CN104184382B  Method for observing speed of permanent magnet motor  Google Patents
Method for observing speed of permanent magnet motor Download PDFInfo
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 CN104184382B CN104184382B CN201410393609.XA CN201410393609A CN104184382B CN 104184382 B CN104184382 B CN 104184382B CN 201410393609 A CN201410393609 A CN 201410393609A CN 104184382 B CN104184382 B CN 104184382B
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Abstract
Description
Technical field
The present invention relates to motor speed observation and speed controlling field, more particularly, to a kind of magneto speed observation side Method.
Background technology
For permagnetic synchronous motor (PMSM) servosystem, the rotorposition of motor and rotating speed are closed loop control systems Requisite feedback quantity in system.In traditional location measurement method, position signalling is many to be obtained by optical encoder.Light Learn encoder and be generally divided into incremental encoder, absolute type encoder and hybrid encoder.Wherein, absolute type encoder energy Enough directly obtain the binary coding of rotor absolute position, each position has unique binary coding.Compile compared to other Code device, absolute type encoder has obvious advantage at aspects such as capacity of resisting disturbance, stationkeeping abilities, thus sets in highaccuracy mechanical The place such as standby has obtained many applications.
The reason such as nonideal being made due to quantizing noise and optical encoder itself, by turning that optical encoder records There is measurement noise in sub position, thus certain error be there is also by the calculated rotating speed of rotor position information.Additionally, passing The encoder of system tests the speed computational methods, such as：The speedmeasuring methods such as measured frequency method, measuring period method, are all based on derivative algorithms solution and turn The meansigma methodss of speed, so cause rotating speed value of calculation to there is error and delay, thus have impact on permanent magnet synchronous electric to a certain extent The dynamic and static performance of machine servo system.In order to reduce the problem that traditional speedmeasuring method exists, generally adopt wave digital lowpass filter To suppress noise, but conventional lowpass filter cannot realize the purpose suppressing noise and reducing time delay simultaneously.
In order to solve the shortcoming of traditional speedmeasuring method, the method that scholars propose multiple observation rotating speeds, such as nonlinear riew Survey device, sliding mode observer etc..System, in the case of low cruise, is not each sampling period to calculate rotating speed, in order to true Protect within each sampling period rotating speed can realtime update, can be using adaptive speed observer, instantaneous velocity observer, complete Dimension or ReducedOrder State Observer are observed and carry out motor control to the rotating speed of magneto, rotorposition etc., but these Method depends on the accurate mathematical model of motor, and systematic function is vulnerable to Parameters variation and the impact of various uncertain factor, makes Obtain its application limited.Because the measurement noise of encoder can be counted as white Gaussian noise, Kalman (Kalman) filtering algorithm As the optimal effectiveness method of estimation in a kind of minimum variance meaning, it using recurrence method directly to random noise disturbance at Reason, and have less dependency to model, therefore, obtain relatively broad application in terms of system speed observation.However, by Need to carry out many experiments to noise parameter in traditional Kalman filter algorithm, just can have preferable observation effect, so, Work efficiency undoubtedly can be reduced, therefore, seek a kind of method solving or substitute this problem urgently important.
Content of the invention
The invention provides a kind of magneto speed observation procedure, present invention, avoiding the differential in traditional speedmeasuring method Process and filtering, make up the measurement error of the absolute type encoder of finite accuracy, thus improve motor speed to control system The control accuracy of system and Immunity Performance, described below：
A kind of magneto speed observation procedure, the method comprising the steps of：
The rotorposition that absolute type encoder is obtained is combined with three parts of designed kalman observer, sees Measure rotor speed and the load torque values of motor, using the rotating speed observed as control system for permanentmagnet synchronous motor der Geschwindigkeitkreis Feedback signal；
The load torque that permagnetic synchronous motor is mutated regards system interference amount as, is seen using constructed kalman observer The electric motor load torque surveyed, as the feedforward signal of electric current loop, builds feedforward control system；
Obtain the switching sequence of inverter by current controller and space vector width pulse modulation method, and then acquisition is passed through The threephase voltage of permagnetic synchronous motor, finally makes magneto with certain rotational speed.
Three parts of described designed kalman observer are specially：
1) by coefficient square based on durface mounted permanent magnet synchronous motor mathematical model is obtained to the design of Kalman's observer Battle array；
2) part is observed according to Kalman's observer, devise the alternative manner of Kalman observer；
3) according to measurement noise self adaptation part, the computational methods of measurement noise are devised.
Described it is specially based on the coefficient matrix of durface mounted permanent magnet synchronous motor mathematical model：
In formula, J is rotary inertia；F is friction torque coefficient；K_{T}For motor torque coefficient；T_{s}For the sampling period.
Described part is observed according to Kalman's observer, the alternative manner devising Kalman observer is specially：
The alternative manner of Kalman observer is
In formula, and x (k  k) it is kth T_{s}The posterior estimate of moment state variable；P (k  k) it is kth T_{s}Moment error covariance Posterior estimate；X (k  k1) it is kth T_{s}Estimated value is tested before the state variable in moment；P (k  k1) it is respectively kth T_{s}Moment Estimated value is tested before error covariance；I is unit matrix；K (k), err (k) are kth T_{s}The Kalman gain in moment and tested The residual error of signal.
Described according to measurement noise self adaptation part, the computational methods devising measurement noise are specially：
Wherein, k is kth time sampling, T_{s}For the sampling period, ω (k  k1) test discreet value for before kth moment state variable, Δ is quantization error.
The beneficial effect of technical scheme that the present invention provides is：
(1) present invention be directed to speed error during magneto low cruise and filter delay problem it is proposed that a kind of from Adapt to Kalman's observer, compared to traditional speedmeasuring method, adaptive Kalman observer proposed by the invention becomes in rotating speed In the case of change, can more accurately realize the identification of rotorposition, and realize the quick tracking of rotating speed.
(2) PMSM can be entered using the rotorposition and rotating speed of adaptive Kalman observer proposed by the present invention identification Row closed loop control well, and there is the less fluctuation of speed, reduce the fluctuation of q shaft current during startup simultaneously.
(3) adaptive Kalman observer can promptly and accurately identifying motor dynamic change when rotating speed so that system tool There is dynamic responding speed faster.
(4) the load change feelings of system can be reflected in time using the load torque that adaptive Kalman observer obtains Condition, the load torque estimated is carried out the feedforward, it is possible to increase the accurate ability of tracking of rotating speed.
Brief description
Fig. 1 is permagnetic synchronous motor Feedforwardfeedback control block diagram；
Fig. 2 measures figure for rotorposition signal, and Fig. 2 (a) is signal measurement figure during motor low cruise；Fig. 2 (b) is electricity Signal measurement figure during machine highspeed cruising；
Fig. 3 is the flow chart of Kalman observer；
Fig. 4 is permagnetic synchronous motor Feedforwardfeedback control simplified block diagram；
Fig. 5 is the experimental waveform under cycle overlay method, and Fig. 5 (a) calculates rotating speed n for cycle overlay method_{3}And i_{q}Waveform；Fig. 5 B () is enlarged drawing when starting；
Fig. 6 is the experimental waveform under Adaptive Kalman observer, and Fig. 6 (a) estimates rotating speed for Kalmani_{q}With's Waveform；Fig. 6 (b) is enlarged drawing when starting；
Fig. 7 is that the observer of the present invention adds experimental waveform under feedforward controller, and Fig. 7 (a) estimates rotating speed for Kalman i_{q}WithWaveform；Fig. 7 (b) is enlarged drawing when starting.
Specific embodiment
For making the object, technical solutions and advantages of the present invention clearer, below embodiment of the present invention is made further Ground describes in detail.
A kind of magneto speed observation procedure, this method carries out rotating speed using the rotorposition that absolute type encoder records And load torque estimates, and controlled using rotating speed, current double closedloop, outer shroud is der Geschwindigkeitkreis, feedback signal is to estimate rotating speed, adopts Ratio and integral controller, abbreviation PI controller, internal ring is electric current loop, and using PI controller, estimating load torque is feedforward letter Number, using feedforward controller；The motor speed measurement based on adaptive Kalman observer of present invention design is by three part groups Become, a part is Kalman's observer modeled segments, and a part is Kalman's observer observation part, another part is that measurement is made an uproar Sound self adaptation part, this three parts collective effect obtains speed feedback signal and the load torque feedforward signal of system, the method Concrete operation step described below：
The present invention devises the permagnetic synchronous motor Feedforwardfeedback control system based on Adaptive Kalman observer, such as Shown in Fig. 1.In figure, permagnetic synchronous motor adopts i_{d}=0 rotating speed, the vector control strategy of current double closedloop, and using limited The absolute type encoder of precision is accurately observed to rotorposition, rotating speed and load torque with adaptive Kalman observer, And using the signal of observation as the feedback signal of der Geschwindigkeitkreis and load torque interference compensation signal.
To control from the analysis of absolute type encoder range rate error, the design of Adaptive Kalman observer, rotating speed PI below The design of link, the design of feedforward compensation link, current controller, space vector pulse width modulation, inverter and PMSM, experiment knot Fruit is analyzed eight aspects and is described further.
1st, absolute type encoder range rate error analysis
The codedisc of n position absolute type encoder is on the donut of circular glass or plastics, depicts n circle and uniformly divides The printing opacity of cloth and light tight alternate groove, the value of adjacent code channel is according to certain rule arrangement, any one radial position Only unique 2 scale codings correspond to therewith, and binary coding scope is 0～2^{n}1.N position absolute type encoder is corresponding Resolution is 1/2^{n}, be equivalent to n position absolute type encoder and be melted into 2 by discrete for the circumference of 2 π rad^{n}Individual differ as 2 pi/2s^{n}The one of rad The position signalling of series.
Fig. 2 (a) and Fig. 2 (b) is respectively under low speed and highspeed case, continuous rotorposition signal, absolute type encoder The position signalling picking out and the position signalling being obtained through digital signal processor (DSP) sampling by absolute type encoder output Curve chart.For the ease of analysis it is assumed that rotating speed is the steady state value more than zero.
In figure, k is sampling number, k=1,2 ...；θ is rotorposition；θ (m) is the rotorposition of the m time reading of DSP, m =1,2 ...；For the derivative of rotorposition, i.e. rotational speed omega；T_{s}Sampling period for controller；T_{1_actual}For absolute encoding The double time interval picking out new rotorposition of device；T_{1}For the double time interval reading new rotorposition of DSP.
As seen from Figure 2, when rotorposition variable quantity is equal to its quantization error Δ=2 pi/2^{n}During rad, absolute type is compiled Code device can obtain the rotorposition of discretization in time, but only when next sampled signal arrives, new rotorposition is Can be read by DSP.This has resulted in exists between the position signalling that the position signalling that absolute type encoder picks out and DSP read Measurement error.When sampling instant just occur before encoder picks out new rotorposition at that moment when, measurement occurs Error is maximum, and its value is quantization error Δ=2 pi/2^{n}rad；And work as sampling instant and just occur to pick out new turning in encoder During sub position, measurement error is minimum, and its value is 0.
By Fig. 2 (a) as can be seen that when system low cruise, rotorposition signal change is slow, absolute type encoder is even Continuous time interval T picking out new rotorposition twice_{1_actual}More than sampling time T_{s}, i.e. the fixing sampling period, now DSP Double time interval T reading new rotorposition_{1}More than T_{s}；By Fig. 2 (b) as can be seen that when system highspeed runs, turning Sub position signalling change is rapid, T_{1_actual}<T_{s}, now T_{1}=T_{s}.
The rotorposition signal derivation that DSP is read, you can obtain tach signal.Traditional speedmeasuring method such as Euler test the speed Method, variable period velocimetry and cycle overlap velocimetry all obtain rotating speed using the method that difference coefficient forward approximately to replace derivative.On State three kinds of algorithms and only after DSP continuously reads new rotorposition signal, just calculate rotating speed, be not within each sampling period All calculate rotating speed, therefore, the speedmeasuring method based on abovementioned algorithm unavoidably has larger speed error and delay of testing the speed.
2nd, the design of Adaptive Kalman observer
1) by coefficient square based on durface mounted permanent magnet synchronous motor mathematical model is obtained to the design of Kalman's observer Battle array；
Voltage equation under synchronous rotating frame (dq) for the durface mounted permanent magnet synchronous motor is
Wherein, ω is the mechanical angular velocity of motor；D axle is rotor magnetic pole axis, q axle advanced 90 degree of spaces of d axle counterclockwise Electrical angle, this dq coordinate system is spatially rotated therefore referred to as synchronously rotating reference frame with electromechanics angular velocity omega together with rotor System；u_{d}、u_{q}、i_{d}、i_{q}、L_{d}、L_{q}It is respectively motor d, q shaft voltage, electric current and stator inductance, and L_{d}=L_{q}；P is number of polepairs；R_{s}It is fixed Sub resistance；ψ_{f}For rotor flux.
Motor movement equation is
In formula, J is rotary inertia；F is friction torque coefficient；K_{T}For motor torque coefficient；T_{L}For load torque, testing the speed One controlling tests the speed, and the cycle is interior it is believed that load torque is definite value, that is,
Wherein, this step is specially：Discretization is carried out to the equation of motion of permagnetic synchronous motor, following karr can be designed Graceful observer：
In formula, k represents sampling number；X=[θ ω T_{L}]^{T}For state variable；U=[i_{q}] it is control signal；Y=[θ] is It is observed signal；W is system noise, the impact that the system parameter error of representative is brought；R is measurement noise, including encoder Other noises in quantization error and measurement process and interference；θ is motor rotor position；ω is the mechanical angular velocity of motor； i_{q}For motor q shaft current；T_{L}For load torque, it is believed that load torque is definite value, that is, within a cycle of testing the speed of control of testing the speed The derivative of load torqueCoefficient matrix is
In formula, T_{s}For the sampling period.
It is generally acknowledged that w (k) and r (k) is stable white Gaussian noise, its meansigma methods is zero, and the variance matrix of noise meets
In formula, Q and R is diagonal matrix, due to being observed signal y=[θ] herein, therefore error r and observational variance R= [R (k)] is first order matrix.
2) part is observed according to Kalman's observer, devise the alternative manner of Kalman observer；
Wherein, the alternative manner of Kalman observer is
In formula, and x (k  k) it is kth T_{s}The posterior estimate of moment state variable；P (k  k) it is kth T_{s}Moment error covariance Posterior estimate；X (k  k1) it is kth T_{s}Estimated value is tested before the state variable in moment；P (k  k1) it is respectively kth T_{s}Moment Estimated value is tested before error covariance；I is unit matrix；K (k), err (k) are kth T_{s}The Kalman gain in moment and tested The residual error of signal, its value can be updated by following formula：
Wherein, y (k  k1) is kth T_{s}The measured signal estimated value in moment, can be seen that survey by above recurrence formula Amount noise variance R (k) impact Kalman gain K (k), and then the correction feelings to x (k  k) for the err (k) and x (k  k1) can be affected Condition.
In traditional Kalman observer, system noise variance Q (k) and measurement noise variance R (k) are all gathered by examination Method, come to determine, needs multigroup repeatability to attempt.After system reaches and stablizes, gain matrix K (k) convergence of Kalman observer For definite value matrix, in each sampling instant, err (k) is identical to the correcting rate of x (k  k1) for that is, traditional Kalman observer. In rotating speed mutation or load torque mutation, K (k) still keeps constant, and this results in traditional Kalman observer cannot be according to tool Body rotating speed is carrying out rational parameter regulation, and then cannot carry out optimal predictor to rotating speed.
3) according to measurement noise self adaptation part, the computational methods of measurement noise are devised；
At low speeds, DSP may not read new rotorposition in each sampling, now T_{1}>T_{s}.In present sample In the cycle, when DSP does not export new rotorposition, there is relatively large measurement error in the position signalling that sampling obtains, that is, think The position signalling that this time sampling obtains is incredible, and being manually set measurement noise is R_{w}, R_{w}For one larger on the occasion of now blocking Gain K is less for Germania, approximates 0, from formula (5) first formula, the observed result x of Kalman (k  k) can be partial to x (k  k 1), ignore measured value y (k), do not carry out estimating the correction of position using the rotorposition that DSP reads, but conduct is estimated Device carries out estimating of rotorposition and rotating speed.
In current sample period, when DSP has read new rotorposition, the measurement error of the position signalling now obtaining is relatively Little, its maximum is The rotating speed estimated for Kalman observer.Because measurement error is as random Variable, with T_{s}Uncorrelated, you can to think measurement error in 0～e_{max}In the range of be equalprobability distribution, the distribution of measurement error is close Degree is inversely proportional to constant interval, then the excursion of measurement error e (t), anticipation error and distribution density are respectively
In formula, e (t) is measurement error value；E [e (t)] is expected error value；F (e, t) is measurement error distribution density.
Can be obtained by formula (7), in current sample period, when DSP reads new rotorposition, measurement noise R_{t}For
The discrete form of above formula is
Using the calculated R of formula (8)_{t}When can reflect under different rotating speeds that DSP reads new rotorposition exactly, Measurement noise between the position signalling being obtained and actual rotor position, by this R_{t}Calculated K can utilize err (k) X (k  k1) is corrected, obtains accurate x (k  k), now Kalman observer as a state observer to state Variable is observed.
To sum up analysis understands, the Adaptive Kalman observer being constructed is carried out to state variable in each sampling instant Estimate, but only when DSP reads new rotorposition, just carry out the correction of state variable.Then Kalman observer is pre Estimate the sampling period T that the cycle is fixation_{s}, the error correction period interval time T that read new rotorposition double with DSP_{1}Phase Deng.
Measurement noise variance yields R (k) of Adaptive Kalman observer is
Wherein, θ (k) is kth T_{s}The rotorposition that moment digital signal processor obtains；R_{t}(k) and R_{w}Value condition such as Under：When digital signal processor (DSP) obtains new rotorposition, the rotorposition recording is relatively accurate, and Kalman observes Device is corrected to predicted state amount using the rotorposition reading, and Kalman's observer enters to quantity of state as state observer Row observation, now the maximum of measurement error is The rotating speed estimated for Kalman observer, now Measurement noise is R_{t}(k)：
Wherein, k is kth time sampling, T_{s}For the sampling period, ω (k  k1) test discreet value for before kth moment state variable, Δ is quantization error.
If DSP does not obtain new rotorposition, the rotor position error recording is larger, and the rotorposition now obtaining is by mistake Difference is larger, and the position signalling that is, this time sampling obtains is insincere, and now measurement noise is set as a higher value R_{w}, now Kalman Gain K is less, approximates 0, iterative from state, and the observed result x of Kalman (k  k) can be partial to x (k  k1), and Ignore measured value y (k), do not carry out estimating the correction of position using the rotorposition that DSP reads, but carry out as prediction device The estimating of rotorposition and rotating speed.The calculating process of Kalman observer is as shown in Figure 3.
3. the design of rotating speed PI controlling unit
Combined with three parts of designed kalman observer using the rotorposition that absolute type encoder obtains, can So that rotor speed and the load torque values of motor quick and precisely must be observed, using the rotating speed observed as permagnetic synchronous motor control The feedback signal of the der Geschwindigkeitkreis of system processed, can improve the dynamic and static state performance of system.
4. the design of feedforward compensation link
In traditional rotating speed, the double PI feedback control system of electric current, in the case of load changing, rotating speed PI controls motor Device cannot be realized following the tracks of the purpose of rotating speed and opposing load disturbance simultaneously.For the problems referred to above, the load torque that PMSM is mutated Regard system interference amount as, by the use of constructed kalman observer observation electric motor load torque as electric current loop feedforward letter Number, build feedforward control system.Fig. 4 is PMSM Feedforwardfeedback control simplified block diagram.
In figure, G_{w}、G_{F}It is respectively rotating speed PI controller, feedforward controller transmission function；G_{I}For system internal ring transmission function, It is approximately the proportional component that proportionality coefficient is 1；G_{T}、G_{M}For motor model parameter.From motor movement equation
From the figure 3, it may be seen that rotating speed with the transmission function of load torque is
In order to reduce the impact to system rotating speed for the load torque interference, G should be made_{F}=G_{T}=1.Due to loading the feedforward Device is worked to PMSM system with rotating speed PI controller simultaneously, therefore, G_{F}Value should choose near 1 it is ensured that feedforward control Under device processed and rotating speed PI controller dual function, rotating speed control effect reaches most preferably.By G_{F}And the observation of Kalman observer is negative Set torque, as PMSM system feedforward compensation link, is combined with speed feedback link, constitutes PMSM Feedforwardfeedback control system System.
5. current controller
Current controller adopts traditional PI controller, and wherein, the setpoint of q shaft current controller is rotating speed PI controller The output valve of output valve and front deaf controller value preset, its value of feedback is the electromagnetic torque of motor；The giving of d shaft current controller Definite value is i_{d}=0, its value of feedback is motor d shaft current.
6. space vector pulse width modulation
Space vector pulse width modulation strategy (SVPWM) to be modulated using seven sections of traditional methods, the input voltage of SVPWM It is to be obtained after antiPARK coordinate transform by the magnitude of voltage of d axle and q axle, wherein, d axle and q shaft voltage value are respectively corresponding electricity The output valve of stream controller, 6 groups of height pulses of its SVPWM output are the on off sequence of inverter.
7. inverter and PMSM
Pulse train using SVPWM output is controlled to the switch of inverter, obtains the threephase voltage of PMSM, PMSM Rotor rotated with certain rotating speed under the driving of threephase voltage.
8. interpretation
Fig. 5 and Fig. 6 is respectively using the cycle overlay method in traditional velocimetry and self adaptation proposed by the invention Kalman observer gained rotating speed carries out the experimental waveform of closed loop control；Fig. 7 is that the Adaptive Kalman that the present invention is designed is seen Survey the experimental waveform that device acquired results carry out Feedforwardfeedback control.
T be can be seen that by Fig. 5 (b) and Fig. 6 (b)_{1}Moment motor starts to start, i_{q}Rapid rising, the cycle, overlay method was in t2 , there is time delay after 7ms in moment ability measuring rotating speed；And when being controlled using this paper observer, it is possible to achieve the accurate control of motor System, and there is the less fluctuation of speed and response speed faster；From Fig. 6 and Fig. 7, when motor load is mutated, adaptive Answer Kalman observer can realize accurately estimating of load torque in about 200ms；And after adopting Feedforwardfeedback control, bear When carrying mutation, the fluctuation of speed is less.
It will be appreciated by those skilled in the art that accompanying drawing is the schematic diagram of a preferred embodiment, the embodiments of the present invention Sequence number is for illustration only, does not represent the quality of embodiment.
The foregoing is only presently preferred embodiments of the present invention, not in order to limit the present invention, all spirit in the present invention and Within principle, any modification, equivalent substitution and improvement made etc., should be included within the scope of the present invention.
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