CN104467596A - Method for reducing torque ripples of switched reluctance motor - Google Patents

Abstract

The invention relates to a method for reducing torque ripples of a switched reluctance motor. According to the method, an NSGA-II (Non-dominated Sorting Genetic Algorithm) technology is adopted to perform parameter optimization and setting on a PI speed controller, a PI current controller and a phase commutation switching angle controller according to a double closed-loop switched reluctance motor control system in the prior art; based on the introduction of the NSGA-II, respective proportional-Integral gain optimization values of the PI speed controller and the PI current controller, as well as optimization values of a switch-on angle and a switch-off angle are generated according to torque ripple and speed ripple minimization; and according to the minimization of speed ripples, the minimization of the ISE (Integral Squared Error) value of speed is adopted as a target, and current is characterized through the ISE value. According to the multi-objective problem, the minimization of the ISE of the motor speed and the minimization of the torque ripples are combined in an optimized manner, and the ISE of current in the inner loop of a control system is adopted as a constraint condition, and therefore, excellent effects can be obtained.

Description

A kind of method reducing switched reluctance motor torque pulsation

Technical field

The present invention relates to switched Reluctance Motor Control field, be specifically related to a kind of control method reducing switched reluctance machines torque pulsation.

Background technology

The torque pulsation of switched reluctance motor, produces velocity fluctuation, noise, the large shortcoming of vibration large three, is to hinder switched reluctance motor speed-adjusting and control system for the bottleneck of the electric transmission field of high-performance always.For many years, the research both at home and abroad with regard to SRM method for suppressing torque ripple is a lot, also has some comparatively practical, plays a good role for reducing torque pulsation.

Although the modern scientist strategies such as Based Intelligent Control also have more apply in switched Reluctance Motor Control System, but system comparatively ripe both at home and abroad at present, or many employing classical PID control algolithms, mostly be PI algorithm, with it, parameter tuning is carried out to system medium velocity, current double closed-loop, but to Torque Ripple Reduction poor effect.

Based on existing mature technology, for reduction motor torque ripple, by being optimized the suppression level of adjusting and then promoting torque pulsation to PI parameter, the optimization method of this respect also has some to put into practice, and achieves certain effect; When considering that switched reluctance machines runs, its angle value turned on and off also has an impact to pulsating torque rate, and the switching angle of fixed angle is also unfavorable for the actual demand that electric efficiency index or Wide Range run; Further, although the pulsation of speed has the factor that comes from torque pulsation and produces, as one of target, the suppressing method of velocity fluctuation is little, and this is also reverse one of mode promoting Torque Ripple Reduction in fact.So, if this multiobject problem of switched reluctance machines Torque Ripple Reduction control seeks multiple target and corresponding control algolithm is more reasonable, should be more effective to the suppression of torque pulsation.

(Non-dominated Sorting Genetic Algorithm is called for short: NSGA-II) be a kind of algorithm being used successfully to some multipurpose project optimization problem fields non-dominated sorted genetic algorithm.Its main advantage is that its character such as non-dominated ranking, elitism strategy can go out high-quality solution by Fast Convergent.

Summary of the invention

According to problem set forth above and background, the present invention proposes the control method that a kind of multiple target reduces switched reluctance machines torque pulsation, NSGA-II is utilized to carry out the selection optimization of the optimization of PI parameter tuning and motor turn-on angle and the pass angle of rupture, with velocity fluctuation value i.e. its integrated square error (Integral Squared Error, be called for short: ISE) to minimize and torque ripple minimization is Bi-objective, current IS E is constraint.Its technical scheme is:

According to two close cycles switched Reluctance Motor Control System prior art, adopt NSGA-II technology that PI speed control, PI current controller, phase-change switch angle controller are carried out to parameter optimization and adjust, velocity fluctuation minimizes and the Bi-objective of torque ripple minimization as optimal control.

Velocity fluctuation minimize be Negotiation speed ISE be minimised as target, the ISE of electric current is also the concept characterizing current pulsation situation.Following two formulas are the ISE calculating PI speed control and PI current controller respectively:

ISE _speed=∫(ω _ref-ω) ²dt

ISE _current=∫(I _ref-I _pha) ²dt

Optimal Parameters comprises: the turn-on angle θ of PI speed control PI gain parameter, PI current controller PI gain parameter, phase-change switch angle controller _onwith pass angle of rupture θ _offbe optimized, the optimum organization select permeability of these parameters, belong to a multi-objective problem, minimize for motor speed ISE and be optimized combination with the target that is minimised as of torque pulsation, be in the ISE of the electric current of control system inner ring as constraints.

According to concrete truth, to the PI gain parameter limited range of PI speed control, PI current controller, turn-on angle and the pass angle of rupture of phase-change switch angle controller limit upper lower limit value respectively; Through tens of independent experiments, by MATLAB/SIMULINK analysis tool, utilize NSGA-II algorithm to obtain velocity fluctuation minimizes, torque ripple minimization, current IS E value time parameters optimal value, and torque situation.

Choosing of NSGA-II parameter needs through study experimental basis enterprising Row sum-equal matrix, except experience tens of tests, also comprises: the coefficient of variation, population scale, the choosing of functional evaluation maximum quantity.

Technique effect of the present invention mainly contains: the effect under PI algorithm independent compared to existing technology, and after introducing NSGA-II, torque pulsation and velocity fluctuation situation are all effectively suppressed.

The introducing of NSGA-II, minimizes target for torque pulsation and velocity fluctuation, produces the respective ratio of PI speed control and PI current controller and storage gain k _p, k _ioptimal value, and turn-on angle θ _onwith pass angle of rupture θ _offoptimal value, achieve good effect.

Although the introducing of new algorithm increases amount of calculation during system cloud gray model, based on high-speed dsp chip, as TMS320F28335, real-time results can be calculated in time fast and fast reaction obtains less torque and velocity fluctuation value.

Accompanying drawing explanation

Figure 1 shows that control principle block diagram of the present invention.

Figure 2 shows that NSGA-II algorithm principle of the present invention.

Figure 3 shows that switched reluctance machines rotor relative position of the present invention and phase winding inductance.

Figure 4 shows that the total torque waveform of switched reluctance machines, wherein: Fig. 4 (a) is the total torque under prior art, Fig. 4 (b) is the total torque under new method.

Figure 5 shows that the velocity wave form of switched reluctance machines, wherein: Fig. 5 (a) is the speed under prior art, Fig. 5 (b) is the speed under new method.

Embodiment

Be described in detail below in conjunction with the technical scheme of attached Example to invention:

The Formula of Electromagnetic of the every phase winding of switched reluctance machines is:

$T_e(\mathrm{\θ},i)=\frac{1}{2}{i}^2\frac{\mathrm{dL}(\mathrm{\θ},i)}{\mathrm{d\θ}}---\left(1\right)$

In formula, θ is position angle; I is phase current; L is phase inductance.Electromagnetic torque is not only the function of electric current, or the function of position angle, and, only just can produce electromagnetic torque in inductance variation zone.

According to the linear flux linkage model that switched reluctance machines simplifies, the total electromagnetic torque of motor is:

$T_{\mathrm{total}}(\mathrm{\θ},i)=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\frac{1}{2}{i}^2\frac{\mathrm{dL}(\mathrm{\θ},i)}{\mathrm{d\θ}}---\left(2\right)$

In formula, m is the number of phases.Thus mechanical equation can be obtained be:

$T_{\mathrm{total}}-T_L=J\frac{\mathrm{d\ω}}{\mathrm{dt}}+\mathrm{F\ω}---\left(3\right)$

T in formula _lfor load torque, N.m; J is moment of inertia; F is damping coefficient.

From above, square being directly proportional of the derivative of electromagnetic torque and inductance, electric current.Assuming that mutual inductance is zero between winding, machine operation is in magnetic linkage linear zone.

The torque pulsation coefficient characterizing torque pulsation situation is defined as:

$T_i=\frac{T_{\max }-T_{\min }}{T_{\mathrm{av}}}---\left(4\right)$

T in formula _max, T _minand T _avthe maximum of synthesis torque, minimum value and mean value respectively.

The generation of torque pulsation, due in switched reluctance machines phase winding, the last electric current turning off winding mutually declines and rear one opens winding current this section that rise mutually and intersect the resultant current of period and produce relative pulsation, and then torque produces pulsation, this also can find out from formula (1)-Shi (3), torque is the function of i and θ, therefore, by controlling electric current, and select suitable winding energising open and turn off angle value (or claiming switching angle), torque value when intersecting period and commutation can be changed, torque pulsation inhibited.

For existing PI two close cycles switched Reluctance Motor Control System, utilize NSGA-II to the turn-on angle θ of PI speed control PI parameter, PI current controller PI parameter, phase-change switch angle controller _onwith pass angle of rupture θ _offbe optimized, torque pulsation and velocity fluctuation, for suppress target, fig. 1 illustrates the switched Reluctance Motor Control System theory diagram of application NSGA-II and new method.

Conveniently, velocity fluctuation minimize be Negotiation speed ISE be minimised as target, the ISE of electric current is also the concept characterizing current pulsation situation.The ISE of following two formulas difference computational speed controllers and current controller:

ISE _speed＝∫(ω _ref-ω) ²dt (5)

ISE _current＝∫(I _ref-I _pha) ²dt (6)

The respective ratio of PI speed control and PI current controller and storage gain k _pand k _i, motor winding switching angle θ _onand θ _offthe optimum organization select permeability of these six parameters, belong to a multi-objective problem, minimize for motor speed ISE and be optimized combination with the target that is minimised as of torque pulsation, be in the ISE of the electric current of control system inner ring as constraints, during low speed, torque pulsation and velocity fluctuation are more obvious, and velocity fluctuation is particularly necessary as the second target, can promote mutually, optimizes mutually with torque pulsation target.These two targets provide as follows:

Velocity fluctuation minimizes its ISE minimum value i.e.:

f ₁=min(ISE_speed) (7)

Torque ripple minimization target is:

f ₂=min(torque_ripple) (8)

Constraints is:

max(ISE_curren)≤ε (9)

The present embodiment NSGA-II basic definition used is:

NSGA-II is the modified model of NSGA, and be one elite's multi-objective genetic algorithm fast that people such as moral uncle grade proposes, according to elitism strategy, it, by the application of progeny selection operator, retains traditional best solution.The schematic diagram of NSGA-II as shown in Figure 2, characterizes the process being generated population of new generation by parent population and progeny population.

Population quantity is represented with N, be compound population, size is the population R of 2N _tuse non-dominated ranking.Due to R _tenumerate initial (parent) population and current (filial generation) population, elitism strategy can realize.Non-dominated ranking layer F in compound population ₁optimum non-dominant layer, F ₁containing the solution that is dominant, F ₁the solution that is dominant in layer must be compared other solutions in compound population and more come into one's own.If F ₁population number be less than N, F ₁layer all population will include new population P in _i+1, P _i+1remaining part select according to hierarchal order from non-dominant layer afterwards, so, here is from F ₂middle selection is separated, and is then from F ₃layer, the like, this step after finding definite N number of solution, compares descending finally by crowding till being continued until non-dominant layer (group) subsequently, and the optimum solution needed for selecting fills up all populations, obtains new P _t+1after population, genetic operator by selecting, intersecting, can to produce a new quantity be the Q of N in mutation _t+1population, the method that the algorithm of tournament selection mode based on crowded comparison operator is separated as selection.

Utilize NSGA-II, for Conventional switched reluctance electric machine control system, by being optimized six operational factors, comprise: the ratio of the ratio of speed control and storage gain, current controller and storage gain, turn-on angle and the pass angle of rupture, be minimised as Bi-objective with torque ripple minimization and velocity fluctuation.

PI speed control designs:

As shown in Figure 1, the input of PI speed control is velocity error, i.e. given reference speed value ω _refwith the difference of actual feedback velocity amplitude ω, the output of PI speed control is current order.Generally, the PI proportional gain k of PI speed control _pthere is provided whole control command to the error signal considering whole gain factor, the PI storage gain k of PI speed control _tsteady-state error is reduced by the low-frequency compensation of integrator.The transfer function of PT speed control can arrange and be written as the following two kinds form:

$G_s\left(s\right)=K_{\mathrm{ps}}(1+\frac{1}{T_{\mathrm{is}}\·s})---\left(10\right)$

$G\left(s\right)=K_{\mathrm{ps}}+\frac{K_{\mathrm{is}}}{s}---\left(11\right)$

K in formula _psrepresent the proportional gain of PI speed control, T _isintegration time constant, and K _is=K _ps/ T _isthen represent the storage gain of PI speed control.In order to Optimal performance, K _psand K _is(or T _is) use NSGA-II to adjust, the ISE value of Negotiation speed realizes as measurement target carrier.

PI current controller designs:

As shown in Figure 1, the current regulator of every phase winding is all that namely PI current controller adds the version of PWM controller by identical Structure composing.PI current controller model is very similar to PI speed control, and its transfer function also can arrange and be written as the following two kinds form:

$G_i\left(s\right)=K_{\mathrm{pi}}(1+\frac{1}{T_{\mathrm{ii}}\·s})---\left(12\right)$

$G_i\left(s\right)=K_{\mathrm{pi}}+\frac{K_{\mathrm{ii}}}{s}---\left(13\right)$

K in formula _pirepresent the proportional gain of PI current controller, T _iiintegration time constant, and K _ii=K _pi/ T _iithen represent the storage gain of PI current controller.In order to Optimal performance, K _piand K _ii(or T _ii) use NSGA-II to adjust, by the ISE value of electric current as constraints.And PWM controller receives the calculating that PI current controller information completes duty ratio, which determine the switch conditions of power inverter breaker in middle pipe, and the supply power voltage size of motor phase windings.

Phase-change switch angle controller designs:

Essentially, turn-on angle and the hold-off angle control strategy decision performance of switched reluctance machines.Torque and velocity interval, electric efficiency, torque pulsation, noise etc. all depend on or depend in a way turn-on angle and close the selection of the angle of rupture.Except the effect of aforementioned PI controller, the optimum choice of switching angle, torque-down rates when can reduce commutation, thus torque pulsation is effectively suppressed.Attached stator and rotor relative position and the phase winding inductance situation that Figure 3 shows that switched reluctance machines, according to the Mathematical Modeling of switched reluctance machines, if the electric current of phase winding is non-zero value arbitrarily, and dL/d θ is negative, then produce brake torque, the region producing forward torque is θ ₂-θ ₃region, θ ₄-θ ₅if region exists electric current, produce negative torque and brake torque, therefore, negative torque zone must avoid winding current to exist.

Turn-on angle needs to be arranged on the minimum region of inductance, namely will at the θ producing positive torque ₂before open-minded in advance, be because according to switched reluctance machines Mathematical Modeling on the one hand, inductance Minimum Area (θ ₁-θ ₂region) electric current the most easily sets up, and second in order to prevent negative torque, closing the angle of rupture must at inductance maximum region (θ ₃-θ ₄) or turn off before.But, can not optimum choice if close the angle of rupture, also can cause the loss of positive torque, and then produce larger torque pulsation.

Therefore the θ producing positive torque is being started ₂open before and become inevitable, the computing formula of turn-on angle is in advance:

${\mathrm{\θ}}_{\mathrm{adv}}=\frac{{\mathrm{\πL}}_i{I}_{\mathrm{cmd}}n}{30U_{\mathrm{bus}}}---\left(14\right)$

In formula, I _cmdit is required phase current; N is motor speed; L _uit is winding inductance; U _busit is direct current common electric voltage.

Non-dominated sorted genetic algorithm (NSGA-II) execution mode based on each controller:

Within the bound of object space, the chromosome of population is all the initialization of randomness, and thus the setting of bound is extremely important.The speed control of the present embodiment and the given range of current controller PI parameter are set as respectively: K _ps∈ [0,30] and K _is∈ [0,1]; K _pi∈ [0,30] and K _ii∈ [0,1].

About turn-on angle with close the upper lower limit value of the angle of rupture, according to four phase 8/6 electrode structure switched reluctance machines, by reference to the accompanying drawings 3, turn-on angle need advance to minimum 0 °, then the words shifted to an earlier date can not produce forward torque.Turn-on angle (the θ of the present embodiment _on) and close the angle of rupture (θ _off) bound scope be defined as: θ _on∈ [0 °, 7 °] and θ _off∈ [15 °, 22.5 °].

The four phase 8/6 pole switching reluctance motor basic parameters of the present embodiment are: rated power 7.5KW, rated speed 1500rpm, DC power supply voltage 350V, maximum current 20A, stator phase winding internal resistance 1.2 Ω, rotor salient pole center line aligned position inductance (maximum induction) 50mH, not lining up position inductance (minimum inductance) is 6mH.

Be target by minimized speed ISE and torque pulsation, utilize NSGA-II, optimize the ratio, the integral gain value that obtain PI speed control and PI current controller, and turn-on angle and shutoff angle value.Because NSGA-II has randomness, embodiment has carried out 20 independent experiments.The various PI controller of statistical analysis and switching angle are at speed ISE (f ₁), torque pulsation (f ₂) and current IS E tri-kinds of prerequisites stress under parameters optimal value, and its torque situation.

Choosing of NSGA-II parameter needs through the enterprising Row sum-equal matrix of study experimental basis, except above-mentioned test number (TN) (20 times), other major parameters are: mutation probability 1/6 (variable number is 6), the coefficient of variation 20, population scale 100, functional evaluation maximum quantity 10000.

First utilize MATLAB/SIMULINK simulation analysis, following table gives the f for each controller under NSGA-II ₁, f ₂with the optimum results of six parameters of current IS E:

Table 1 each controller PI parameter and switching angle optimal value

Following table 2 statistical analyses torque situation of each controller, the f under NSGA-II ₁, f ₂with current IS E, torque maximum value, minimum value, mean value, torque pulsation coefficient are added up.From table 1 and table 2, after application NSGA-II, switched Reluctance Motor Control System has possessed good robustness.

Under table 2NSGA-II various control objectives torque and independent PI control under torque ratio comparatively

Visible, the torque pulsation under prior art independence PI algorithm prerequisite apparently higher than the three kinds of forms of other under NSGA-II new algorithm, and with f ₁and f ₂be minimised as common objective, current IS E is constraints, optimizes each parameter, can reach the optimal value of speed and torque ripple minimization to greatest extent.

Accompanying drawing 4 (a), (b) are respectively the total torque waveform at the independent PI algorithm of prior art and new algorithm, and Fig. 5 (a), (b) are respectively corresponding velocity wave form.Total torque under PI algorithm independent compared to existing technology and velocity variations waveform, after introducing NSGA-II, torque pulsation and velocity fluctuation situation are all effectively suppressed.

The switched reluctance machines of the present embodiment for load, new method is put into practice, with high speed TMS320F28335 for acp chip in the switched Reluctance Motor Control System basis that existing PI controls with high-accuracy magnetic hysteresis dynamometer machine.

The introducing of NSGA-II, minimizes target for torque pulsation and velocity fluctuation, produces the respective ratio of speed and current double-closed loop controller and storage gain k _p, k _ioptimal value, and turn-on angle θ _onwith pass angle of rupture θ _offoptimal value, achieve good effect.

Claims (5)

1. one kind is reduced the method for switched reluctance machines torque pulsation, according to two close cycles switched Reluctance Motor Control System prior art, adopt NSGA-II technology that PI speed control, PI current controller, phase-change switch angle controller are carried out to parameter optimization and adjust, velocity fluctuation minimizes and the Bi-objective of torque ripple minimization as optimal control.

2. method according to claim 1, is characterized in that: described velocity fluctuation minimize be Negotiation speed ISE be minimised as target, the ISE of electric current is also the concept characterizing current pulsation situation.Following two formulas are the ISE value calculating PI speed control and PI current controller respectively:

ISE _speed=∫(ω _ref-ω) ²dt

ISE _current=∫(I _ref-I _pha) ²dt

。

3. method according to claim 1, is characterized in that: described Optimal Parameters comprises: the turn-on angle θ of PI speed control PI gain parameter, PI current controller PI gain parameter, phase-change switch angle controller _onwith pass angle of rupture θ _off, the optimum organization select permeability of these parameters, belongs to a multi-objective problem, minimizes and is optimized combination with the target that is minimised as of torque pulsation, be in the ISE of the electric current of control system inner ring as constraints for motor speed ISE.

4. the method according to claim 1,3, is characterized in that: the PI gain parameter of described PI speed control, PI current controller needs limited range, and turn-on angle and the pass angle of rupture of phase-change switch angle controller limit upper lower limit value respectively; Through tens of independent experiments, by MATLAB/SIMULINK analysis tool, utilize NSGA-II algorithm to obtain velocity fluctuation minimizes, torque ripple minimization, current IS E value time parameters optimal value.

5. the method according to claim 1,4, it is characterized in that: the needs of choosing of described NSGA-II parameter pass through the enterprising Row sum-equal matrix of study experimental basis, except experience tens of tests, also comprise: choosing of the coefficient of variation, population scale, functional evaluation maximum quantity etc.