CN105897110A - Proportional integral (PI) parameter setting method for high-performance controller of permanent-magnet synchronous motor - Google Patents

Abstract

The invention discloses a proportional integral (PI) parameter setting method for a high-performance controller of a permanent-magnet synchronous motor, and belongs to the technical field of motor control. The method comprises the following steps of sampling the current of a motor winding; building a mathematical model of a motor driving system; drawing PI parameter stable domain; analyzing stability according to phase margin and magnitude margin of a frequency domain performance index, and drawing an expect margin domain; analyzing dynamic property according to overshoot and adjustment time of a time domain performance index, and drawing a three-dimensional diagram of a PI parameter and the performance indexes; and completing multi-objective optimization on the PI parameter, wherein a setting result is taken as a coefficient of a PI regulator in the controller. The method provided by the invention has the advantages that 1, a plurality of indexes of time domain and frequency domain are compatible, and a system is enabled to have relatively high robustness and favorable dynamic property; 2, the change relation between the performance indexes and the parameter of the system is directly disclosed by visual analysis, and the debugging direction of the PI parameter is indicated; and 3, modularization and programming are achieved, and the portability is high.

Description

The PI parameter tuning method of permagnetic synchronous motor high performance controller

Technical field

The present invention relates to electric machine control system electric current loop PI parameter tuning method, particularly relate to time domain and frequency domain The visual analysis method of multiple performance indications, belongs to motor control technology field.

Background technology

Permagnetic synchronous motor (PMSM) has high power density, high efficiency and low noise and other advantages, electronic Automotive field is more and more applied.Electric machine controller (being also called motor driven systems) is electronic vapour " brain " of car, the basic demand for electric machine controller has: 1) safe and reliable, in system parameter variations Time system still stable operation；2) torque response is fast, meet vehicle quick start, the requirement such as overtake other vehicles；3) Weak magnetic voltage-regulation is fast, adapts to vehicle high-speed and runs.Electric current loop is the internal ring of control system, current sampling data The tracking to set-point is realized by pi regulator.Therefore improve electric machine controller performance, need to adjust out Excellent PI parameter, meets multiple performance indications requirement.

The setting method of PI parameter is a lot, adjusts PI parameter according to whether by performance indications, can be divided into two Class: first kind method is direct Tuning, obtains PI parameter by engineering experience or rule, then solves performance Index verifies the effect of adjusting of PI parameter；Equations of The Second Kind method is indirect Tuning, and the performance first analyzing system refers to Mark, then adjusted PI parameter by given index.

Directly Tuning mainly has: Ziegler-Nichols method, manually regulation method and canonical system Tuning. Ziegler-Nichols method is most widely used in engineering, and its tuning process is: first have to facing of acquisition system Boundary's Frequency point information, then obtains PI coefficient according to ZN rule.Directly Tuning has the disadvantage that

1) empirical value is relied on, it is difficult to reaching desired performance indications, effect of adjusting is poor；

2) cannot exposing system performance indications and the variation relation of parameter, the debugging direction of parameter is unknown, needs Examination is gathered repeatedly.

Tuning goes out to send PI parameter of adjusting from system performance index indirectly.Document " Lidozzi A, Solero L, Crescimbini F,et al.Direct tuning strategy for speed controlled PMSM drives[C]// IEEE International Symposium on Industrial Electronics.2010:1265-1270. " (" speed Control PMSM drive system directly debugs strategy ", " IEEE industrial electronic international symposium ", 2010 years the 1265-1270 page) calculate PI parameter by given open-loop cut-off frequency and phase margin, expectation can be met Dynamic property.The method passes through analytic expression derivation nargin and the relation of PI parameter, and operand is bigger.Document “Fung H W,Wang Q G,Lee T H.PI Tuning in Terms of Gain and Phase Margins[J]. Automatica, 1998,34 (9): 1145-1149 " (" a kind of PI control method based on amplitude and phase margin ", " automatization ", volume 59 the 9th phase 1145-1149 page in 1998) propose to use graphical method to adjust PI first Parameter, it is to avoid a large amount of budgets of analytic expression method.Document " Hamamci S E, Tan N.Design of PI controllers for achieving time and frequency domain specifications simultaneously[J]. Isa Transactions, 2006,45 (4): 529-543. " (" PI simultaneously realizing time domain and frequency domain performance indications controls Device designs ", " Isa Transactions ", volume 45 the 4th phase 529-543 page in 2006) give expected performance and refer to Mark and the pictorial relationships of parameter, realize time domain and the design of frequency domain performance indications simultaneously.These methods exist with Lower deficiency:

1) ignore or time delay process in approximate processing digitized process, PMSM drive system is approximately Linear system, reduces the accuracy of PI parameter tuning；

2) for PMSM controller, the PI parameter tuning method that neither one is general, can obtain satisfied The parameter group of time domain and the multiple performance indications of frequency domain solves, it is impossible to complete multiple-objection optimization.

Summary of the invention

The technical problem to be solved in the present invention is for need repeatedly to try effect of gathering and adjust present in prior art The poorest problem, it is provided that a kind of visual analysis method that can take into account time domain and the multiple performance indications of frequency domain, It is met all solutions of expectation index, and indicates the direction of performance improvement, it is considered to digitized process prolongs Time impact, improve PI parameter precision of adjusting.

For solving the technical problem of the present invention, the technical scheme used is:

1, the PI parameter tuning method of a kind of permagnetic synchronous motor high performance controller, diagrammatically realizes System stability and the analysis of dynamic index and PI parameter multiple-objection optimization, described PI parameter includes PI Actuator proportional COEFFICIENT K_pWith pi regulator integral item coefficient, it is characterised in that comprise the following steps:

Step 1, sampling obtains discrete three-phase windings current signal, and its dominant frequency spectral amplitude ratio decays to continuous signal 'sT_sFor the sampling period, three-phase windings current signal obtains biphase rotatory current i through coordinate transform_dAnd i_q, i_dFor d shaft current, i_qFor q shaft current；

Step 2, sets up motor driven systems mathematical model, is shown below:

$\mathrm{\φ}\left(s\right)=\frac{(1-e^{-{\mathrm{sT}}_s})e^{-{\mathrm{sT}}_s}{K}_{p}s+(1-e^{-{\mathrm{sT}}_s})e^{-{\mathrm{sT}}_s}{K}_i}{{\mathrm{LT}}_s{s}^3+{\mathrm{RT}}_s{s}^2+(1-e^{-{\mathrm{sT}}_s})e^{-{\mathrm{sT}}_s}{K}_{p}s+(1-e^{-{\mathrm{sT}}_s})e^{-{\mathrm{sT}}_s}{K}_i}$

Wherein, φ (s) is system closed loop transfer function, and L is motor inductances, and R is electric motor resistance, K_pFor PI Actuator proportional coefficient, K_iFor pi regulator integral item coefficient,Control for using delayed one to clap to introduce Time delay,Be equivalent to the time delay of zero-order holder for PWM output procedure, s is Laplace operator；

Step 3, with K_pFor transverse axis, K_iFor the longitudinal axis, set up PI parameter plane coordinate system, draw PI parameter steady Localization, obtains K_pAnd K_iStable region；

Step 4, according to frequency domain performance indications phase marginSystem stability is analyzed, at PI with magnitude margin A In parameter plane coordinate system, draw and meetAnd A > A_expExpectation nargin territory, whereinFor in engineering The phase margin lower limit required, A_expFor the magnitude margin lower limit required in engineering；

Step 5, according to time-domain response criterion overshoot δ and regulating time t_sAnalyze system dynamics, in step In the expectation nargin territory of 4 gained, with K_pAnd K_iFor independent variable, make respectively with δ and t_sFor object function three Dimension figure；

Step 6, carries out PI parameter optimization in the graphics of step 5 gained, i.e. analyzes dynamic performance index With the variation relation of PI parameter, to reduce δ and t_sFor target, the PI parameter value of optimum of adjusting out, as electricity The coefficient of pi regulator in machine controller.

Preferably, the step of the drafting PI parametric stability region described in step 3 comprises the following steps:

(1) according to system closed loop transfer function φ (s) described in step 2, frequency characteristic D (j ω) letter of system The expression formula of number is as follows:

$D\left(j\mathrm{\ω}\right)=-{\mathrm{jLT}}_s{\mathrm{\ω}}^3-{\mathrm{RT}}_s{\mathrm{\ω}}^2+j(1-e^{-{\mathrm{j\ωT}}_s})e^{-{\mathrm{j\ωT}}_s}{K}_p\mathrm{\ω}+(1-e^{-{\mathrm{j\ωT}}_s})e^{-{\mathrm{j\ωT}}_s}{K}_i$

Wherein, ω is the frequency of system, and j is imaginary unit；

(2) according to the frequency characteristic described in step (1), make D (j ω)=0 aspire for stability border, join at PI In number plane coordinate system, the stability boundaris B of system is expressed as follows:

B=B₀UB_ωUB_∞

Wherein, B₀For stability boundaris during ω=0, B_ωIt is 0 < ω < stability boundaris during ∞, B_∞During for ω=∞ Stability boundaris, U represents union；

(3) PI parameter K is solved according to the stability boundaris B described in step (2)_pAnd K_iIf, B₀ObtainB_∞Obtain and K_pAnd K_iUnrelated solution, B_ωThe PI parameter expression obtained is:

$K_p=\frac{{\mathrm{LT}}_s{\mathrm{\&omega;}}^2\left(cos\right({\mathrm{\&omega;T}}_s)-cos(2{\mathrm{\&omega;T}}_s\left)\right)+{\mathrm{RT}}_s\mathrm{\&omega;}\left(sin\right({\mathrm{\&omega;T}}_s)-sin(2{\mathrm{\&omega;T}}_s\left)\right)}{2-2cos\left({\mathrm{\&omega;T}}_s\right)}$

$K_i=\frac{{\mathrm{LT}}_s{\mathrm{\&omega;}}^3\left(sin\right(2{\mathrm{\&omega;T}}_s)-sin({\mathrm{\&omega;T}}_s\left)\right)+{\mathrm{RT}}_s{\mathrm{\&omega;}}^2\left(cos\right({\mathrm{\&omega;T}}_s)-cos(2{\mathrm{\&omega;T}}_s\left)\right)}{2-2\cos \left({\mathrm{\&omega;T}}_s\right)}$

(4) according to the PI parameter expression described in step (3), draw out in PI parameter plane coordinate system System neutrality curve, obtains K_pAnd K_iStable region.

Preferably, the drafting expectation nargin territory described in step 4 comprises the following steps:

(1) PI parameter K is set_pAnd K_iWith magnitude margin A, phase marginParameter expression as follows:

(2) nargin curve is drawn according to the expression formula described in step (1): make A=A_exp,Draw Magnitude margin is A_expCurve GM；Make A=1,Drafting phase margin isCurve PM；

(3) GM and PM that step (2) obtains is plotted in same PI parameter plane coordinate system, The common factor part surrounding region is expectation nargin territory, the most satisfiedAnd A > A_exp。

Preferably, overshoot δ described in step 5 is shown below:

$\mathrm{\&delta;}=\frac{c\left(t_p\right)-c\left(\mathrm{\&infin;}\right)}{c\left(\mathrm{\&infin;}\right)}\&times;100\%$

Wherein, t_pFor time to peak, c (t_p) it is that system step responds maximum, c (∞) is system step response Stable state output.

Preferably, the regulating time t described in step 5_sRepresent system step response output c (t_p) it is maintained at 5% Error band within minimum time, be shown below:

0.95c(∞)<c(t_s)<1.05c(∞)

c(t_s) represent that system step responds at t_sThe output in moment.

After using the present invention, the optimal solution meeting expected performance index can be chosen efficiently, have as follows simultaneously Advantage:

1, multiple performance indications of direct exposing system and the variation relation of parameter, specify PI parameter testing Direction, it is simple to multiple-objection optimization；

2, consider the impact of time delay in digitized process, improve the accuracy of PI parameter tuning；

3, provide the algorithm of a kind of modularity, sequencing, if systematic parameter and constraint condition change, only need Change subprogram is portable strong.

Accompanying drawing explanation

Fig. 1 is the implementing procedure figure of the inventive method.

Fig. 2 is the structured flowchart of PMSM Drive System.

Fig. 3 is the complete stable region of system in the embodiment of the present invention.

Fig. 4 is the expectation nargin territory in the embodiment of the present invention.

Fig. 5 is open-loop cut-off frequency and the quantitative relationship figure of PI parameter in the embodiment of the present invention.

Fig. 6 is the quantitative relationship figure of system overshoot and regulating time and PI parameter in the embodiment of the present invention.

Fig. 7 is the inventive method and the step response comparison diagram of Ziegler-Nichols method setting valve.

Detailed description of the invention

Below in conjunction with the accompanying drawings, the detailed description of the invention of the present invention is described.

Fig. 1 is the inventive method flow chart, mainly includes sample motor winding current S01, sets up motor and drives The mathematical model S02 of system, draws PI parametric stability region S03, draws expectation nargin territory S04, draws dynamically Index graphics S05 and PI parameter multiple-objection optimization S06.

Sample motor winding current S01, obtains discrete three-phase windings current signal, and its dominant frequency spectral amplitude ratio decays For continuous signalT_sFor the sampling period, obtain d axle and the biphase rotatory current of q axle through coordinate transform.

Set up the mathematical model S02 of motor driven systems, it is considered in digitized process delayed one clap control time delay and Zero-order holder time delay, obtains the closed loop transfer function of system.

Drawing PI parametric stability region S03, PI parameter includes K_pAnd K_i, K_pFor pi regulator proportional coefficient, K_iFor pi regulator integral item coefficient.With K_pFor transverse axis, K_iFor the longitudinal axis, set up parameter plane coordinate system, paint PI parametric stability region processed, obtains K_pAnd K_iStable region.

Draw expectation nargin territory S04, according to frequency domain performance indications phase marginSystem is analyzed with magnitude margin A Stability.In order to improve system robustness, when operating condition and Parameters variation system can with stable operation, The nargin scope of given systemAnd A > A_exp, whereinFor in engineering require phase margin lower limit, A_expFor the magnitude margin lower limit required in engineering.Draw out nargin curve, and obtain expecting nargin territory.

Draw dynamic indicator graphics S05, according to time-domain response criterion overshoot δ and regulating time t_sAnalyze system System dynamic, in expectation nargin territory, with K_pAnd K_iFor independent variable, make respectively with δ and t_sFor target letter The graphics of number.

PI parameter multi-objective optimization S06, analyzes the variation relation of dynamic performance index and PI parameter, to reduce δ And t_sFor target, the PI parameter value of optimum of adjusting out, as the coefficient of pi regulator in electric machine controller.

The embodiment of the method is illustrated as a example by a 30kW permagnetic synchronous motor.Known motor Parameter is: L_d=0.31mH, L_q=1.04mH, R=6m Ω, the sample frequency of system is T_s=8400Hz. The PI parameter tuning method realizing permagnetic synchronous motor high performance controller comprises the following steps:

Step 1, sampling obtains discrete three-phase windings current signal, and its dominant frequency spectral amplitude ratio decays to continuous signal 'sT_sFor the sampling period, three-phase windings current signal obtains biphase rotatory current i through coordinate transform_dAnd i_q, i_dFor d shaft current, i_qFor q shaft current.

Step 2, sets up motor driven systems mathematical model, is shown below:

$\mathrm{\&phi;}\left(s\right)=\frac{(1-e^{-{\mathrm{sT}}_s})e^{-{\mathrm{sT}}_s}{K}_{p}s+(1-e^{-{\mathrm{sT}}_s})e^{-{\mathrm{sT}}_s}{K}_i}{{\mathrm{LT}}_s{s}^3+{\mathrm{RT}}_s{s}^2+(1-e^{-{\mathrm{sT}}_s})e^{-{\mathrm{sT}}_s}{K}_{p}s+(1-e^{-{\mathrm{sT}}_s})e^{-{\mathrm{sT}}_s}{K}_i}$

Wherein, φ (s) is system closed loop transfer function, and L is motor inductances, and R is electric motor resistance, K_pFor PI Actuator proportional coefficient, K_iFor pi regulator integral item coefficient,Control for using delayed one to clap to introduce Time delay,Be equivalent to the time delay of zero-order holder for PWM output procedure, s is Laplace operator.

Making a concrete analysis of as a example by q axle, after adding feedforward current decoupling, the mathematical model of motor becomesu_qFor motor q shaft voltage, L_qFor motor q axle inductance, R is electric motor resistance.Examine The impact of time delay during worry Digital Control:

(1) sample and calculating process causes maximum duty cycle limited, use delayed one to clap and control, prolonging of introducing Shi Wei

(2) PWM output procedure is equivalent to zero-order holder, is expressed as

Fig. 2 is the q axle control block diagram of motor driven systems, q shaft current i_qObtain through over-current sensor sampling Discrete current signal i_qs, current instruction valueWith i_qsDifference as the input of pi regulator.Pi regulator Output clap time delay through one and obtain voltage modulation signal, then produce the driving letter of switching tube through PWM Number, wherein PWM gain table is shown as K_pwm, after standardization, its value is 1.Electric machine controller output voltage u_qAct on motor q axle, produce electric current i_q。

Obtain the q axle closed loop transfer function φ of system_qS () is shown below:

${\mathrm{\&phi;}}_q\left(s\right)=\frac{(1-e^{-{\mathrm{sT}}_s})e^{-{\mathrm{sT}}_s}{K}_{p}s+(1-e^{-{\mathrm{sT}}_s})e^{-{\mathrm{sT}}_s}{K}_i}{L_q{T}_s{s}^3+{\mathrm{RT}}_s{s}^2+(1-e^{-{\mathrm{sT}}_s})e^{-{\mathrm{sT}}_s}{K}_{p}s+(1-e^{-{\mathrm{sT}}_s})e^{-{\mathrm{sT}}_s}{K}_i}$

Step 3, with K_pFor transverse axis, K_iFor the longitudinal axis, set up PI parameter plane coordinate system, draw PI parameter steady Localization, obtains K_pAnd K_iStable region.

Specifically include following steps:

(1) according to the q axle closed loop transfer function φ described in step 2_qS (), obtains frequency characteristic D_q(j ω's) Expression formula is as follows:

$D_q\left(j\mathrm{\&omega;}\right)=-{\mathrm{jL}}_q{T}_s{\mathrm{\&omega;}}^3-{\mathrm{RT}}_s{\mathrm{\&omega;}}^2+j(1-e^{-{\mathrm{j\&omega;T}}_s})e^{-{\mathrm{j\&omega;T}}_s}{K}_p\mathrm{\&omega;}+(1-e^{-{\mathrm{j\&omega;T}}_s})e^{-{\mathrm{j\&omega;T}}_s}{K}_i$

Wherein, ω is the frequency of system, and j is imaginary unit；

(2) according to the frequency characteristic expression formula described in step (1), D is made_qAspire for stability border in (j ω)=0, In PI parameter plane coordinate system, the stability boundaris B of system is expressed as follows:

B=B₀UB_ωUB_∞

Wherein, B₀For stability boundaris during ω=0, B_ωIt is 0 < ω < stability boundaris during ∞, B_∞During for ω=∞ Stability boundaris, U represents union；

(3) PI parameter K is solved according to the stability boundaris B described in step (2)_pAnd K_iIf, B₀ObtainB_∞Obtain and K_pAnd K_iUnrelated solution, B_ωThe PI parameter expression obtained is:

$K_p=\frac{L_q{T}_s{\mathrm{\&omega;}}^2\left(cos\right({\mathrm{\&omega;T}}_s)-cos(2{\mathrm{\&omega;T}}_s\left)\right)+{\mathrm{RT}}_s\mathrm{\&omega;}\left(sin\right({\mathrm{\&omega;T}}_s)-sin(2{\mathrm{\&omega;T}}_s\left)\right)}{2-2cos\left({\mathrm{\&omega;T}}_s\right)}$

$K_i=\frac{L_q{T}_s{\mathrm{\&omega;}}^3\left(sin\right(2{\mathrm{\&omega;T}}_s)-sin({\mathrm{\&omega;T}}_s\left)\right)+{\mathrm{RT}}_s{\mathrm{\&omega;}}^2\left(cos\right({\mathrm{\&omega;T}}_s)-cos(2{\mathrm{\&omega;T}}_s\left)\right)}{2-2cos\left({\mathrm{\&omega;T}}_s\right)}$

(4) according to the PI parameter expression described in step (3), draw out in PI parameter plane coordinate system System neutrality curve, obtains K_pAnd K_iStable region.

Shadow region in Fig. 3 is the PI parametric stability region drawn out, and is met the whole of system stability PI parameter.K_pThe maximum that can choose is 9.58, now K_i=0；K_iThe maximum that can choose is 18356, Now K_pIt is 5.73.In PI parametric stability region, optimizing can ensure that system all-the-time stable, improves and optimizes efficiency.

Step 4, according to frequency domain performance indications phase marginSystem stability is analyzed, at PI with magnitude margin A In parameter plane coordinate system, draw and meetAnd A > A_expExpectation nargin territory, whereinFor in engineering The phase margin lower limit required, A_expFor the magnitude margin lower limit required in engineering.

In the present embodiment, owing to system parameter variations can affect system stability, engineering requiring, amplitude is abundant Degree is more than 50 ° more than 10dB, phase margin.In parameter plane coordinate system, draw and meetAnd A > 10dB Expectation nargin territory.

Described drafting expectation nargin territory comprises the following steps:

(1) PI parameter K is set_pAnd K_iWith magnitude margin A, phase marginParameter expression as follows:

(2) nargin curve is drawn according to the expression formula described in step (1): make A=3.1623,Paint Magnitude margin processed is the curve GM of 10dB；Make A=1,Draw the curve PM that phase margin is 50 °；

(3) GM and PM that step (2) obtains is plotted in same PI parameter plane coordinate system, The common factor part surrounding region is expectation nargin territory, the most satisfiedAnd A > A_exp。

Dash area in Fig. 4 is expectation nargin territory, is met whole PI parameters of margin requirement.When When PI parameter is PM curve and GM intersections of complex curve, i.e. K_p=2.86, K_iWhen=1631, the magnitude margin of system For 10dB, phase margin is 50 °.When PI parameter be expectation nargin territory in some time, the magnitude margin of system is big In 10dB, phase margin is more than 50 °.Optimizing in expectation nargin territory, meets Robustness Design requirement.

Step 5, according to time-domain response criterion overshoot δ and regulating time t_sAnalyze system dynamics, in step In the expectation nargin territory of 4 gained, with K_pAnd K_iFor independent variable, make respectively with δ and t_sFor object function three Dimension figure.

Described overshoot δ is shown below:

$\mathrm{\&delta;}=\frac{c\left(t_p\right)-c\left(\mathrm{\&infin;}\right)}{c\left(\mathrm{\&infin;}\right)}\&times;100\%$

Wherein, t_pFor time to peak, c (t_p) it is that system step responds maximum, c (∞) is system step response Stable state output.

Described regulating time t_sRepresent system step response output c (t_p) be maintained at the error band of 5% within Minimum time, is shown below:

0.95c(∞)<c(t_s)<1.05c(∞)

c(t_s) represent that system step responds at t_sThe output in moment.

Fig. 5 is PI parameter K_p、K_iWith the graphics of overshoot δ, it can be seen that K_pIn the case of constant, Increase K_i, the overshoot of system increases, and maximum can reach 30.5%.Can intuitively be met constant from figure The PI parameter region of overshoot, it is also possible to know the PI parameter region that overshoot is less.

Fig. 6 is PI parameter K_p、K_iWith regulating time t_sVariation relation, it can be seen that PI parameter value is relatively Hour, regulating time is relatively big, and maximum can reach 0.0962s.Regulating time can be intuitively met from figure Less PI parameter region

Step 6, carries out PI parameter optimization in the graphics of step 5 gained, i.e. analyzes dynamic performance index With the variation relation of PI parameter, to reduce δ and t_sFor target, the PI parameter value of optimum of adjusting out, as electricity The coefficient of pi regulator in machine controller.

Realize PI parameter multiple-objection optimization and adjust, mainly from the standpoint of two:

(1) system has higher robustness, still stable in the case of the Parameters variation such as inductance, magnetic linkage Run.All draw on the basis of Fig. 4 expects nargin territory due to Fig. 5 and Fig. 6, meet system Shandong Rod requirement.

(2) system has torque response and weak magnetic voltage-regulation faster, can meet electric automobile and quickly rise Move, overtake other vehicles and high-speed cruising.In conjunction with Fig. 5 and Fig. 6, carry out for target reducing overshoot and regulating time Optimizing, obtains one group of optimum PI parameter, can meet dynamic performance requirement.

The PI parameter chosen by method for visualizing is designated as K_{p_V}And K_{i_V}, obtain by adjusting: work as K_{p_V}=2.7, K_{i_V}When=80, system meets frequency domain and time domain multiple performance indications requirement.

Widely used Ziegler-Nichols method in engineering is selected to compare with the inventive method, by the method The PI parameter chosen is designated as K_{p_ZN}And K_{i_ZN}.Use Ziegler-Nichols method to adjust PI parameter, first make K_i=0, regulate K_pUntil service system threshold oscillation.Threshold oscillation gain K_cIt is 9.5, critical period of the oscillation T_cFor 0.714ms.Then further according to ZN rule, K can be obtained_{p_ZN}=0.4K_c=3.8, K_{i_ZN}=0.8/T_c=1120.

The effect of adjusting of two kinds of methods is compared respectively in terms of stability and dynamic two.

1) stability compares.When pi regulator coefficient selects (K_{p_V},K_{i_V}) time, the magnitude margin of system is 11dB, phase margin is 63 °, meets stability indicator design requirement.When pi regulator coefficient selects (K_{p_ZN},K_{i_ZN}) time, the magnitude margin of system is 7.81dB, and phase margin is 48.2 °, does not meets stable Property index Design requirement.And Ziegler-Nichols method is not pointed out to debug direction, need repeatedly to try to gather The parameter meeting expectation nargin can be found.

2) dynamic compares.Fig. 7 is the step response diagram of system, contrasts two kinds of method setting valves dynamically The effect of aspect of performance.Solid line represents the context of methods setting valve selected, and i.e. selects (K when PI parameter_{p_V},K_{i_V}) Time, the overshoot of system is 1.7%, and regulating time is 0.8ms.Dotted line represents selects Ziegler-Nichols Method setting valve, i.e. selects (K when PI parameter_{p_ZN},K_{i_ZN}) time, the overshoot of system is 24.5%, during regulation Between be 4.9ms.Comparing Ziegler-Nichols method, the PI parameter that context of methods is adjusted out makes the dynamic of system Performance is greatly improved.

The method that the present invention provides can take into account frequency domain and time-domain response criterion, makes system meet good stablizing Property and dynamic property.In PI parameter field, represent the quantitative relationship of performance indications, can obtain intuitively and have The solution of construction value.When optimization aim and constraint condition change, it is only necessary to change subprogram, can move Planting property is strong.Additionally, the method applies also for using the system of PR actuator, it is different for being also applied for controlled device Step motor or the control system of combining inverter.

Claims (5)

1. a PI parameter tuning method for permagnetic synchronous motor high performance controller, diagrammatically Realize system stability and the analysis of dynamic index and PI parameter multiple-objection optimization, described PI parameter Including pi regulator proportional COEFFICIENT K_pWith pi regulator integral item coefficient K_i, it is characterised in that include Following steps:

Step 1, sampling obtains discrete three-phase windings current signal, and its dominant frequency spectral amplitude ratio decays to continuously SignalT_sFor the sampling period, three-phase windings current signal obtains biphase electric rotating through coordinate transform Stream i_dAnd i_q, i_dFor d shaft current, i_qFor q shaft current；

Step 2, sets up motor driven systems mathematical model, is shown below:

$\mathrm{\&phi;}\left(s\right)=\frac{(1-e^{-{\mathrm{sT}}_s})e^{-{\mathrm{sT}}_s}{K}_{p}s+(1-e^{-{\mathrm{sT}}_s})e^{-{\mathrm{sT}}_s}{K}_i}{{\mathrm{LT}}_s{s}^3+{\mathrm{RT}}_s{s}^2+(1-e^{-{\mathrm{sT}}_s})e^{-{\mathrm{sT}}_s}{K}_{p}s+(1-e^{-{\mathrm{sT}}_s})e^{-{\mathrm{sT}}_s}{K}_i}$

Wherein, φ (s) is system closed loop transfer function, and L is motor inductances, and R is electric motor resistance, K_pFor Pi regulator proportional coefficient, K_iFor pi regulator integral item coefficient,For using delayed one to clap control The time delay that making enters,Be equivalent to the time delay of zero-order holder for PWM output procedure, s is for drawing General Laplacian operater；

Step 3, with K_pFor transverse axis, K_iFor the longitudinal axis, set up PI parameter plane coordinate system, draw PI ginseng Number stable region, obtains K_pAnd K_iStable region；

Step 4, according to frequency domain performance indications phase marginSystem stability is analyzed with magnitude margin A, In PI parameter plane coordinate system, draw and meetAnd A > A_expExpectation nargin territory, wherein For the phase margin lower limit required in engineering, A_expFor the magnitude margin lower limit required in engineering；

Step 5, according to time-domain response criterion overshoot δ and regulating time t_sAnalyze system dynamics, In the expectation nargin territory of step 4 gained, with K_pAnd K_iFor independent variable, make respectively with δ and t_sFor target The graphics of function；

Step 6, carries out PI parameter optimization in the graphics of step 5 gained, i.e. analyzes dynamic property and refers to Mark and the variation relation of PI parameter, to reduce δ and t_sFor target, the PI parameter value of optimum of adjusting out, As the coefficient of pi regulator in electric machine controller.

The PI parameter tuning side of permagnetic synchronous motor high performance controller the most according to claim 1 Method, it is characterised in that the step of the drafting PI parametric stability region described in step 3 comprises the following steps:

(1) according to system closed loop transfer function φ (s) described in step 2, frequency characteristic D (j ω) is obtained Expression formula is as follows:

$D\left(j\mathrm{\&omega;}\right)=-{\mathrm{jLT}}_s{\mathrm{\&omega;}}^3-{\mathrm{RT}}_s{\mathrm{\&omega;}}^2+j(1-e^{-{\mathrm{j\&omega;T}}_s})e^{-{\mathrm{j\&omega;T}}_s}{K}_p\mathrm{\&omega;}+(1-e^{-{\mathrm{j\&omega;T}}_s})e^{-{\mathrm{j\&omega;T}}_s}{K}_i$

Wherein, ω is the frequency of system, and j is imaginary unit；

(2) according to the frequency characteristic described in step (1), D (j ω)=0 is made to aspire for stability border, at PI In parameter plane coordinate system, the stability boundaris B of system is expressed as follows:

B=B₀UB_ωUB_∞

Wherein, B₀For stability boundaris during ω=0, B_ωIt is 0 < ω < stability boundaris during ∞, B_∞For ω=∞ Time stability boundaris, U represents union；

(3) PI parameter K is solved according to the stability boundaris B described in step (2)_pAnd K_iIf, B₀ObtainB_∞Obtain and K_pAnd K_iUnrelated solution, B_ωThe PI parameter expression obtained is:

$K_p=\frac{{\mathrm{LT}}_s{\mathrm{\&omega;}}^2\left(cos\right({\mathrm{\&omega;T}}_s)-cos(2{\mathrm{\&omega;T}}_s\left)\right)+{\mathrm{RT}}_s\mathrm{\&omega;}\left(sin\right({\mathrm{\&omega;T}}_s)-sin(2{\mathrm{\&omega;T}}_s\left)\right)}{2-2cos\left({\mathrm{\&omega;T}}_s\right)}$

$K_i=\frac{{\mathrm{LT}}_s{\mathrm{\&omega;}}^3\left(sin\right(2{\mathrm{\&omega;T}}_s)-sin({\mathrm{\&omega;T}}_s\left)\right)+{\mathrm{RT}}_s{\mathrm{\&omega;}}^2\left(cos\right({\mathrm{\&omega;T}}_s)-cos(2{\mathrm{\&omega;T}}_s\left)\right)}{2-2\cos \left({\mathrm{\&omega;T}}_s\right)}$

(4) according to the PI parameter expression described in step (3), paint in PI parameter plane coordinate system Make system neutrality curve, obtain K_pAnd K_iStable region.

The PI parameter tuning side of permagnetic synchronous motor high performance controller the most according to claim 1 Method, it is characterised in that the drafting expectation nargin territory described in step 4 comprises the following steps:

(1) PI parameter K is set_pAnd K_iWith magnitude margin A, phase marginParameter expression as follows:

(2) nargin curve is drawn according to the expression formula described in step (1): make A=A_exp,Paint Magnitude margin processed is A_expCurve GM；Make A=1,Drafting phase margin isCurve PM；

(3) curve GM step (2) obtained and curve PM is plotted in same PI parameter and puts down In areal coordinate system, the common factor part surrounding region is expectation nargin territory, the most satisfiedAnd A > A_exp。

The PI parameter tuning side of permagnetic synchronous motor high performance controller the most according to claim 1 Method, it is characterised in that overshoot δ described in step 5 is shown below:

$\mathrm{\&delta;}=\frac{c\left(t_p\right)-c\left(\mathrm{\&infin;}\right)}{c\left(\mathrm{\&infin;}\right)}\&times;100\%$

Wherein, t_pFor time to peak, c (t_p) it is that system step responds maximum, c (∞) is that system step rings Answer stable state output.

The PI parameter tuning side of permagnetic synchronous motor high performance controller the most according to claim 1 Method, it is characterised in that the regulating time t described in step 5_sRepresent system step response output c (t_p) protect Hold the minimum time within the error band of 5%, be shown below:

0.95c(∞)<c(t_s)<1.05c(∞)

c(t_s) represent that system step responds at t_sThe output in moment.