CN104779873B - A kind of predictive functional control algorithm for PMSM servo-drive systems - Google Patents
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Abstract
The invention discloses a kind of predictive functional control algorithm for PMSM servo-drive systems, this method gathers the rotor-position signal θ and motor current signal i of PMSM servo-drive systems firstq, using Kalman filter observation rotor loading disturbance, obtain rotor loading torqueAnd rotor speedThen by the rotor loading torqueWith optimum control amountThe rotor speed forecast unit of Predictive function control (PFC) is fed back to, the predicted value ω of rotor speed is obtainedm, by rotor speedAnd the predicted value ω of rotor speedmInput to the error prediction unit of Predictive function control, obtain the speed error value e of rotor；Finally, by e, ωmWithInput to the optimal control unit of Predictive function control, obtain optimum control amountRealize high-precision control of the PMSM servo-drive systems under disturbing influence.This method organically combines Kalman filter and Predictive function control, and both are complementary, can optimize the controlled quentity controlled variable of servo-drive system, improves the control accuracy and Ability of Resisting Disturbance of PMSM servo-drive systems.
Description
Technical Field
The invention relates to a prediction function control method for a Permanent Magnet Synchronous Motor (PMSM) servo system, and belongs to the technical field of high-precision servo control systems.
Background
With the increasing demands on the control accuracy of servo systems, disturbances have become a significant problem that is not negligible. The disturbance often comes from uncertain factors ignored in the modeling process, load sudden change in the system operation process, parameter change and the like. The presence of these factors makes the closed loop system performance worse or even unstable. Therefore, in order to improve the control performance of the servo system, the controller is required to overcome the influence of external disturbance on the system.
In a PMSM servo control system, the PMSM is used as a multivariable, nonlinear and strongly coupled controlled object and has the characteristics of nonlinearity, uncertainty and the like. In order to realize high-precision servo control, the influence of uncertainty factors of controlled objects including a PMSM and a load and external disturbance on the system performance must be overcome. The traditional feedback control strategy, such as a high-gain PID control method, has the advantages of simple structure, easy realization and the like, and can obtain better performance under the condition of parameter matching generally, but the system can oscillate and destabilize due to overhigh gain in the actual engineering.
In practical industrial application, more or less interference including friction and load disturbance always occurs, and in order to eliminate the influence caused by the disturbance and improve the control performance of a servo system, a large amount of research is carried out by domestic and foreign scholars. Predictive Functional Control (PFC) is a class of computer Control algorithms that have been developed in recent years. The method adopts control strategies such as multi-step testing, feedback correction and the like, has the advantages of online optimization, constraint processing, less online calculated amount and the like, is simple to use, can realize simple and visual design criteria, has good control effect, and is suitable for controlling an industrial production process which is difficult to establish an accurate digital model and is relatively complex. The literature (in summer, zhangguang, prediction function control and simulation research [ J ] in the servo system, china motor engineering report, 2005,25 (14): 130-.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a prediction function control method for a PMSM servo system, which organically combines a Kalman filter and a Prediction Function Control (PFC) technology, and the Kalman filter and the PFC technology are complementary to each other, so that the control quantity of the servo system can be optimized, and the control precision and the disturbance resistance of the PMSM servo system are improved.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
a prediction function control method for a PMSM (permanent magnet synchronous motor) servo system is characterized by firstly acquiring a rotor position signal theta and a motor current signal i of the PMSM servo systemqThe rotor position signal theta and the motor current signal iqAs input signal of Kalman filter, based on rotor position signal theta and motor current signal iqObserving the rotor load disturbance by using a Kalman filter to obtain the rotor load torqueAnd rotor speedThen, assuming that a Predictive Function Control (PFC) including an optimization control unit, an error prediction unit and a rotation speed prediction unit loads the rotor with a torqueAnd optimizing the optimal control quantity output by the control unitInput to a rotating speed prediction unit to obtain a predicted value omega of the rotating speed of the rotormWhile rotating the rotorAnd predicted value omega of rotor speedmInputting the rotation speed error value e of the rotor into an error prediction unit; finally, the error value e of the rotor rotation speed and the predicted value omega of the rotor rotation speed are calculatedmAnd rotor speedInput into an optimization control unit of Prediction Function Control (PFC) to obtain an optimal control quantityHigh-precision control of the PMSM servo system under the influence of disturbance is realized; wherein,
the Kalman filter is built based on the following formula:
in the formula (4), the reaction mixture is,the rotor load disturbance estimation value of a Kalman filter at the time k of the servo system is marked with 'A' to represent the estimation meaning; f is the coefficient of the rotor load disturbance estimated value, G is the coefficient of the rotor load disturbance coefficient matrix;the left inverse matrix of the rotor load disturbance coefficient matrix at the moment k-1 is represented as follows:
wherein,input matrix D for servo system at time k-1k-1The superscript "T" of the transpose of (a) is a symbol of the matrix transpose; dk-1The input matrix is discrete at the moment k-1, and the expression is as follows:
wherein, TsSampling period time of a servo system, and J is load moment of inertia of a motor;
in the formula (4), Ak-1The matrix is a discrete matrix of the servo system at the moment k-1, and the expression is as follows:
wherein B is a viscous friction coefficient;
in the formula (4), xk|kDiscrete prediction value x for k-th time Kalman filter pairkA priori predicted value of xkThe discrete predicted value at the kth moment of the motor state variable x is shown as the following expression: x ═ ω θ TL]TWhere ω is rotor speed, θ is rotor position, TLLoading the rotor with torque;kalman filter pair discrete estimates for time k-1The posterior estimate of (a) is,as state variables of the machineThe discrete estimate value at the k-1 th time,the expression of (a) is:the upper mark 'Λ' represents the estimated meaning; u. ofk-1The discrete output quantity of the system to the motor state variable u at the moment k-1 is represented by the following expression: u ═ Te]Which isIn, TeIs the motor electromagnetic torque;
predicted value omega of the rotor speedmEstablished based on the following formula:
in the formula, ωm(K + i) is a predicted value of the rotor speed of the servo system at the moment K + i, i is 1,2, … P, P is the length of a prediction optimization time domain, and K ismA first coefficient of a rotational speed prediction unit for a Prediction Function Control (PFC), expressed as: km＝(1-αm)Kt/B，αmA second coefficient of the rotational speed prediction unit for the Prediction Function Control (PFC), expressed as:to the power of i, K, of a second coefficient of a rotational speed prediction unit for the control of a Prediction Function (PFC)tAs a function of the rotor load torque constant,for optimal control of the servo system at time k, TL(k) The rotor load torque value of the servo system at the moment k is obtained;
the rotational speed error value e of the rotor is established based on the following formula:
where e (k + i) is an error value of the rotor speed at the time k + i, i is 1,2, … P, P is the length of the prediction optimization time domain,for the rotor speed value, omega, observed by the Kalman filter at the k momentm(k) The predicted value of the rotor speed of the servo system at the moment k is obtained;
the optimum control amountBased on the following formula:
in the formula (14), W1An optimal control unit first coefficient matrix for Predictive Function Control (PFC), expressed as:
q is an input quantity weighting coefficient matrix of the optimization control unit, and the expression is as follows:wherein,the square of the weighting coefficient for optimizing the input quantity of the control unit; r is a control quantity weighting coefficient matrix of the optimization control unit, and the expression is as follows: r ═ R2]Wherein r is2The square of the control quantity weighting coefficient for optimizing the control unit; w2(k) And a second coefficient matrix of the optimization control unit for Prediction Function Control (PFC) at the k moment, wherein the expression is as follows: w2(k)＝[ωr(k+1)…ωr(k+P)]TWherein, ω isr(k +1) is a rotor speed reference value of the servo system at the moment of k + 1; w3(k) And the third coefficient matrix of the optimization control unit for the Prediction Function Control (PFC) at the k moment is expressed as follows:e (k) is a rotating speed error matrix of the rotor, and the expression is as follows: e (k) ═ e (k +1) … e (k + P)]T。
According to the technical scheme, the following beneficial effects can be realized:
the method organically combines a Kalman filter with a Prediction Function Control (PFC) technology, and combines a rotation speed error value e of a motor rotor and a rotor rotation speed predicted value omegamAnd rotor speedInput into an optimal control unit of Prediction Function Control (PFC) to obtain the optimal control quantity of the rotorHigh-precision control of the PMSM servo system under the influence of disturbance is achieved, and the disturbance resistance of the servo system is improved.
Drawings
FIG. 1 is a block diagram of a PMSM servo system of the present invention;
FIG. 2 is a flow chart of a predictive function control method for a PMSM servo system in accordance with the present invention;
FIG. 3 is a graph of the results of a speed response experiment of a PMSM servo system employing the method of the present invention;
fig. 4 is a graph showing a result of a speed response experiment of a PMSM servo system using a conventional prediction function control method.
Detailed Description
The accompanying drawings disclose a schematic structural diagram of a preferred embodiment of the present invention without limitation, and the technical solution of the present invention will be described in detail below with reference to the accompanying drawings.
Referring to fig. 1, a system block diagram of a prediction function control method for a PMSM servo system according to the present invention is disclosed, which uses a photoelectric encoder to acquire a position signal θ of a PMSM servo motorThe electric encoder is arranged inside the motor, and a Hall current sensor is adopted to acquire a current signal i of the motoru、ivAnd subjecting it to Clark transformation and park transformation to obtain id、iqThe motor position signal theta and the motor current signal i are usedqFeeding back to a Kalman filter, observing the rotor load torque, the rotor speed and the rotor position by using the Kalman filter, feeding back the observation result to a Prediction Function Control (PFC), and adjusting by the PFC to obtain the optimal control quantityObtained by means of a PI regulatorAndthen the reference value of the stator phase voltage under α - β coordinate system is obtained by inverse park transformation of the position signal observed by the Kalman filterAndand generating a PWM control signal by using a space vector pulse width debugging technology, and controlling a three-phase inverter by the PWM control signal to invert required three-phase alternating current to drive a motor to run.
Specifically, the method comprises the following steps: the prediction function control method for the PMSM servo system comprises the following four steps:
the first step is as follows: constructing a Kalman Filter
Collecting rotor position signal theta and current signal i of PMSM servo systemqThen the rotor position signal theta and the current signal iqAs an input signal of a Kalman filter, observing rotor load disturbance by using the Kalman filter to obtain rotor load torqueAnd rotor speedThe steps of constructing the Kalman filter are as follows:
step 1: collecting rotor position signal theta and current signal iq
Position signals theta of a PMSM servo motor are collected by using a photoelectric encoder, and PMSM stator current i is collected by using a current sensoruAnd ivObtaining d-axis current i under a two-phase rotating coordinate system through Clark transformation and park transformationdAnd q-axis current iq；
Step 2: disturbance observer for constructing discrete load of rotor
Substituting the rotor load disturbance and the measurement error in the servo system into a state equation of the motor to obtain a discrete equation set of the servo system as follows:
in the formula, xkThe discrete predicted value at the kth moment of the motor state variable x is shown as the following expression: x ═ ω θ TL]TWhere ω is rotor speed, θ is rotor position, TLLoading the rotor with torque; y iskInputting a discrete predicted value of the variable y at the kth moment for the system; u. ofkThe discrete output quantity of the system to the motor state variable u at the moment k-1 is represented by the following expression: u ═ Te]Wherein, TeIs the motor electromagnetic torque; w is akIs a disturbance of the rotor load, vkIs the measurement error, AkIs a discrete system matrix corresponding to the k moment of the servo system, and the expression is as follows:Dkis the input matrix corresponding to the instant k of the servo system,the expression is as follows:Ckis an output matrix corresponding to the k moment of the servo system, and the expression is as follows: ck＝[01 0]Wherein, TsThe sampling period time of the servo system is B, the viscous friction coefficient is B, and J is the rotational inertia of the motor load;
in order to estimate the rotor load disturbance value at the moment k +1 of the servo system, equation (1) is:
in the formula,a Kalman filter at time k for the servo system perturbs the estimated value of the rotor load,+for the load disturbance coefficient matrix, the load disturbance w to the servo systemkAnd estimating, wherein a rotor discrete load disturbance observer is as follows:
in the formula,the left inverse matrix of the rotor load disturbance coefficient matrix at the moment k-1 is represented as follows:
wherein,input matrix D for servo system at time k-1k-1Transposing; phi (z) is low passA filter, whose expression is: phi (z) ═ H (zI-F)-1G; f is the coefficient of the rotor load disturbance value of the system, and G is the coefficient of the rotor load disturbance coefficient matrix of the system; h is a constant coefficient matrix;
and step 3: construction of Kalman Filter
According to a principle algorithm of a Kalman filter and a discrete load disturbance observer, the required Kalman filter is obtained and established based on the following formula:
the second step is that: calculating the predicted value of the rotor speed
FIG. 2 is a flow chart of a predictor function control method for a PMSM servo system in accordance with the present invention, showing a Kalman filter and a Predictor Function Control (PFC) including an optimization control unit, an error prediction unit and a speed prediction unit that perturbs an observed rotor loadAnd optimizing the optimal control quantity output by the control unitObtaining a predicted value omega of the rotor speed as an input signal of a speed prediction unit of a Prediction Function Control (PFC)mIn the permanent magnet synchronous motor servo system, for decoupling the rotating speed and the current, the method adoptsVector control of (the given value of d-axis current is constantly 0), and according to Laplace transform, a mechanical equation model of motor dynamics is obtained as follows:
in the formula (5), ω(s) is the mechanical angular velocity of the motor, KtAs a result of the torque constant of the system,for the rotor control quantity, equation (5) is written as a difference equation:
in the formula (6), ωm(K +1) is a predicted value of the rotor speed of the servo system at the time of K +1, KmA first coefficient of a rotational speed prediction unit for a Prediction Function Control (PFC), expressed as: km＝(1-αm)Kt/B，αmA second coefficient of the rotational speed prediction unit for the Prediction Function Control (PFC), expressed as:for optimal control of the servo system at time k, TL(k) The rotor load torque value of the servo system at the moment k is obtained;
at the next sampling instant k +2 in the system, there is
The optimal control variable of the servo system at a future time is assumed to have a value of:
substituting formula (6) for formula (7) to obtain:
sequentially superposing the above formula (6), formula (7) and formula (8) to obtain:
in the formula (9), ωm(k + i) is a predicted value of the rotor speed of the system at the time k + i, i is 1,2, … P, P is the length of the prediction time domain,rotational speed prediction unit second coefficient α for Prediction Function Control (PFC)mTo the power of i;
the third step: and calculating the rotating speed error e of the rotor according to the following calculation formula:
in equation (10), e (k + i) is an error value of the rotor speed at the time k + i, i is 1,2, … P, P is a length of the prediction optimization time domain,rotor speed value, omega, observed for k-time Kalman filterm(k) The predicted value of the rotor speed of the servo at the moment k is obtained;
the fourth step: the rotation speed error value e of the rotor and the predicted value omega of the rotation speed of the rotor are calculatedmAnd rotor speedInput into an optimization control unit of Prediction Function Control (PFC) to obtain an optimal control quantityThe method for realizing the high-precision control of the PMSM servo system under the influence of disturbance comprises the following steps:
step 1: setting an output control quantity basis function of Prediction Function Control (PFC), wherein the expression is as follows:
in the formula (11), the reaction mixture is,for the optimum control quantity, f, at the moment of system k + ij(i) For the basis function at t ═ iTsStep value of time, TsSampling the cycle time for the system; i is 1,2, … P, P is the length of the prediction optimization time domain, j is 1,2, … N, and N is a natural number; mu.sjFor the coefficients of the basis function, a step function is adopted as the basis function, N is 1, f1(i) 1, its basis function is:
step 2: setting a reference track of the rotating speed of the rotor, wherein the expression is as follows:
in the formula (12), ωr(k + i) is the rotor speed reference trajectory, ω, of the system at time k + i*For a given rotor speed of the system at time k,for the rotor rotating speed value observed by the Kalman filter at the k moment,for a given coefficient of the difference between the rotor speed and the rotor speed by subtraction, the expression:Tris the expected response time of the PMSM servo system.
And step 3: the rotation speed error e of the rotor and the predicted value omega of the rotation speed of the rotor are calculatedmAnd rotor speedInput into an optimization control unit of Prediction Function Control (PFC) to obtain an optimal control quantity
Cost function for PMSM servo system, noteThe calculation formula is as follows:
in the formula (13), the reaction mixture is,is a cost function; in order to ensure that the water-soluble organic acid,determining a cost function of the PMSM servo systemThe coefficients of the coefficient matrix of the optimization control unit are updated in real time at each sampling moment, and the optimal control quantity of the servo system is obtained as follows:
in the formula (14), W1Optimization of control unit first coefficient matrix for Predictive Function Control (PFC), table thereofThe expression is as follows:q is an input quantity weighting coefficient matrix of the optimization control unit, and the expression is as follows:wherein,the square of the weighting coefficient for optimizing the input quantity of the control unit; r is a control quantity weighting coefficient matrix of the optimization control unit, and the expression is as follows: r ═ R2]Wherein r is2The square of the control quantity weighting coefficient for optimizing the control unit; w2(k) And a second coefficient matrix of the optimization control unit for Prediction Function Control (PFC) at the k moment, wherein the expression is as follows: w2(k)＝[ωr(k+1)…ωr(k+P)]TWherein, ω isr(k +1) is a rotor speed reference value of the servo system at the moment of k + 1; w3(k) And the third coefficient matrix of the optimization control unit for the Prediction Function Control (PFC) at the k moment is expressed as follows:e (k) is a rotating speed error matrix of the rotor, and the expression is as follows: e (k) ═ e (k +1) … e (k + P)]T。
Referring to fig. 3, a prediction function control method for a PMSM servo system is shown, when the PMSM servo system faces a sudden load change, the recovery time of the rotor speed is 0.21s, and the maximum rotor speed drops by 24 rpm; referring to fig. 4, when a PMSM servo system adopting the conventional prediction function control method faces a sudden load change, the rotor speed recovery time is 0.51s, and the maximum rotor speed drops by 68rpm, comparing the rotor speed recovery time and the maximum rotor speed drop data of the two methods, it can be seen from comparison between fig. 3 and fig. 4 that the prediction function control method for the PMSM servo system of the present invention has better performance in disturbance resistance.
The invention is provided withThe experimental platform of the embodiment adopts an ARM-based full digital control implementation mode, and the programming language is C language. The system takes an XMC4500 chip of the English flying company as a core to form a control circuit part; hall current sensor for collecting two paths of current signals iuAnd iv(ii) a The rotor position detection part is a 2500-line incremental photoelectric encoder and is used for acquiring a rotor position signal of the motor; the inverter circuit takes an intelligent power device as a core, and converts power supply input into corresponding three-phase alternating-current voltage according to a space vector pulse width modulation control signal generated by the XMC4500 chip for driving the motor to work; the rated power of the load motor is 3kW, and the rotor position sensor is a 24-bit multi-turn absolute encoder.
Claims (1)
1. A prediction function control method for a PMSM (permanent magnet synchronous motor) servo system is characterized by firstly acquiring a rotor position signal theta and a motor current signal i of the PMSM servo systemqThe rotor position signal theta and the motor current signal iqAs input signal of Kalman filter, based on rotor position signal theta and motor current signal iqObserving the rotor load disturbance by using a Kalman filter to obtain the rotor load torqueAnd rotor speedThen, assuming that a Predictive Function Control (PFC) including an optimization control unit, an error prediction unit and a rotation speed prediction unit loads the rotor with a torqueAnd optimizing the optimal control quantity output by the control unitInput to a rotating speed prediction unit to obtain a predicted value omega of the rotating speed of the rotormWhile rotating the rotorAnd predicted value omega of rotor speedmInputting the rotation speed error value e of the rotor into an error prediction unit; finally, the error value e of the rotor rotation speed and the predicted value omega of the rotor rotation speed are calculatedmAnd rotor speedInput into an optimization control unit of Prediction Function Control (PFC) to obtain an optimal control quantityHigh-precision control of the PMSM servo system under the influence of disturbance is realized; wherein,
the Kalman filter is built based on the following formula:
in the formula (4), the reaction mixture is,the rotor load disturbance estimation value of a Kalman filter at the time k of a servo system is marked with a character lambada to represent the estimation valueDefining; f is the coefficient of the rotor load disturbance estimated value, G is the coefficient of the rotor load disturbance coefficient matrix;the left inverse matrix of the rotor load disturbance coefficient matrix at the moment k-1 is represented as follows:
wherein,input matrix D for servo system at time k-1k-1The superscript "T" of the transpose of (a) is a symbol of the matrix transpose; dk-1The input matrix is discrete at the moment k-1, and the expression is as follows:
wherein, TsSampling period time of a servo system, and J is load moment of inertia of a motor;
in the formula (4), Ak-1The matrix is a discrete matrix of the servo system at the moment k-1, and the expression is as follows:
wherein B is a viscous friction coefficient;
in the formula (4), xk|kDiscrete prediction value x for k-th time Kalman filter pairkA priori predicted value of xkThe discrete predicted value at the kth moment of the motor state variable x is shown as the following expression: x ═ ω θ TL]TWhere ω is rotor speed, θ is rotor position, TLLoading the rotor with torque;kalman filter pair discrete estimates for time k-1The posterior estimate of (a) is,as state variables of the machineThe discrete estimate value at the k-1 th time,the expression of (a) is:the upper mark 'Λ' represents the estimated meaning; u. ofk-1The discrete output quantity of the system to the motor state variable u at the moment k-1 is represented by the following expression: u ═ Te]Wherein, TeIs the motor electromagnetic torque;
predicted value omega of the rotor speedmEstablished based on the following formula:
in the formula, ωm(K + i) is a predicted value of the rotor speed of the servo system at the time K + i, i is 1,2, … P, P is the length of a predicted time domain, and K ismA first coefficient of a rotational speed prediction unit for a Prediction Function Control (PFC), expressed as: km＝(1-αm)Kt/B，αmA second coefficient of the rotational speed prediction unit for the Prediction Function Control (PFC), expressed as: as a function of predictionControl (PFC) speed prediction unit to the power of i, K of a second coefficienttAs a function of the rotor load torque constant,for optimal control of the servo system at time k, TL(k) The rotor load torque value of the servo system at the moment k is obtained;
the rotational speed error value e of the rotor is established based on the following formula:
where e (k + i) is an error value of the rotor speed at the time k + i, i is 1,2, … P, P is the length of the prediction optimization time domain,for the rotor speed value, omega, observed by the Kalman filter at the k momentm(k) The predicted value of the rotor speed of the servo system at the moment k is obtained;
the optimum control amountBased on the following formula:
in the formula (14), W1An optimal control unit first coefficient matrix for Predictive Function Control (PFC), expressed as:
q is an input quantity weighting coefficient matrix of the optimization control unit, and the expression is as follows:wherein,the square of the weighting coefficient for optimizing the input quantity of the control unit; r is a control quantity weighting coefficient matrix of the optimization control unit, and the expression is as follows: r ═ R2]Wherein r is2The square of the control quantity weighting coefficient for optimizing the control unit; w2(k) And a second coefficient matrix of the optimization control unit for Prediction Function Control (PFC) at the k moment, wherein the expression is as follows: w2(k)＝[ωr(k+1)…ωr(k+P)]TWherein, ω isr(k +1) is a rotor speed reference value of the servo system at the moment of k + 1; w3(k) And the third coefficient matrix of the optimization control unit for the Prediction Function Control (PFC) at the k moment is expressed as follows:e (k) is a rotating speed error matrix of the rotor, and the expression is as follows: e (k) ═ e (k +1) … e (k + P)]T。
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