calculation, the present invention further includes the following steps:
according to the sector where the actual stator flux linkage vector is located, candidate effective voltage vectors which reduce the stator flux linkage control error are screened out by judging the actual stator flux linkage vector amplitude and the reference stator flux linkage vector amplitude, the number of the candidate effective voltage vectors is reduced from six to three, and the calculation burden is simplified.
Example 2
The scheme of example 1 is further described below in conjunction with specific formulas and examples, as described below:
1. modeling of permanent magnet synchronous motor system
The stator voltage equation for a permanent magnet synchronous motor can be expressed as:
wherein u is s (t) is the stator voltage vector, R s Is the stator resistance, i s (t) is the stator current vector, ψ s And (t) is a stator flux linkage vector.
Wherein the actual stator flux linkage vector can be expressed as a rotor flux linkage vector:
Ψ s (t)＝Ψ r (t)+L s i s (t) (2)
wherein, ψ is r (t) is the rotor flux linkage vector, L s Is the stator inductance.
Wherein, the electromagnetic torque of the permanent magnet synchronous motor can be expressed as:
where p is the pole pair number,
is the magnitude of the rotor flux linkage vector, +.>
Is the amplitude of the stator flux linkage vector, the difference between the stator and rotor electric angles +.>
Is the electrical angle of the rotor position +.>
Is the electrical angle of the stator position.
The reference stator flux linkage vector may be expressed as:
wherein omega is e Is the electric angular frequency, and the difference reference value theta of the electric angles of the stator and the rotor es,ref Can be expressed as:
in the method, in the process of the invention,
is the amplitude of the reference stator flux linkage vector, T S Is the sampling period, T e,ref Is a torque reference. />
In order to simplify the design process, R in formula (1) is smaller because of the smaller stator resistance s i s (t) may be omitted. Thus, the predicted stator flux linkage vector can be expressed as:
wherein t is 0 Is the initial time, t is the time of action of the stator voltage vector. It can be seen that the stator flux linkage vector at time t can be predicted from the stator voltage vector and its time of action.
Thus, modeling of the permanent magnet synchronous motor system is finished.
2. Predictive flux linkage control based on variable control period and dual voltage vectors
(1) Minimum design of cost function based on flux linkage error
Conventional predictive flux-linkage control based on a fixed control period and a dual voltage vector has a fixed control period, which is typically a sampling period. The optimum effective voltage vector is first applied to the motor with an action time equal to the optimum action time calculated based on the cost function. Then a zero voltage vector is inserted for the remaining time of the entire control period. Conventional predictive flux linkage control based on a fixed control period and dual voltage vectors can result in large torque ripple and severe stator current harmonics due to limited control freedom.
To solve this problem, embodiments of the present invention propose a novel predictive flux linkage control strategy based on variable control periods and dual voltage vectors. In an embodiment of the invention, the control period of the dual voltage vector is variable.
Both the reference stator flux vector and the predicted stator flux vector are time-varying and they can be expressed as a function of time. The locus of the reference stator flux linkage vector is a circle, which can be expressed as:
in the embodiment of the invention, there are six candidate effective voltage vectors, i.e., u 1 (100)、u 2 (110)、u 3 (010)、u 4 (011)、u 5 (001) And u 6 (101). The zero voltage vector includes u 0 (000) And u 7 (111)。
The influence of the zero voltage vector on the amplitude of the stator flux linkage vector is negligible, so that one of the two zero voltage vectors can be selected, and u is adopted in the embodiment of the invention 0 . According to equation (6), the predicted stator flux linkage vector can be expressed as:
wherein u is a Is a candidate effective voltage vector, a=1, 2, …,6.t is t a And t b The time of action of the candidate effective voltage vector and the zero voltage vector, respectively.
In order to track the reference stator flux vector with minimal control error, embodiments of the present invention construct a cost function with respect to the stator flux vector control error. The constructed cost function only contains the control error of the stator flux linkage vector, compared with the traditional model predictive torque control, the weighting factor of the cost function is eliminated, and the control complexity is reduced. It can be expressed as t a And t b Is a function of:
F＝[ΔΨ s (t a )|u a ] 2 +[ΔΨ s (t a +t b )|u a ,u 0 ] 2 (9)
wherein F is a cost function, Δψ s (t a ) For time t a Stator flux control error, Δψ s (t a +t b ) For time t a +t b The stator flux linkage control error.
Where the control error between the reference stator flux vector and the predicted stator flux vector can be expressed as:
wherein ψ is s,ref (t a ) For time t a A reference stator flux linkage vector at the time,
for time t a Predicted stator flux linkage vector at time, ψ s,ref (t a +t b ) For time t a +t b Reference stator flux vector at time,/->
For time t a +t b Predicted stator flux vectors at that time.
By solving the equation (11), the time of action t of the double voltage vector can be calculated a And t b ：
Therefore, each candidate effective voltage vector and zero voltage vector can be substituted into formula (11) to calculate the corresponding optimal action time.
And then a second step of cost function minimization is performed. Substituting each candidate effective voltage vector, zero voltage vector and corresponding optimal action time into formula (9), wherein the optimal effective voltage vector can be expressed as:
wherein u is a,opt Is the optimal effective voltage vector.
The optimal time of action of the optimal effective voltage vector and the zero voltage vector can be expressed as:
t a,opt ＝t a ,t b,opt ＝t b (13)
wherein t is a,opt An optimal time of action, t, for an optimal effective voltage vector b,opt Is the optimal time of action for the zero voltage vector.
The trajectories of the reference stator flux vectors and the predicted stator flux vectors are shown in fig. 1. As can be seen from fig. 1, the optimum effective voltage vector u 2 At t=t a Ending the operation when the control error is Deltapsib s (t a,opt ). After inserting the zero voltage vector, the predicted stator flux linkage vector amplitude is unchanged and can be expressed as:
wherein, the liquid crystal display device comprises a liquid crystal display device,
for time t a,opt +t b,opt Stator flux control error at time, +.>
For time t a,opt The stator flux linkage control error.
When t=t a +t b At the time, control error Δψ s (t a,opt +t b,opt ) At a minimum, as indicated by the dashed line in fig. 1.
In the whole prediction process, after the optimal dual-voltage vector is acted, the updated optimal dual-voltage vector continues to act. In this way, the predicted stator flux vector may track the reference stator flux with minimal control errorAnd (5) vector. Compared with model predictive control based on a fixed control period and a dual voltage vector, the control period t of the embodiment of the invention a,opt +t b,opt No longer fixed, providing additional degrees of control freedom.
(2) Simplified design of candidate effective voltage vectors
To obtain the optimal effective voltage vector and the optimal action time, six candidate effective voltage vectors need to be substituted into equations (11 to 13) to obtain the optimal solution, but this causes a large computational burden. To solve this problem, a simplified algorithm is employed to reduce the number of candidate effective voltage vectors that need to be evaluated.
Fig. 2 shows a simplified candidate effective voltage vector for when the actual stator flux linkage vector is located in a different sector. For example, when the actual stator flux vector is located in sector I, the actual stator flux vector is associated with u 1 、u 2 And u 6 The included angle between them (i.e. theta 1 、θ 2 And theta 3 ) All less than 90 deg.. If the magnitude of the actual stator flux linkage vector is less than the magnitude of the reference stator flux linkage vector, u 1 、u 2 And u 6 Candidate effective voltage vector as cost function minimization, excluding candidate effective voltage vector u that increases stator flux linkage error 3 、u 4 And u 5 . Similarly, when the actual stator flux vector is located in sector III, the actual stator flux vector is associated with u 5 、u 6 And u 1 The included angle between them (i.e. theta 4 、θ 5 And theta 6 ) All greater than 90 deg.. If the magnitude of the actual stator flux linkage vector is greater than the magnitude of the reference stator flux linkage vector, the number of candidate effective voltage vectors may be reduced from six to three, i.e., u 1 、u 5 And u 6 。
To this end, predictive flux linkage control based on variable control periods and dual voltage vectors has been described.
3. Digital implementation of predictive flux linkage control
(1) Digital implementation based on control mode
The embodiment of the invention provides a digital implementation of predictive flux linkage controlThe method. In the embodiment of the invention, the switching action of the voltage vector can occur not only at the sampling point but also between two adjacent sampling points. In order to reduce the computational burden of the embodiment of the invention, the sampling period is set to be T s And the voltage vector can only be switched at most once within one sampling period. Vect=0, 1,2 indicates three different control modes. A specific analysis of the kth sampling process is as follows.
(a) Vect=2 is the initialization mode, or represents that the optimal dual voltage vector ends at the kth sample point. Therefore, u needs to be calculated according to the formulas (11 to 13) a,opt 、t a,opt And t b,opt . By determining t a,opt 、t b,opt And T s And (3) performing updating operation at the kth sampling point according to the relation between the sampling points. When t a,opt >T s When u a,opt Will continue to function for the (k+1) th sampling period. Thus, the update formula at the kth sample point can be expressed as:
wherein t is 0 Is the acting time of the optimal voltage vector of the last sampling period in the kth sampling period, t 1 Is the acting time of the optimal voltage vector of the current sampling period in the kth sampling period, t 2 Is the time of action of the optimal voltage vector for the current sampling period at the next sampling period or several sampling periods. At initialization, t needs to be set 0 、t 1 And t 2 Set to zero.
Conversely, when t a,opt ≤T s And t is b,opt ≤T s –t a,opt When u a,opt The effect will end before the (k + 1) th sample point. To avoid switching twice in one sampling period, t is b,opt Reset to T s –t a,opt . The update formula at the kth sample point can be expressed as:
when t a,opt ≤T s And t is b,opt >T s –t a,opt When u 0 Will continue to function for the (k+1) th sampling period. The update formula at the kth sample point can be expressed as:
(b) Vect=1 indicates that at the kth sample point, the optimum effective voltage vector acts. When t 2 (k–1)>T s When u a,opt Will continue to function for the (k+1) th sampling period. The update formula at the kth sample point can be expressed as:
conversely, when t 2 (k–1)≤T s And t is b,opt ≤T s –t 2 At (k-1), u a,opt Will end its action before the (k+1) th sample point, u 0 Acting in the kth sampling period.
To avoid the problem of switching twice in one sampling period, t needs to be set b,opt Reset to T s –t 2 (k-1). The update formula at the kth sample point can be expressed as:
when t 2 (k–1)≤T s And t is b,opt >T s –t 2 At (k-1), u a,opt Will end its action before the (k+1) th sample point, u 0 Will continue to function for the (k+1) th sampling period. The update formula at the kth sample point can be expressed as:
(c) Vect=0 indicates that at the kth sample point, the zero voltage vector acts. When t 2 (k–1)>T s The zero voltage vector continues to function during the (k+1) th sampling period. The update formula at the kth sample point can be expressed as:
conversely, when t 2 (k–1)>T s When u 0 The effect ends before the (k+1) th sampling point. u (u) a,opt 、t a,opt And t b,opt The optimal dual voltage vector updated in the kth sampling period is required to be recalculated according to equations (11-13) to begin to function. Assuming that the updated optimum effective voltage vector and the optimum active time are u a,new And t a,new The optimal time of action of the zero voltage vector is t b,new . When t a,new ≤T s –t 2 (k-1) at t a,new Reset to T s –t 2 (k-1) to ensure that the voltage vector can only switch once in one sample period.
The update formula at the kth sample point can be expressed as:
when t 2 (k–1)>T s And t is a,new >T s –t 2 At (k-1), u a,new The operation continues for the (k+1) th sampling period. The update formula at the kth sample point can be expressed as:
to this end, the digitization of the kth sampling process is complete.
(2) Specific examples of digital implementations
Fig. 3-6 show schematic diagrams of switching between an optimal voltage vector and a zero voltage vector under different conditions. Assuming that the dual voltage vectors for the kth sampling period are (100) and (000), the updated dual voltage vectors are (110) and (000).
As shown in FIG. 3, when T s <t a,opt ≤2T s And t is b,opt >T s –t 2 (k) At the time, the corresponding action time and control pattern are updated according to the equation (15) at the kth sampling point, and according to the equation (20) at the (k+1) th sampling point. It should be noted that t 0 (k+1)＝t 2 (k)。
As shown in fig. 4, when t a,opt >2T s At the kth sampling point, the corresponding time of action and control pattern are still updated according to equation (15). At the (k+1) th sampling point, the residual acting time of the optimal effective voltage vector is still greater than T s The corresponding time of action and control pattern are thus updated according to equation (18).
As shown in fig. 5, when t a,opt <T s And T is s <t a,opt +t b,opt <2T s At the time, the corresponding action time and control mode are updated according to equation (17) at the kth sampling point. The candidate effective voltage vector and the zero voltage vector have finished acting before the (k+2) th sampling point, so that it is necessary to judge t at the (k+1) th sampling point a,new And t b,new . When t a,new >T s –t 2 (k) When the corresponding action time and control mode are updated according to equation (23). T can be seen in the figure 0 (k+1)＝t 2 (k)。
As shown in fig. 6, when t a,opt <T s And T is s <t a,opt +t b,opt >2T s At that time, the corresponding on-time and control pattern is still updated at the kth sample point according to equation (17). Unlike fig. 5, the corresponding action time and control pattern are updated according to equation (21) at the (k+1) th sampling point.
A control system block diagram of the permanent magnet synchronous motor is shown in fig. 7, wherein the speed controller employs a two degree of freedom proportional integrator.
The digitized implementation of predictive flux linkage control has been described so far.
Example 3
To verify the validity of predictive flux linkage control based on variable control periods, experimental comparison methods have predictive flux linkage control based on fixed control periods and magnetic field orientation control with space vector modulation.
(1) Steady state experimental verification
A steady-state waveform diagram when the reference torque is 15 N.m and the rotation speed is 150r/min is shown in FIG. 8. In order to ensure that the switching losses caused by the predictive flux linkage control based on the fixed control period and the predictive flux linkage control based on the variable control period are equal, experiments were performed under the condition that the average switching frequencies are approximately the same. At an average switching frequency of about 3kHz, the stator flux linkage fluctuates less and the fluctuation range is substantially the same. When predictive flux linkage control based on a fixed control period is adopted, the torque peak-to-peak value is as high as 3.20 N.m, the torque standard deviation is 0.42 N.m, the three-phase current contains a large number of harmonic components, and the total harmonic distortion of the phase current is 9.76%. When predictive flux linkage control based on a variable control period is adopted, torque pulsation is suppressed to 1.90 N.m, the torque standard deviation is reduced to 0.25 N.m, harmonic components in three-phase currents are obviously reduced, and the total harmonic distortion of the phase currents is 4.85%.
Similarly, a steady-state waveform when the reference torque is 15 N.m and the rotation speed is 300r/min is shown in FIG. 9. The fluctuation range of the stator flux linkage is still approximately the same at an average switching frequency of approximately 3kHz. As shown in fig. 9 (a), when predictive flux linkage control based on a fixed control period is adopted, the torque peak-to-peak value is as high as 3.42n·m, the torque standard deviation is 0.45n·m, and the total harmonic distortion of the phase current is 9.76%. As shown in fig. 9 (b), when the predictive flux linkage control based on the variable control period is adopted, the torque peak-to-peak value is 2.08n·m, the torque standard deviation is 0.28n·m, the harmonic component in the three-phase current is also greatly reduced, and the total harmonic distortion thereof is 6.47%.
To further verify the steady state performance of the predicted flux linkage control based on the variable control period, experiments were performed at different reference torques and speeds, with a histogram of torque performance as shown in fig. 10. As can be seen from the figure, the predictive linkage control based on the variable control period can achieve smaller torque peak-to-peak value and torque standard deviation than the predictive linkage control based on the fixed control period.
(2) Dynamic experimental verification
In order to verify the effectiveness of the predictive flux linkage control based on the variable control period under the dynamic condition, a dynamic waveform diagram when the reference torque is changed from 10n·m step to 15n·m is shown in fig. 11. The rotation speed is 150r/min, and the average switching frequency is about 3kHz. As can be seen from the figure, when predictive flux linkage control based on a fixed control period is employed, the torque can quickly track its reference value within a transient time of around 1 ms. Due to the advantages of predictive control, predictive flux linkage control based on variable control periods may achieve faster dynamic response. And when the reference torque step changes, the stator flux linkage changes negligibly.
Fig. 12 shows a rise time plot of torque when the reference torque is stepped from 10n·m to 15n·m when predictive flux linkage control based on a variable control period, predictive flux linkage control based on a fixed control period, and magnetic field orientation control with space vector modulation are employed. As can be seen from the figure, the rise time of the predicted flux linkage control based on the variable control period is slightly smaller or approximately equal to the rise time of the predicted flux linkage control based on the fixed control period, which is much smaller than the rise time of the magnetic field orientation control.
Further, a dynamic waveform chart when the rotation speed is stepped from 100r/min to 200r/min is shown in FIG. 13. In the experiment, the maximum torque was set to 17 N.m. At the moment of the step, the torque is first stepped to a maximum value, the three-phase current changes rapidly, and the overshoot is negligible. After a brief dynamic process, the torque returns to a stable value and the rotational speed changes rapidly to track its reference value. While the stator flux linkage is hardly affected. As can be seen from the figure, faster torque and rotational speed dynamics can be obtained when predictive flux control based on variable control periods is employed.
(3) Calculation burden comparison
In order to compare the calculation load of the predictive flux linkage control based on the variable control period and the predictive flux linkage control based on the fixed control period, experiments were performed at a sampling frequency of 50 kHz. By statistical calculation, the average calculation time of the predictive linkage control based on the fixed control period was 15.88 μs, and the average calculation time of the predictive linkage control based on the variable control period was 12.52 μs. Even with sampling frequencies up to 50kHz, the average computation time is less than 20 mus. Therefore, the computational burden of the predictive flux linkage control based on the variable control period is within an acceptable range.
So far, the experimental verification is finished.
The embodiment of the invention does not limit the types of other devices except the types of the devices, so long as the devices can complete the functions.
Those skilled in the art will appreciate that the drawings are schematic representations of only one preferred embodiment, and that the above-described embodiment numbers are merely for illustration purposes and do not represent advantages or disadvantages of the embodiments.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (3)
1. A permanent magnet synchronous motor predictive flux linkage control method based on a variable control period, the method comprising:
acquiring an actual stator flux linkage vector according to the rotor flux linkage vector and the stator current vector; acquiring a reference stator flux linkage vector according to the electromagnetic torque, the rotor flux linkage amplitude, the stator flux linkage amplitude and the electrical angular frequency;
obtaining a cost function which does not contain a weighting factor according to a control error between the reference stator flux linkage vector and the predicted stator flux linkage vector; determining an optimal effective voltage vector and an optimal acting time thereof and an optimal acting time of a zero voltage vector by minimizing a cost function in two steps;
forming a variable control period by the optimal effective voltage vector and the optimal action time of the zero voltage vector;
the cost function that does not include a weighting factor is:
F＝[△Ψ s (t a )|u a ] 2 +[△Ψ s (t a +t b )|u a ,u 0 ] 2
wherein F is a cost function, Δψ s (t a ) For time t a Stator flux linkage control error, Δψ s (t a +t b ) For time t a +t b Stator flux linkage control error; u (u) a Is a candidate effective voltage vector, t a And t b The acting time of the candidate effective voltage vector and the zero voltage vector are respectively; u (u) 0 Is a zero voltage vector;
the two-step minimization is specifically as follows:
the first step: obtaining the acting time of each candidate effective voltage vector and the acting time of the zero voltage vector through minimizing the cost function;
and a second step of: determining an optimal effective voltage vector and the optimal acting time thereof and the optimal acting time of the zero voltage vector from candidate effective voltage vectors by further minimizing a cost function;
substituting each candidate effective voltage vector, zero voltage vector and corresponding optimal acting time into a cost function for calculation;
the optimum effective voltage vector is expressed as:
the optimal time of action of the optimal effective voltage vector and the zero voltage vector is expressed as:
t a,opt ＝t a ,t b,opt ＝t b
wherein t is a,opt An optimal time of action, t, for an optimal effective voltage vector b,opt Is the optimal time of action for the zero voltage vector.
2. The variable control period based permanent magnet synchronous motor predictive flux linkage control method of claim 1, further comprising:
and according to the sector where the actual stator flux linkage vector is located, candidate effective voltage vectors which reduce the stator flux linkage control error are screened out by judging the actual stator flux linkage vector amplitude and the reference stator flux linkage vector amplitude, and the number of the candidate effective voltage vectors is simplified.
3. The method for predictive flux linkage control of a permanent magnet synchronous motor based on a variable control period of claim 1, wherein the control period is no longer fixed, providing additional degrees of control freedom.
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