CN104779873A - Prediction function control method for PMSM servo system - Google Patents

Abstract

The invention discloses a prediction function control method for a PMSM servo system. The method comprises the following steps: firstly collecting rotor position signals theta and motor current signals iq of the PMSM servo system, observing rotor load disturbance through a Kalman filter, so as to obtain a rotor load torque T^L and a rotor rotate speed omega^, then feeding back the rotor load torque T^L and optimal control quantity i*q to a rotate speed predication unit of prediction function control (PFC), so as to obtain a prediction value (omega)m of the rotor rotate speed, inputting the rotor rotate speed omega^ and the predication value (omega)m of the rotor rotate speed into an error predication unit of predication function control, so as to obtain a rotate speed error value e of a rotor, and finally inputting e, (omega)m and omega^ into an optimal control unit of predication function control, so as to obtain optimal control quantity i*q to realize the high-precision control of the PMSM servo system under disturbance influence. The method organically combines the Kalman filter and predication function control, and the complementation of the Kalman filter and predication function control can optimize the control quantity of the servo system and improve the control precision and disturbance rejection capacity of the PMSM servo system.

Description

A kind of predictive functional control algorithm for PMSM servo system

Technical field

The present invention relates to a kind of predictive functional control algorithm for permagnetic synchronous motor (PMSM) servo system, belong to the technical field of high-precision servo control system.

Background technology

Along with the raising to servo system control required precision, disturbance has become a major issue of can not ignore.Disturbance often derive from ignore in modeling process uncertain factor, load changing and Parameters variation etc. in system operation.The existence of these factors makes Performance of Closed Loop System variation even unstable.Therefore, for improving the control performance of servo system, its controller will overcome the impact of external disturbance on system.

In PMSM servo-control system, PMSM, as the controlled device of a multivariable, non-linear and close coupling, has the features such as non-linear and uncertain.Controlling for realizing high-precision servo, the impact that PMSM and load cause systematic function in interior controlled device uncertain factor and external disturbance must be overcome.Traditional feedback control strategy, as High-gain PID control method, have structure simple, be easy to the advantages such as realization, usually can obtain good performance when parameter matching, but gain too high in Practical Project can cause system oscillation, unstability.

In practical application in industry, always there will be interference more or less, comprise frictional force and load disturbance, in order to eliminate the impact that disturbance brings, improve the control performance of servo system, Chinese scholars has carried out large quantifier elimination.Predictive function control (Predictive Functional Control, PFC) is the class computer control algorithm that development in recent years is got up.The control strategies such as multistep test and feedback compensation are adopted due to it, there is the advantages such as on-line optimization, constraint process and less on-line calculation, it uses simple, easy design criterion intuitively can be realized, control effects is good, is applicable to control not easily to set up accurate digital model and the industrial processes of more complicated.Document (Xia Zezhong, Zhang Guangming. Predictive function control and the simulation study in servo system [J] thereof. Proceedings of the CSEE, 2005, 25 (14): 130-134.) predictive functional control algorithm of typical servo control system is proposed, simulation result shows, the method can improve tracking performance in servo system, but, in practical application in industry, this predictive functional control algorithm cannot suppress the rotor loading disturbance of servo system, because the method does not consider that rotor loading disturbance suddenlys change, when PMSM servo system is in the face of rotor loading disturbance, the sudden change impact of rotor loading disturbance cannot be eliminated, the control performance of servo system is deteriorated.

Summary of the invention

The present invention is directed to prior art deficiency, a kind of predictive functional control algorithm for PMSM servo system is provided, Kalman filter and Predictive function control (PFC) technology organically combine by the method, both are complementary, the controlled quentity controlled variable of servo system can be optimized, and then improve control precision and the Ability of Resisting Disturbance of PMSM servo system.

For realizing above technical purpose, the present invention will take following technical scheme:

For a predictive functional control algorithm for PMSM servo system, it is characterized in that, first, gather rotor-position signal θ and the motor current signal i of PMSM servo system _q, by rotor-position signal θ and motor current signal i _qas the input signal of Kalman filter, according to rotor-position signal θ and motor current signal i _q, utilize Kalman filter to observe rotor loading disturbance, obtain rotor loading torque and rotor speed then, if Predictive function control (PFC) comprises optimal control unit, error prediction unit and rotor speed forecast unit, by this rotor loading torque with the optimal control amount that optimal control unit exports input to rotor speed forecast unit, obtain the predicted value ω of rotor speed _m, meanwhile, by rotor speed and the predicted value ω of rotor speed _minput to error prediction unit, obtain the speed error value e of rotor; Finally, by rotor speed error amount e, rotor speed predicted value ω _mand rotor speed input to the optimal control unit of Predictive function control (PFC), obtain optimal control amount realize the high accuracy of PMSM servo system under disturbing influence to control; Wherein,

Described Kalman filter is set up based on following formula:

${\hat{w}}_k=F{\hat{w}}_{k-1}+G{\mathrm{\Γ}}_{k-1}^{+}(x_{k|k}-A_{k-1}{\hat{x}}_{k-1|k-1}-D_{k-1}{u}_{k-1})---\left(4\right)$

In formula (4), for servo system in the Kalman filter in k moment to rotor loading disturbance estimated value, the implication that subscript " ∧ " representative is estimated; The coefficient that the coefficient that F is rotor loading disturbance estimated value, G are rotor loading coefficient of disturbance matrix; for rotor loading coefficient of disturbance matrix is at the left inverse matrix in k-1 moment, its expression formula is:

${\mathrm{\Γ}}_{k-1}^{+}={\left(D_{k-1}^T{D}_{k-1}\right)}^{-1}{D}_{k-1}^T$

Wherein, for servo system is at the input matrix D in k-1 moment _k-1transposition, the symbol that its subscript " T " is matrix transpose; D _k-1for at k-1 moment discrete input matrix, its expression formula is:

$D_{k-1}={\left[\begin{array}{ccc}\frac{T_s}{J}& 0& 0\end{array}\right]}^T$

Wherein, T _sfor servo system sample period time, J is motor load moment of inertia;

In formula (4), A _k-1for servo system is at k-1 moment discrete matrix, its expression formula is:

$A_{k-1}=\left[\begin{array}{ccc}1-\frac{B{T}_s}{J}& 0& -\frac{T_s}{J}\\ T_s& 1& 0\\ 0& 0& 1\end{array}\right],$

Wherein, B is viscous friction coefficient;

In formula (4), for kth moment Kalman filter is to discrete predicted value x _kpriori prediction value, x _kfor the kth moment discrete predicted value of motor status variable x, the expression formula of x is: x=[ω θ T _l] ^t, wherein, ω is spinner velocity, and θ is rotor-position, T _lfor rotor loading torque; for kth-1 moment Kalman filter is to discrete estimation value posterior estimate, for motor status variable kth-1 moment discrete estimation value, expression formula be: $\hat{x}={\left[\begin{array}{ccc}\widehat{\mathrm{\ω}}& \widehat{\mathrm{\θ}}& {\hat{T}}_L\end{array}\right]}^T,$ The implication that subscript " ∧ " representative is estimated; u _k-1discrete output variable for system in the k-1 moment to motor status variable u, the expression formula of u is: u=[T _e], wherein, T _efor motor electromagnetic torque;

The predicted value ω of described rotor speed _m, set up based on following formula:

${\mathrm{\ω}}_m(k+i)={\mathrm{\α}}_m^i{\mathrm{\ω}}_m\left(k\right)+K_m(1+...+{\mathrm{\α}}_m^{i-1})i_q^{*}\left(k\right)+K_m(1+...+{\mathrm{\α}}_m^{i-1})T_L\left(k\right)/K_t---\left(9\right)$

In formula, ω _m(k+i) for servo system is in the rotor speed predicted value in k+i moment, i=1,2 ... P, P are the length of prediction optimization time domain, K _mfor rotor speed forecast unit first coefficient of Predictive function control (PFC), its expression formula is: K _m=(1-α _m) K _t/ B, α _mfor rotor speed forecast unit second coefficient of Predictive function control (PFC), its expression formula is: for the i power of rotor speed forecast unit second coefficient of Predictive function control (PFC), K _tfor rotor loading torque constant, for servo system is in the optimal control amount in k moment, T _lk () is for servo system is at the rotor loading torque value in k moment;

The speed error value e of described rotor sets up based on following formula:

e(k+i)＝…＝e(k+1)＝e(k)＝ω(k)-ω _m(k)(10)

In formula, e (k+i) is the error amount of the rotor speed in the k+i moment, i=1,2 ... P, P are the length of prediction optimization time domain, for k moment Kalman filter observes the rotor speed value obtained, ω _mk () is the rotor speed predicted value of servo system in the k moment;

Described optimal control amount set up based on following formula:

$i_q^{*}={({W_1}^{T}Q{W}_1+R)}^{-1}{W_1}^{T}Q[W_2\left(k\right)-W_3\left(k\right)-E\left(k\right)-W_1{T}_L\left(k\right)/K_t]---\left(14\right)$

In formula (14), W ₁for optimal control unit first coefficient matrix of Predictive function control (PFC), its expression formula is:

$W_1={[K_m...K_m(1+...+{\mathrm{\α}}_m^{P-1})]}^T$

Q is the input variable weighting coefficient matrix of optimal control unit, and its expression formula is: wherein, for optimal control unit input variable weight coefficient square; R is the controlled quentity controlled variable weighting coefficient matrix of optimal control unit, and its expression formula is: R=[r ²], wherein, r ²for optimal control unit controlled quentity controlled variable weight coefficient square; W ₂k optimal control unit second coefficient matrix that () is k moment Predictive function control (PFC), its expression formula is: W ₂(k)=[ω _r(k+1) ... ω _r(k+P)] ^t, wherein, ω _r(k+1) for servo system is in the rotor speed reference value in k+1 moment; W ₃k optimal control unit the 3rd coefficient matrix that () is k moment Predictive function control (PFC), its expression formula is: the speed error matrix that E (k) is rotor, its expression formula is: E (k)=[e (k+1) ... e (k+P)] ^t.

According to above technical scheme, following beneficial effect can be realized:

Kalman filter and Predictive function control (PFC) technology organically combine, by the speed error value e of rotor, rotor speed predicted value ω by the method _mand rotor speed input to the optimal control unit of Predictive function control (PFC), obtain the optimal control amount of rotor realize the high accuracy of PMSM servo system under disturbing influence to control, improve the Ability of Resisting Disturbance of servo system.

Accompanying drawing explanation

Fig. 1 is PMSM servo system block diagram of the present invention;

Fig. 2 is the flow chart of a kind of predictive functional control algorithm for PMSM servo system proposed by the invention;

Fig. 3 is the speed responsive experimental result picture of the PMSM servo system adopting the inventive method;

Fig. 4 is the speed responsive experimental result picture of the PMSM servo system adopting Classical forecast function control method.

Embodiment

The nonrestrictive structural representation disclosing a preferred embodiment involved in the present invention of accompanying drawing, below with reference to accompanying drawing detailed description technical scheme of the present invention.

As shown in Figure 1, it discloses the system block diagram of a kind of predictive functional control algorithm for PMSM servo system of the present invention, it adopts photoelectric encoder to gather the position signalling θ of PMSM servomotor, this photoelectric encoder is installed on motor internal, adopts Hall current sensor to gather the current signal i of motor simultaneously _u, i _v, and Clarke transform is carried out to it and park transforms obtains i _d, i _q, by motor position signal θ, motor current signal i _qfeed back to Kalman filter, Kalman filter is utilized to carry out the observation of rotor loading torque, rotor speed and rotor-position, observation is obtained result feedback to Predictive function control (PFC), through the adjustment of Predictive function control (PFC), obtain optimal control amount obtained by pi regulator with the position signalling observed with Kalman filter again, through Parker's inverse transformation, obtains the reference value of stator phase voltage under alpha-beta coordinate system with utilize space vector pulse width debugging technique to produce pwm control signal, then pwm control signal controls three-phase inverter thus, inversion goes out required three-phase alternating current electric drive motor running.

Specifically: described a kind of predictive functional control algorithm for PMSM servo system comprises following four steps:

The first step: build Kalman filter

Gather rotor-position signal θ and the current signal i of PMSM servo system _q, then by rotor-position signal θ and current signal i _qas the input signal of Kalman filter, utilize Kalman filter to observe rotor loading disturbance, obtain rotor loading torque and rotor speed the step building Kalman filter is as follows:

Step 1: gather rotor-position signal θ and current signal i _q

Utilize photoelectric encoder to gather the position signalling θ of PMSM servomotor, utilize current sensor to gather PMSM stator current i _uand i _v, the d shaft current i under Clarke transform and park transforms obtain two-phase rotating coordinate system _dwith q shaft current i _q;

Step 2: build rotor Discrete Load Disturbance Observer

Servo system rotor load disturbance and measure error are substituted into the state equation of motor, the discrete equation group obtaining servo system is:

$\left\{\begin{array}{c}{x}_{k+1}=A_k{x}_k+D_k{u}_k+w_k\\ y_k=C_k{x}_k+v_k\end{array}\right.---\left(1\right)$

In formula, x _kfor the kth moment discrete predicted value of motor status variable x, the expression formula of x is: x=[ω θ T _l] ^t, wherein, ω is spinner velocity, and θ is rotor-position, T _lfor rotor loading torque; y _kfor the kth moment discrete predicted value of system input variable y; u _kdiscrete output variable for system in the k-1 moment to motor status variable u, the expression formula of u is: u=[T _e], wherein, T _efor motor electromagnetic torque; w _krotor loading disturbance, v _kmeasure error, A _kbe the discrete system matrix in corresponding servo system k moment, its expression formula is: $A_k=A_{k-1}=\left[\begin{array}{ccc}1-\frac{B{T}_s}{J}& 0& -\frac{T_s}{J}\\ T_s& 1& 0\\ 0& 0& 1\end{array}\right],$ D _kbe the input matrix in corresponding servo system k moment, its expression formula is: $D_k=D_{k-1}={\left[\begin{array}{ccc}\frac{T_s}{J}& 0& 0\end{array}\right]}^T,$ C _kbe the output matrix in corresponding servo system k moment, its expression formula is: C _k=[0 1 0], wherein, T _sfor the sample period time of servo system, B is viscous friction coefficient, and J is motor load moment of inertia;

In order to estimate the rotor loading disturbed value in servo system k+1 moment, formula (1) is:

$x_{k+1}=A_k{x}_k+D_k{u}_k+{\mathrm{\Γ}}^{+}{\hat{w}}_k---\left(2\right)$

In formula, for servo system in the Kalman filter in k moment to rotor loading disturbance estimated value, Γ ⁺for load disturbance coefficient matrix, to servo system load disturbance w _kestimate, rotor Discrete Load Disturbance Observer is:

${\hat{w}}_k=\mathrm{\Φ}\left(z\right){\mathrm{\Γ}}^{+}(x_k-A_k{x}_{k-1}+D_k{u}_{k-1})---\left(3\right)$

In formula, for rotor loading coefficient of disturbance matrix is at the left inverse matrix in k-1 moment, its expression formula is:

${\mathrm{\Γ}}_{k-1}^{+}={\left(D_{k-1}^T{D}_{k-1}\right)}^{-1}{D}_{k-1}^T,$

Wherein, for servo system is at the input matrix D in k-1 moment _k-1transposition; Φ (z) is low pass filter, and its expression formula is: Φ (z)=H (zI-F) ^-1g; The coefficient that the coefficient that F is the rotor loading disturbed value of system, G are the rotor loading coefficient of disturbance matrix of system; H is constant coefficients matrix;

The structure of step 3:Kalman filter

According to principle algorithm and the Discrete Load Disturbance Observer of Kalman filter, obtain required Kalman filter and set up based on following formula:

${\hat{w}}_k=F{\hat{w}}_{k-1}+G{\mathrm{\Γ}}_{k-1}^{+}(x_{k|k}-A_{k-1}{\hat{x}}_{k-1|k-1}-D_{k-1}{u}_{k-1})---\left(4\right)$

Second step: calculate rotor speed predicted value

Fig. 2 is the flow chart of a kind of predictive functional control algorithm for PMSM servo system proposed by the invention, show Kalman filter and Predictive function control (PFC), Predictive function control (PFC) comprises optimal control unit, error prediction unit and rotor speed forecast unit, by the rotor loading disturbance of observation with the optimal control amount that optimal control unit exports as the input signal of the rotor speed forecast unit of Predictive function control (PFC), obtain rotor speed predicted value ω _m, in PMSM Servo System, for making rotating speed and Current Decoupling, adopt the vector control of (the set-point perseverance of d shaft current is 0), according to Laplace transform, the mechanical equation model obtaining motor dynamics is:

$\mathrm{\ω}\left(s\right)=\frac{K_t{i}_q^{*}\left(s\right)-T_L\left(s\right)}{\mathrm{Js}+B}---\left(5\right)$

In formula (5), ω (s) is electromechanics angular speed, K _tfor system torque constant, for rotor controlled quentity controlled variable, formula (5) is write as difference equation and is:

${\mathrm{\ω}}_m(k+1)={\mathrm{\α}}_m{\mathrm{\ω}}_m\left(k\right)+K_m{i}_q^{*}\left(k\right)+K_m{T}_L\left(k\right)/K_t---\left(6\right)$

In formula (6), ω _m(k+1) for servo system is in the predicted value of the rotor speed in k+1 moment, K _mfor rotor speed forecast unit first coefficient of Predictive function control (PFC), its expression formula is: K _m=(1-α _m) K _t/ B, α _mfor rotor speed forecast unit second coefficient of Predictive function control (PFC), its expression formula is: for servo system is in the optimal control amount in k moment, T _lk () is for servo system is at the rotor loading torque value in k moment;

At next sampling instant of system k+2, have

${\mathrm{\ω}}_m(k+2)={\mathrm{\α}}_m{\mathrm{\ω}}_m(k+1)+K_m{i}_q^{*}(k+1)+K_m{T}_L(k+1)/K_t---\left(7\right)$

Suppose that the value of the control variables of servo system at the optimal control variable of future time instance servo system is:

$i_q^{*}\left(k\right)=i_q^{*}(k+1)=...=i_q^{*}(k+P-1),T_L\left(k\right)=T_L(k+1)=...=T_L(k+P-1),$

Formula (6) is substituted into formula (7) obtain:

${\mathrm{\ω}}_m(k+2)={\mathrm{\α}}_m^2{\mathrm{\ω}}_m\left(k\right)+K_m(1+{\mathrm{\α}}_m)i_q^{*}\left(k\right)+K_m(1+{\mathrm{\α}}_m)T_L\left(k\right)/K_t---\left(8\right)$

Above-mentioned formula (6), formula (7), formula (8) are superposed successively, obtain:

${\mathrm{\ω}}_m(k+i)={\mathrm{\α}}_m^i{\mathrm{\ω}}_m\left(k\right)+K_m(1+...+{\mathrm{\α}}_m^{i-1})i_q^{*}\left(k\right)+K_m(1+...+{\mathrm{\α}}_m^{i-1})T_L\left(k\right)/K_t---\left(9\right)$

In formula (9), ω _m(k+i) for system is in the predicted value of the rotor speed in k+i moment, i=1,2 ... P, P are the length of prediction time domain, for rotor speed forecast unit second factor alpha of Predictive function control (PFC) _mi power;

3rd step: the speed error e calculating rotor, its calculating formula is:

$e(k+i)=...=e(k+1)=e\left(k\right)=\widehat{\mathrm{\ω}}\left(k\right)-{\mathrm{\ω}}_m\left(k\right)---\left(10\right)$

In formula (10), the error amount that e (k+i) is the rotor speed in k+i moment, i=1,2 ... P, P are the length of prediction optimization time domain, for the rotor speed value of k moment Kalman filter observation, ω _mk () is the rotor speed predicted value of servo in the k moment;

4th step: by the speed error value e of rotor, rotor speed predicted value ω _mand rotor speed input to the optimal control unit of Predictive function control (PFC), obtain optimal control amount realize the high accuracy of PMSM servo system under disturbing influence to control, comprise the following steps:

Step 1: the output controlled quentity controlled variable basic function of setting Predictive function control (PFC), its expression formula is:

$i_q^{*}(k+1)=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_j{f}_j\left(i\right)---\left(11\right)$

In formula (11), for the optimal control amount in system k+i moment, f _ji () is for basic function is at t=iT _sthe step value in moment, T _sfor the system communication cycle time; I=1,2 ... P, P are the length of prediction optimization time domain, j=1,2 ... N, N are natural number; μ _jfor the coefficient of basic function, adopt step function as basic function, N=1, f ₁(i)=1, its basic function is:

Step 2: setting rotor speed reference locus, its expression formula is:

${\mathrm{\ω}}_r(k+i)={\mathrm{\ω}}^{*}(k+i)-{\mathrm{\α}}_r^i[{\mathrm{\ω}}^{*}\left(k\right)-\widehat{\mathrm{\ω}}\left(k\right)]---\left(12\right)$

In formula (12), ω _r(k+i) for system is at the rotor speed reference locus in k+i moment, ω ^*for system is in the given rotor speed in k moment, for k moment Kalman filter observes the rotor speed value obtained, for the coefficient of the difference that given rotor speed and rotor speed are subtracted each other, its expression formula is: t _rfor the Expected Response time of PMSM servo system.

Step 3: by the speed error e of rotor, rotor speed predicted value ω _mand rotor speed input to the optimal control unit of Predictive function control (PFC), obtain optimal control amount

For the cost function of PMSM servo system, be designated as its calculating formula is:

In formula (13), for cost function; Order, determine the cost function of above-mentioned PMSM servo system minimum value, in the coefficient real-time update of each sampling instant to the coefficient matrix of optimal control unit, the optimal control amount obtaining servo system is:

$i_q^{*}={({W_1}^{T}Q{W}_1+R)}^{-1}{W_1}^{T}Q[W_2\left(k\right)-W_3\left(k\right)-E\left(k\right)-W_1{T}_L\left(k\right)/K_t]---\left(14\right)$

In formula (14), W ₁for optimal control unit first coefficient matrix of Predictive function control (PFC), its expression formula is: q is the input variable weighting coefficient matrix of optimal control unit, and its expression formula is: wherein, for optimal control unit input variable weight coefficient square; R is the controlled quentity controlled variable weighting coefficient matrix of optimal control unit, and its expression formula is: R=[r ²], wherein, r ²for optimal control unit controlled quentity controlled variable weight coefficient square; W ₂k optimal control unit second coefficient matrix that () is k moment Predictive function control (PFC), its expression formula is: W ₂(k)=[ω _r(k+1) ... ω _r(k+P)] ^t, wherein, ω _r(k+1) for servo system is in the rotor speed reference value in k+1 moment; W ₃k optimal control unit the 3rd coefficient matrix that () is k moment Predictive function control (PFC), its expression formula is: the speed error matrix that E (k) is rotor, its expression formula is: E (k)=[e (k+1) ... e (k+P)] ^t.

With reference to Fig. 3, show and adopt a kind of predictive functional control algorithm for PMSM servo system of the present invention, PMSM servo system is when in the face of load changing, and spinner velocity recovery time is 0.51s, and rotor speed is maximum falls 68rpm; With reference to Fig. 4, show and adopt the PMSM servo system of Classical forecast function control method when in the face of load changing, spinner velocity recovery time is 0.21s, rotor speed is maximum falls 24rpm, spinner velocity recovery time of contrast two kinds of methods and rotor speed is maximum falls data, compare from Fig. 3 and Fig. 4, can draw, a kind of predictive functional control algorithm for PMSM servo system of the present invention performance in disturbance rejection is more excellent.

Specific embodiments of the invention experiment porch adopts the all-digitized demodulator implementation based on ARM, and programming language is C language.System with the XMC4500 chip of company of Infineon for core composition control circuit part; Hall current sensor is for gathering two-way current signal i _uand i _v; Rotor-position detection part is 2500 line incremental optical-electricity encoders, for gathering the rotor-position signal of motor; Inverter circuit take smart power device as core, the space vector pulse width modulation control signal that it generates according to XMC4500 chip, converts power supply input to corresponding three-phase alternating voltage, for drive motors work; Load motor rated power is 3kW, and rotor-position sensor is 24 multi-turn absolute type encoders.

Claims (1)

1. for a predictive functional control algorithm for PMSM servo system, it is characterized in that, first, gather rotor-position signal θ and the motor current signal i of PMSM servo system _q, by rotor-position signal θ and motor current signal i _qas the input signal of Kalman filter, according to rotor-position signal θ and motor current signal i _q, utilize Kalman filter to observe rotor loading disturbance, obtain rotor loading torque and rotor speed then, if Predictive function control (PFC) comprises optimal control unit, error prediction unit and rotor speed forecast unit, by this rotor loading torque with the optimal control amount that optimal control unit exports input to rotor speed forecast unit, obtain the predicted value ω of rotor speed _m, meanwhile, by rotor speed and the predicted value ω of rotor speed _minput to error prediction unit, obtain the speed error value e of rotor; Finally, by rotor speed error amount e, rotor speed predicted value ω _mand rotor speed input to the optimal control unit of Predictive function control (PFC), obtain optimal control amount realize the high accuracy of PMSM servo system under disturbing influence to control; Wherein,

Described Kalman filter is set up based on following formula:

${\hat{w}}_k={F\hat{w}}_{k-1}+{\mathrm{G\Γ}}_{k-1}^{+}(x_{k|k}-A_{k-1}{\hat{x}}_{k-1|k-1}-D_{k-1}{u}_{k-1})---\left(4\right)$

In formula (4), for servo system in the Kalman filter in k moment to rotor loading disturbance estimated value, the implication that subscript " ^ " representative is estimated; The coefficient that the coefficient that F is rotor loading disturbance estimated value, G are rotor loading coefficient of disturbance matrix; for rotor loading coefficient of disturbance matrix is at the left inverse matrix in k-1 moment, its expression formula is:

${\mathrm{\Γ}}_{k-1}^{+}={\left(D_{k-1}^T{D}_{k-1}\right)}^{-1}{D}_{k-1}^T$

Wherein, for servo system is at the input matrix D in k-1 moment _k-1transposition, the symbol that its subscript " T " is matrix transpose; D _k-1for at k-1 moment discrete input matrix, its expression formula is:

$D_{k-1}{\left[\begin{array}{ccc}\frac{T_s}{J}& 0& 0\end{array}\right]}^T$

Wherein, T _sfor servo system sample period time, J is motor load moment of inertia;

In formula (4), A _k-1for servo system is at k-1 moment discrete matrix, its expression formula is:

$A_{k-1}=\left[\begin{array}{ccc}1-\frac{{\mathrm{BT}}_s}{J}& 0& -\frac{T_s}{J}\\ T_s& 1& 0\\ 0& 0& 1\end{array}\right]$

Wherein, B is viscous friction coefficient;

In formula (4), x _k|kfor kth moment Kalman filter is to discrete predicted value x _kpriori prediction value, x _kfor the kth moment discrete predicted value of motor status variable x, the expression formula of x is: x=[ω θ T _l] ^t, wherein, ω is spinner velocity, and θ is rotor-position, T _lfor rotor loading torque; for kth-1 moment Kalman filter is to discrete estimation value posterior estimate, for motor status variable kth-1 moment discrete estimation value, expression formula be: $\hat{x}={\left[\begin{array}{ccc}\widehat{\mathrm{\ω}}& \widehat{\mathrm{\θ}}& {\hat{T}}_L\end{array}\right]}^T,$ The implication that subscript " ^ " representative is estimated; u _k-1discrete output variable for system in the k-1 moment to motor status variable u, the expression formula of u is: u=[T _e], wherein, T _efor motor electromagnetic torque;

The predicted value ω of described rotor speed _m, set up based on following formula:

${\mathrm{\ω}}_m(k+i)={\mathrm{\α}}_m^i{\mathrm{\ω}}_m\left(k\right)+K_m(1+...+{\mathrm{\α}}_m^{i-1})i_q^{*}\left(k\right)+K_m(1+...+{\mathrm{\α}}_m^{i-1})T_L\left(k\right)/K_t---\left(9\right)$

In formula, ω _m(k+i) for servo system is in the rotor speed predicted value in k+i moment, i=1,2 ... P, P are the length of prediction time domain, K _mfor rotor speed forecast unit first coefficient of Predictive function control (PFC), its expression formula is: K _m=(1-α _m) K _t/ B, α _mfor rotor speed forecast unit second coefficient of Predictive function control (PFC), its expression formula is: for the i power of rotor speed forecast unit second coefficient of Predictive function control (PFC), K _tfor rotor loading torque constant, for servo system is in the optimal control amount in k moment, T _lk () is for servo system is at the rotor loading torque value in k moment;

The speed error value e of described rotor sets up based on following formula:

e(k+i)＝…＝e(k+1)＝e(k)＝ω(k)-ω _m(k) (10)

In formula, e (k+i) is the error amount of the rotor speed in the k+i moment, i=1,2 ... P, P are the length of prediction optimization time domain, for k moment Kalman filter observes the rotor speed value obtained, ω _mk () is the rotor speed predicted value of servo system in the k moment;

Described optimal control amount set up based on following formula:

$i_q^{*}={(W_1^T{\mathrm{QW}}_1+R)}^{-1}{W}_1^{T}Q[W_2\left(k\right)-W_3\left(k\right)-E\left(k\right)-W_1{T}_L\left(k\right)/K_t]---\left(14\right)$

In formula (14), W ₁for optimal control unit first coefficient matrix of Predictive function control (PFC), its expression formula is:

$W_1={[K_m...K_m(1+...+{\mathrm{\α}}_m^{P-1})]}^T;$

Q is the input variable weighting coefficient matrix of optimal control unit, and its expression formula is: wherein, for optimal control unit input variable weight coefficient square; R is the controlled quentity controlled variable weighting coefficient matrix of optimal control unit, and its expression formula is: R=[r ²], wherein, r ²for optimal control unit controlled quentity controlled variable weight coefficient square; W ₂k optimal control unit second coefficient matrix that () is k moment Predictive function control (PFC), its expression formula is: W ₂(k)=[ω _r(k+1) ... ω _r(k+P)] ^t, wherein, ω _r(k+1) for servo system is in the rotor speed reference value in k+1 moment; W ₃k optimal control unit the 3rd coefficient matrix that () is k moment Predictive function control (PFC), its expression formula is: the speed error matrix that E (k) is rotor, its expression formula is: E (k)=[e (k+1) ... e (k+P)] ^t.