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Fuzzy Adaptive Internal Model Control Schemes for__PMSM Speed-Regulation System

Fuzzy Adaptive Internal Model Control Schemes for__PMSM Speed-Regulation System
Fuzzy Adaptive Internal Model Control Schemes for__PMSM Speed-Regulation System

Fuzzy Adaptive Internal Model Control Schemes for PMSM Speed-Regulation System

Shihua Li,Senior Member,IEEE,and Hao Gu

Abstract—In this paper,the speed regulation problem for per-manent magnet synchronous motor(PMSM)system under vector control framework is studied.First,a speed regulation scheme based on standard internal model control(IMC)method is de-signed.For the speed loop,a standard internal model controller is ?rst designed based on a?rst-order model of PMSM by analyzing the relationship between reference quadrature axis current and speed.For the two current loops,PI algorithms are employed respectively.Second,considering the disadvantages that the standard IMC method is sensitive to control input saturation and may lead to poor speed tracking and load disturbance rejection performances,a modi?ed IMC scheme is developed based on a two-port IMC method,where a feedback control term is added to form a composite control structure.Third,considering the case of large variations of load inertia,two adaptive IMC schemes with two different adaptive laws are proposed.A method based on disturbance observer is adopted to identify the inertia of PMSM and its load.Then a linear adaptive law is developed by analyzing the relationship between the internal model and identi?ed inertia. Considering the control input saturation in practical applications, a fuzzy adaptive law based IMC scheme is developed based on apriori experimental tests and experiences,where a fuzzy in-ferencer based supervisor is designed to automatically tune the parameter of speed controller according to the identi?ed inertia. The effectiveness of the proposed methods have been veri?ed by Matlab simulation and TMS320F2808DSP experimental results. Index Terms—Adaptive control,control saturation,fuzzy infer-encer,inertial identi?cation,internal model control,PMSM.

I.I NTRODUCTION

A MONG various types of ac motors,permanent magnet

synchronous motor(PMSM)has been widely used in many industrial applications due to its advantageous features such as high ef?ciency,high power density,torque to inertia ratio.Linear control schemes,e.g.,proportional-integral(PI) control schemes,are already widely applied in PMSM systems [1].However,PMSM servo system is a nonlinear system with multiple coupled states and parameter variations[2].So it is very dif?cult for linear control algorithms to obtain a suf?-ciently high performance for this kind of nonlinear systems.

Manuscript received August17,2011;revised December18,2011;accepted February22,2012.Date of publication June21,2012;date of current version October18,2012.This work was supported by New Century Excellent Talents in University(NCET-10-0328)and National863Project of the Twelfth Five-Year Plan of China(2011AA04A106).Paper No.TII-11-422.

S.Li is with School of Automation,Southeast University,Nanjing210096, China(e-mail:lsh@https://www.sodocs.net/doc/d117635646.html,).

H.Gu is with Huawei Technologies Company,Ltd.,Nanjing210012,China (e-mail:guhao1985@https://www.sodocs.net/doc/d117635646.html,).

Digital Object Identi?er10.1109/TII.2012.2205581

Recently,with the development of modern control theory and motor control techniques,many nonlinear control methods have been reported for PMSM systems,e.g.,sliding mode control[3], adaptive control[4]–[7],robust control[8],[9],fractional order control[10],disturbance rejection control[2],[11],?nite-time control[12],predictive control[13],[14],and intelligent control [15],[16].These methods not only enrich PMSM control theory, but also improve the performance of PMSM system from dif-ferent aspects.

Internal model control(IMC)method was introduced by Garcia and Morari[17]and then was under intensive research and development during the past decades[18],[19].The IMC method includes an internal model and an internal model controller which consists of the inverse internal model and a ?lter.It has good abilities of tracking,disturbance rejection and robustness.It also provides an effective framework for the anal-ysis of control system performance,especially for the stability and robustness issues[17],[19].Among these results,different kinds of modeling methods about IMC have been developed, including traditional mathematics modeling[17]–[19],neural networks modeling[20],fuzzy modeling[21],volterra series modeling[22],etc.

The internal model control method was originally applied to process control systems[18],[19]and then extended to motor control systems[23],[24].In[23],an IMC method is applied to the current control of ac motors.In[24],an adaptive IMC method which is obtained by using Lyapunov stability theory, is proposed to control the speed of PMSM system.

It has been pointed out that although the conventional IMC method can provide an adequate suppressing ability for the dis-turbances added to the output channel,it may not provide a satis-factory load disturbance rejection property for the disturbances added to the input channel when the process dynamics are much slower than the desired closed loop dynamics[25].The reason is explained and a modi?ed design on the IMC?lter is proposed for improving the performance of load disturbance rejection in [26].Moreover,the conventional IMC control method does not consider the control input saturation in the design procedure, this may degrade the control performance and lead to windup problems[27].Some methods have been proposed to solve this problem.In[28],an antiwindup scheme is proposed to optimize the error between the outputs of the system generated by the constrained and unconstrained control inputs.In[29],a two-port IMC control structure is proposed,where a feedback control part is added to the conventional internal model control part to form a composite controller.It is suitable for the optimum resolution of controller design trade-off between the tracking and load dis-turbance rejection performances.

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Fig.1.Principle block diagram of PMSM speed regulation system based on vector control.

As already mentioned,the main feature of IMC is that its im-plementation includes an explicit internal model to be as part of the controller.However,When the mismatch between the controlled plant and internal model is large,the control perfor-mance will be diminished[30].In some applications,e.g.,elec-tric winding machine,transfer robots with heavy loads,welding robots,etc.,the inertia of the whole system increases as time goes by.When the inertia of system is increased to more than several times of the original inertia,the large mismatch between the controlled plant and internal model will cause a degrada-tion of the closed loop performance if no corresponding control scheme is designed.In[4],by using inertia identi?cation tech-niques and disturbance estimation techniques,an disturbance re-jection based adaptive control scheme for PMSM speed system is presented.The feedforward compensation gain is tuned auto-matically corresponding to the inertia estimation value.

In this paper,different internal model control design schemes are studied for PMSM speed regulation system.First,a?rst order model of PMSM by analyzing the relationship between reference quadrature axis current and the speed output,and a standard internal model controller is obtained for the speed loop. For the two current loops,PI algorithms are employed,respec-tively.Second,considering that the standard IMC method is sensitive to control input saturation and provides a poor load dis-turbance rejection property,a modi?ed IMC method proposed in [29]is introduced here and an improved IMC scheme is devel-oped to enhance the tracking and disturbance rejection abilities. Third,further considering the case of load inertia variations,two adaptive IMC schemes are developed respectively.A torque dis-turbance observer(DOB)based method is employed to estimate the inertia of PMSM with load.Since the varying inertia can be estimated,the corresponding control(inertia)parameter in the internal model and the internal model controller can be lin-early tuned with the change of inertia,then an adaptive IMC scheme based on linear adaptive law is developed.This method is straightforward and easy to implement.However,due to the existence of saturation,the linear adaptive law may not most suitably represent the relationship between the corresponding control(inertia)parameter and the varying inertia.Therefore,a fuzzy adaptive law is built based on apriori experimental tests and experiences to automatically tune the parameter of speed controller according to the identi?ed inertia.Both simulation and experimental results are provided to verify the effectiveness of these IMC schemes.

II.P ROBLEM D ESCRIPTION

In d-q coordinates,the model of the surface mounted PMSM can be described as[31]

(1) where and d-axis and q-axis stator currents,and

d-axis and q-axis stator voltages,number of pole pairs, stator resistance,stator inductance,torque constant,an-gular velocity,viscous friction coef?cient,moment of in-ertia,and load torque.

The principle diagram of PMSM system based on vector con-trol is shown in Fig.1.Here,strategy is used and two PI algorithms are used in the two current-loops respectively.In this paper,we concentrate on the design of speed controller.

III.C ONTROL S TRATEGY

A.Speed Controller Design for PMSM

1)Standard Internal Model Controller for PMSM:The Standard IMC method is considered as a robust control method which includes an internal model,and an internal model con-troller which consists of the inverse internal model and a?lter. It can guarantee the stability of system for open loop stable plants[17],[19].The standard IMC structure for PMSM is shown in Fig.2,where the“generalized PMSM”includes the PMSM model and the other components of the two current loops,similar to that of Fig.1,is the internal model, and is the internal model controller.

From(1),we can have

(2)

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Fig.2.Block diagram of the standard IMC method for PMSM system.

where represents the lumped distur-bance,including the load disturbance,and the tracking error of current loop of .

Therefore,the generalized PMSM (the controlled model)can be described simply as

(3)

where ,.The internal model is described as

(4)

where

are the internal model parameters.It should be noted that for the standard IMC method,if the in-ternal model is accurate,i.e.,,the closed loop system is stable only if and are both stable [16].In this case,the internal model controller is de ?ned as

,then ,that is the output of system attains the

of system instantaneously.But it is clear that this ideal re-sult can not be obtained due to some reasons,e.g.,is hardly ever proper,highly sensitive to model errors in-clude nonlinearity,unmodeled dynamics,and so on.Therefore,we design the internal model controller as follows:

(5)

where

is a low-pass ?lter,is the time constant of ?lter.From Fig.2,we can obtain

(6)

If the internal model is accurate,i.e.,,from (5)

and (6),we can obtain

(7)

It can be seen from (7)that

is included in the transfer function between and and affects the load distur-

bance rejection performance,no matter how the parameter of the IMC ?lter is tuned.Especially for a plant with a large time constant,the recovery trajectory of the load distur-bance rejection may have “a long tail”[25],[26].On the other

Fig.3.Block diagram of the modi ?ed IMC method for PMSM system.

hand,all control systems have some type of control input satu-ration in real applications.Although we can make the parameter small enough to improve the load disturbance rejection perfor-mance (e.g.,less amplitude of speed ?uctuation),the output of internal model controller may exceed the saturation limit of and this will degrade the tracking performance to some The reason is that if there is no model error and disturbance,the IMC system will become an open loop system.Due to con-trol input saturation,some desired control information may lost,which may generate a short-sightedness property that can seri-ously degrade the performance of control system [32].

2)Modi ?ed Internal Model Controller for PMSM:In order to enhance the abilities of tracking and load disturbance rejec-tion of the system,a feedback control term is designed based on the standard internal model control https://www.sodocs.net/doc/d117635646.html,ing the two-port IMC structure in [29],a modi ?ed IMC scheme for PMSM is proposed,as shown in Fig.3.Note that the control input in practice usually is limited in amplitude.Thus the re-lationship between and is

The feedback control term is designed as a proportional term simply,which is shown as follows:

(8)

For the convenience of analysis,just let ,regardless of

saturation.From Fig.3,we can obtain

(9)

If the internal model is accurate,i.e.,,from

(5),(8),and (9),we can also obtain (10)

For load disturbance rejection performance,compared with

(7),it can be seen that the feedback control term can be ad-justed properly to reduce the time constant,i.e.,

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,which can make the recovery trajectory in the presence of load disturbance fast to void“a long tail.”Besides,when the output of the modi?ed IMC controller is saturated,the output of the feedback control term can compensate for the effect of control input saturation as antiwindup compensation to improve the tracking performance.Through adjusting the parameter properly,the closed loop system can obtain a good ability of tracking and load disturbance rejection.

3)Simulation and Experiment Results:To test the perfor-mance of the standard IMC method,simulation,and experi-ments on PMSM system have been performed.

The parameters of the PMSM used in the simulation and ex-periment are given as follows:rated speed, rated torque,number of pairs,stator resistance,stator inductances,mo-ment of inertia,torque constant

,and viscous coef?cient

.

Here,in the simulation,assuming that the internal model is accurate,i.e.,,

,we choose different values of to test the performance of standard IMC method.The PI parameters of both current loops are the same,where the proportional gains are50and integral gains are2500.The saturation limit of-axis reference current is9.42A.

The solid lines in Fig.4show the response curves of speed and under where(b)is a partial enlargement graph of The value of does not exceed the saturation limit and the speed response no overshoot and a short settling time (0.04s).As analyzed in Section III-A1,we can reduce the value of to make the speed response faster theoretically.The dotted lines in Fig.4show the response curves of speed and under without considering any saturation limit.It been seen that at the start-up phase of motor,the maximum value of is14A and the speed response has a much shorter settling

(0.02s).However,if we consider the control saturation, things become much different.The dashed lines in Fig.4show the simulation results under with considerations on the saturation limit.It can been seen that at the start-up phase of motor,the calculation output is over the saturation limit9.42 A,so the value of is cut down to9.42A.In such case,it can be observed that speed response has a much longer settling time(2.6s).These simulation results show that in the presence of control input saturation,the tracking performance of standard IMC method is degraded.

To test disturbance rejection performance of standard IMC method,a load torque is applied at. As shown in Fig.5,the maximum amplitude of speed decrease under is about174.8rpm and the speed recovery time is10s.When,the maximum amplitude of speed decrease is about88.4rpm and the speed recovery time is almost the same.

Here,in the experiment,the standard IMC controller param-eters of speed loop are selected as:

,

.Then,we choose different values of to test the performance of standard IMC method.The parameters PI of both current loops are the same,where the proportional gains Fig.4.Responses under standard IMC(simulation).(a)Speed.(b)Local curve of(a).(c).

are42,and the integral gains are2600.The saturation limit of the q-axis reference current is9.42A.

The solid lines in Fig.6show the response curves of speed and under.The response of does not exceed the limit and the speed response no overshoot and a short settling time(0.22s).The dotted lines in Fig.6show the experimental results under.It can been seen that at the start-up phase of motor,the value of is limited to9.42A and the speed response has a much settling time.

To test the load disturbance rejection performance of standard IMC method,tests have been done to evaluate the performance of PMSM system under sudden load disturbance impact,i.e., when the motor is running at the steady speed of1000rpm, the rated load is added suddenly.As shown in Fig.7,the maximum amplitude of speed decrease under is about 175.3rpm and the speed recovery time is more than4s.When

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Fig.5.Responses under standard IMC method

in the presence of load torque disturbance (simulation).(a)Speed.(b).

Fig.6.Responses under standard IMC (experiment).(a)Speed.(b).

,the maximum amplitude of speed decrease is about

118.5rpm and the speed recovery time is almost the same.From these simulation and experimental results,

it can be con-cluded that the standard IMC method is sensitive to control input

Fig.7.Responses under standard IMC method in the presence of load torque disturbance (experiment).(a)Speed.(b).

saturation and may lead to poor speed tracking and load distur-bance rejection performances.In order to enhance the ability of antiwindup and load disturbance rejection of the system,the modi ?ed internal model control method is applied as mentioned in Section III-A2.To show the effectiveness of the modi ?ed control method,simulation and experiments on PMSM system have been performed,which are compared with the standard IMC method.

Here,in the simulation,the controller parameters of speed loop are selected as:for the standard IMC method,

,,;the

parameters of the modi ?ed IMC method are the same as the standard IMC,where .

The dashed lines in Fig.8show the response curves of speed and under the modi ?ed IMC.Fig.8(b)is a partial enlargement of Fig.8(a).The speed response has a small overshoot (5.12%)and a short settling time (0.021s).The solid lines in Fig.8show the simulation results about the standard IMC.The speed response has no overshoot,but has a much longer settling time (2.6s).

To compare disturbance rejection performance of both two methods,a load torque is applied at .As shown in Fig.9,the maximum amplitude of speed decrease under the standard IMC method is about 88.4rpm and that of the modi ?ed IMC method is much less (28rpm).Besides this,compared with the speed recovery time under the standard IMC method (10s),the modi ?ed IMC method has a less speed re-covery time (0.05s).

In the experiment,the speed controller parameters of the stan-dard IMC method are selected as ,

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Fig.8.Responses under standard IMC and modi?ed IMC methods(simula-tion).(a)Speed.(b)Local curve of(a).(c).

,.The parameters of the modi?ed IMC method are the same as that of the standard IMC method except the additional parameter.

Fig.10(b)is a partial enlargement graph of Fig.10(a).Com-pared with that under the standard IMC method(almost5.5s set-tling time),the speed response under the modi?ed IMC method has a much shorter settling time(0.026s).

To compare the load disturbance rejection performance of both methods,tests have been done to evaluate the performance of PMSM system.As shown in Fig.11,compared with the speed decrease amplitude under the standard IMC method (118.5rpm),the modi?ed IMC method has a less maximum amplitude of speed decrease(21.5rpm).Besides this,compared with the speed recovery time under the standard IMC

method (more than4s),the modi?ed IMC method has a less speed recovery time(0.22s).Fig.9.Responses under standard IMC and modi?ed IMC methods in the pres-ence of load torque disturbance(simulation).(a)Speed.(b)Local curve of(a).

(c).

From these simulation and experimental results,it can be con-cluded that the modi?ed IMC method has improved the tracking and load disturbance rejection performances.

B.Adaptive Internal Model Controller Design of PMSM

1)Performance Analysis:The above modi?ed internal model control scheme for PMSM is robust to some extent. However,in practical motion control systems,there may exist cases of large variations of load inertia.For example,the inertia of electric winding machine may increase to more than several times of the original inertia.In this case,there exists a serious problem of mismatch between the internal model and the controlled plant model,which will diminish the control quality of system if the corresponding control parameters are still?xed.So for such case of parameter variations,some

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Fig.10.Responses under standard IMC and modi ?ed IMC methods (experi-ment).(a)Speed.(b)Local curve of (a).(c).

adequate adaptive control laws should be considered in the control design.

Next,we will show this phenomenon by simulation and ex-perimental results.The parameters of the PMSM used in the simulation and experiment are the same as Section III-A3.Here,at the initial stage,the motor inertia is assumed to be

.In the simulation,the control parameters of speed loop

are selected as ,

,,.

The dashed lines in Fig.12show the response curves of speed and ,when the inertia of the system is .The speed response has a overshoot (6.12%)and a short settling time (0.01s).The solid lines in Fig.12show the simulation results when the inertia of the system is increased to .The speed response has a bigger overshoot (17.81%)and a longer settling time (0.024

s).The control quality of the speed controller gets worse if the parameters of the speed controller are still ?xed when the in-ertia of the system is increased to .The reason is that the

Fig.11.Responses under standard IMC and modi ?ed IMC methods in the pres-ence of load torque disturbance (experiment).(a)Speed.(b).

parameters of the plant model is still ?xed to be ,while

it is theoretically supposed to vary with the variation of inertia.In the experiment,the speed controller parameters of the speed loop are selected as ,

,,.

The dashed lines in Fig.13show the response curves of speed and ,when the inertia of the system is .The speed response has a small overshoot (10.1%)and a short settling time (0.011s).The solid lines in Fig.13show the experimental results when the inertia of the system is increased to .The speed response has a bigger overshoot (18.1%)and a longer settling time (0.09s).According to the simulation and experimental results,we can see that as the inertia of the whole system varies largely,the con-trol performance of the closed loop system will get worse if the parameters of the speed controller are not adjusted accordingly.2)Adaptive Internal Model Control Design:For the inertia variation case,to ensure the adaptation ability of closed loop system,it is expected that if the inertia varies,the internal model and the control parameters based on the internal model can be intelligently changed.Thus,an adaptive IMC control scheme can be developed.

The block diagram of adaptive IMC scheme for PMSM speed regulation system is shown in Fig.14,where (a)shows the whole block diagram and (b)shows the detail diagram of adap-tive IMC design.A parameter autotuning strategy is adopted to tune the parameter by using the estimated inertia .

The expression of adaptive internal model controller is as follows:

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Fig.12.Responses

in the case of and

(simulation).

(a)Speed.(b).

Fig.13.Responses in the case of and (experiment).

(a)Speed.(b).

1)The internal model

(11)

2)Internal model controller

(12)

where

can be tuned according to the identi ?ed inertia.

C.Inertia Identi ?cation

In this paper,we adopt the method based on DOB to iden-tify inertia.The method estimates the external disturbances and friction in the model by disturbance estimators and then obtain an estimate of inertia [6],[33],[34].The detailed process of this method can be found in [33],which is omitted here.The effec-tiveness of the method is veri ?ed by experimental results.

In this method,a test signal for inertia identi ?cation is the periodic speed command that satis ?es

where

is the period of speed command.

D.Adaptive Laws

1)Linear Adaptive Law:When inertia varies,we can tune

the parameter

of the speed controller by the estimation of inertia.To ensure the performance of the system,a linear rela-tionship between and is established,e.g.,.We can obtain the ratio of the actual inertia to the original in-ertia by the estimation of inertia.The ?nal parameter can be expressed as follows:

(13)

2)Fuzzy Adaptive Law:

is theoretically supposed to be linearly tuned with the change of inertia,i.e.,.How-ever,in practical applications,due to the existence of control input saturation,the linear adaptive law may not be the most adequate solution.

To obtain a better performance of the system,a practical rela-tionship between and should be established.Some apriori experimental tests should be done to help to decide the tuning expression for the parameter .So the internal model con-troller and the internal model both are adjusted properly according to the parameter ,which is consistent with internal model design method [17],[19].

To this end,a fuzzy inference engine [35],[36]is chosen to describe the autotuning function for the parameter .The fuzzy implement is the one-input-one-output case.By simu-lation and experimental tests,we ?nally obtain the available groups of membership functions and fuzzy rules,as shown in Fig.15.

We can obtain the ratio of the actual inertia to the original inertia by the estimation of inertia.The inertia ratio is used as the input of the fuzzy inference engine,while

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Fig.14.Adaptive control scheme for PMSM speed regulation system.(a)The whole schematic diagram.(b)The detail diagram of adaptive

IMC.

Fig.15.Membership functions.(a)Membership function of inertia ratio.

(b)Membership function of.

is utilized as the output of the fuzzy inference engine.The?nal parameter after fuzzy tuning can be expressed as follows:

(14) where is the proportional factor.

Here,we assume that the range of the ratio of inertia is(0,25].Then,the fuzzy set of can be chosen as

.The fuzzy set of can also be chosen as.The range of the ratio of is(0,20].The membership

functions of the two fuzzy sets are shown in Fig.15.The fuzzy inference rules are Fig.16.Identi?cation of inertia(solid line)and real inertia(dashed line) (simulation).

as follows:If is,then is.In this paper,we use a Mamdani-type fuzzy inference engine and ob-tain by using the center of gravity https://www.sodocs.net/doc/d117635646.html,ing(12),the parameter is decided after fuzzy inference.

IV.S IMULATION AND E XPERIMENTAL R ESULTS

The speci?cation of the PMSM and other parameters of sim-ulation are the same as Section III-A3.To test the inertia,the speed command signal is chosen as,

.

Fig.16is the simulation result of inertia identi?cation when the inertia of system is increased to.The dashed line is

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Fig.17.Responses under linear adaptive control law and nonadaptive control law(simulation).(a)Speed.(b).

real inertia.After inertia identi?cation,the ratio of inertia is ob-tained,i.e.,.According to(11),.The speed response before and after parameter autotuning is shown in https://www.sodocs.net/doc/d117635646.html,pared with the speed response without adaptive tuning(17.81%overshoot and0.023s settling time),the speed response under adaptive linear parameter tuning has a smaller overshoot(5.12%)and a shorter settling time(0.021s).

In the same case,assuming that after inertia identi?cation, the ratio of inertia is obtained,i.e.,.For the fuzzy adap-tive law,according to the fuzzy rule and fuzzy inference,the output of the fuzzy inference engine is,thus

.Fig.18shows the comparisons under linear adaptive tuning and fuzzy adaptive https://www.sodocs.net/doc/d117635646.html,pared with the speed response with linear adaptive tuning(5.12%overshoot and0.021s settling time),the speed response under fuzzy adap-tive tuning has a smaller overshoot(2.12%)and a shorter set-tling time(0.015s).

A.Experimental Results

To evaluate the performance of the proposed method,an ex-perimental setup system for the speed control of a PMSM is built.The con?guration and experimental test setup are shown in Figs.19and20,respectively.All of the speed control al-gorithms,including the SVPWM technique,are implemented by the program of the DSP TMS320F2808with a clock fre-quency of100MHz,using a C-program.The speed and cur-rent loop sampling periods are250and60,respectively.The saturation limit of

the q-axis reference current is9.42A.The PMSM is driven by a three-phase PWM inverter with an intelli-gent power module

with a switching frequency of10kHz.The

Fig.18.Responses under linear adaptive control law and fuzzy adaptive con-trol law(simulation).(a)Speed.(b).

Fig.19.Con?guration of experimental system.

Fig.20.Experimental test setup.

phase currents are measured by Hall-effect devices and are con-verted through two12-bit A/D converters.An incremental po-

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Fig.21.Identi ?cation of inertia (solid line)and real inertia (dashed line)

(experiment).

Fig.22.Responses under linear adaptive control law and nonadaptive control law.(a)Speed.(b).

sition encoder of 2500lines is used to measure the rotor speed and absolute rotor position.

The speci ?cation of the PMSM and the parameters of exper-iments are the same as Section III-A3.To test the inertia,the speed command signal is chosen as .Different specially designed mechanical inertia pans can be se-lected to attach to the motor so that the inertia of whole system is increased to different times of .In this experiment,four kinds of inertia pans,which are about 5,10,15,20times of respectively,are used to help us decide the fuzzy tuning imple-mentation

for the parameter and verify the performance of the proposed adaptive control scheme.

Fig.23.Responses under linear adaptive control law and fuzzy adaptive con-trol law.(a)Speed.(b)Local curve of (a).(c).

Fig.21shows the experimental result of inertia identi ?cation when the inertia of system is added to .Note that a small es-timation error between the estimated inertia and the real inertia has little in ?uence on the ?nal control effect,since our adaptive control scheme does not need to be sensitive to the variations of inertia.

After inertia identi ?cation,the ratio of inertia is obtained,i.e.,.According to (11),.The speed response before and after parameter autotuning is shown in https://www.sodocs.net/doc/d117635646.html,pared with the speed response without adaptive tuning (18.1%overshoot and 0.09s settling time),the speed response under linear adaptive parameter tuning has a smaller overshoot (1.75%)and a shorter settling time (0.026s).

For the same case of inertia variation,according to the fuzzy rule and fuzzy inference,the output of the fuzzy inference en-gine is ,Thus .Fig.23shows the comparisons under linear adaptive tuning and fuzzy adaptive tuning.Fig.23(b)is a partial enlargement graph of Fig.23(a).

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Compared with the speed response with linear adaptive tuning (1.75%overshoot and0.026s settling time),the speed response under fuzzy adaptive tuning has almost no overshoot and a little longer settling time(0.03s).

From these simulation and experimental results,it can be con-cluded that the speed controller with parameter autotuning pos-sesses a good adaptation and much better dynamic performance against inertia variations.

V.C ONCLUSION

The speed regulation problem for a permanent magnet synchronous motor(PMSM)based on internal model control methods has been studied.First,a standard internal model control scheme has been designed based on a?rst order model of PMSM by analyzing the relationship between reference quadrature axis current and speed output.Second,since the standard IMC method is sensitive to control input saturation and may lead to poor tracking and disturbance rejection per-formances,a modi?ed internal model control scheme has been developed based on a two-port internal model control method. Third,considering the case of large variations of load inertia, two adaptive IMC schemes with two different adaptive laws have been proposed.A method based on DOB has been adopted to identify the inertia of the PMSM and load.A linear adaptive law has been developed by analyzing the relationship between the internal model and identi?ed inertia.Considering the con-trol input saturation in practical applications,a fuzzy adaptive law based IMC scheme has been developed based on a priori experimental tests and experiences,where a fuzzy inferencer based supervisor has been designed to automatically tune the parameter of speed controller according to the identi?ed inertia. The effectiveness of the proposed methods have been veri?ed by simulation and experimental results.

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Shihua Li(M’05–SM’10)was born in Pingxiang, Jiangxi Province,China.in1975.He received the B.Sc.,M.Sc.,and Ph.D.degrees from Southeast University,Nanjing,China,in1995,1998and2001, respectively,all in automatic control.

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systems.Hao Gu was born in Changzhou,Jiangsu Province, China,in1985.He received the B.Sc.degree in auto-matic control from Hohai University,Nanjing,China, in2008,and the M.Sc.degree in automation from Southeast University,Nanjing,China,in2011. Since2011,he has been with Huawei Technologies Company,Ltd.,Nanjing,China.

等效电路模型参数在线辨识

第四章 等效电路模型参数在线辨识 通过第三章函数拟合的方法可以确定钒电池等效电路模型中的参数,但是在实际运行过程中模型参数随着工作环境温度、充放电循环次数、SOC 等因素发生变化,根据离线试验数据计算得到的参数值估算电池SOC 可能会造成较大的估计误差。因此,在实际运行时,应对钒电池等效电路模型参数进行在线辨识,做出实时修正,提高基于模型估算SOC 的精度。 4.1 基于遗忘因子的最小二乘算法 参数辨识是根据被测系统的输入输出来,通过一定的算法,获得让模型输出值尽量接近系统实际输出值的模型参数估计值。根据能否实时辨识系统的模型参数,可以将常用的参数辨识方法分为离线和在线两类,离线辨识只能在数据采集完成后进行,不能对系统模型实时地在线调整参数,对于具有非线性特性的电池系统往往不能得到满意的辨识结果;在线辨识方法一般能够根据实时采集到的数据对系统模型进行辨识,在线调整系统模型参数。常用的辨识方法有最小二乘法、极大似然估计法和Kalman 滤波法等。因最小二乘法原理简明、收敛较快、容易理解和掌握、方便编程实现等特点,在进行电池模型参数辨识时采用了效果较好的含遗忘因子的递推最小二乘法。 4.1.1 批处理最小二乘法简介 假设被辨识的系统模型: 12121212()()()1n n n n b z b z b z y z G z u z a z a z a z ------+++==++++L L (4-1) 其相应的差分方程为: 1 1 ()()()n n i i i i y k a y k i b u k i ===--+-∑∑(4-2) 若考虑被辨识系统或观测信息中含有噪声,则被辨识模型式(4-2)可改写为: 1 1 ()()()()n n i i i i z k a y k i b u k i v k ===--+-+∑∑(4-3) 式中, ()z k 为系统输出量的第k 次观测值;()y k 为系统输出量的第k 次真值,()y k i -为系统输出量的第k i -次真值;()u k 为系统的第k 个输入值,()u k i -为 系统的第k i -个输入值;()v k 为均值为0的随机噪声。

蔬菜病虫害防治技术(汇总)讲义

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细菌性病害是植株由于受到细菌侵染而引起的一种病害,一般表现出坏死、腐烂、萎蔫、畸形的特点。 软腐病 您瞧这颗大白菜,叶球直接露出来了,叶柄基部和根茎处的心髓部组织已经完全腐烂,充满了灰黄色的粘稠物,还散发出很大的臭味,这就是软腐病的典型症状。 软腐病又叫做烂疙瘩、烂葫芦、腐烂病、水烂病等,发生极为普遍。它的主要特点是轻轻一掰,植株就倒了,病部呈黏滑软腐状.并伴有恶臭味。小白菜、菜心等白菜类蔬菜发生软腐病时,症状与大白菜基本相似。 拿大白菜来说,大白菜定植后直到形成心叶的这个过程是长外叶的过程,这个过程中软腐病不会发生。而当植株外叶即将罩严地面的时候,大白菜渐渐进入壮心期,这时软腐病开始发生,从壮心开始至收获的整个过程中都有发病的可能,如果在这个时期,一开始植株外围的叶片在烈日下表现出萎蔫,但早晚尚能恢复,慢慢儿地外叶不能恢复的话,那您就要注意了,这有可能是得软腐病的早期症状。 黑腐病 您瞧这棵大白菜,从叶片的边缘往两侧和里边扩展,形成“V”字形黄褐色枯斑,病斑的周边呈淡黄色,这就是黑腐病的症状。以后,病原菌还会沿着叶脉向里扩展,形成大块黄褐色病斑或网状黑脉,并感染叶柄。大白菜一般在莲座期以后容易得这种病,它也是由细菌引起的。

蔬菜病虫害防治

蔬菜——不用农药怎么防止病虫害? ?A+ ?A- 2017-04-05 10:01:47农产信息网关注 说实话,作物病虫害防治不用农药很不现实,比较麻烦且费人力,但要有想学习如何不用农药来防治病虫害的朋友可以来看一下。 蔬菜虫害是蔬菜种植户们非常头疼的问题,若是用传统的农药喷洒方式解决虫害,会因为农药残留影响蔬菜的品质。这里和大家分享一下蔬菜虫害的科学防治方法。

一、伴生植物法: 1.青椒和大蒜间作。由于大蒜有一种特殊气味,能使为害青椒的害虫闻之即逃,避免青椒受害。 2.番茄和甘蓝套种。番茄的叶片会散发一种特殊的气味,可驱赶走为害甘蓝的菜青虫和蚜虫。除此之外,这两种蔬菜吸收的营养有很强的互补性,能充分发挥地力。 3.葱头与胡萝卜间作。它们各自散发的气味能驱走相互间的害虫。若单一种植胡萝卜,为防止虫害,可在地内或四周种上几棵葱头,这也能起到驱虫的作用。 并非所有的蔬菜都可以间作,如甘蓝和芹菜、黄瓜和番茄等不宜间作在一起,因为它们各自的分泌物能抑制对方的生长。 这种方法对适用于种植户和家庭小面积种植者。 二、自然材料治虫

1.草木灰液治虫。草木灰10千克对水50千克浸泡24小时,取滤液喷洒可有效地防治蚜虫、黄守虫。若葱、蒜、韭菜受种蝇、葱蝇的蛆虫危害,每亩沟施或撒施草木灰20~30千克,既治蛆又增产。 2.红糖液防治病。害红糖300克溶于500毫升清水中,加入10克白衣酵母,置于温室或大棚内,每天搅拌1次,发酵15~20天,待其表面出现白膜层为止。然后将此发酵液再加入米醋、烧酒各100克,对入100千克水。每隔10天1次,连喷4~5次,防治黄瓜细菌性斑点病和灰霉病有良好效果。 3.兔粪治地老虎每10千克水加兔粪1千克,装入瓦缸内密封沤15~20天,用时搅拌均匀,浇于瓜菜根部,可防治地老虎。 4.尿洗合剂治菜蚜用洗衣粉、尿素、水按1∶4∶400的比例制成混合液,可防治菜蚜,杀虫率达90%以上。 5.猪胆液治病虫10%浓度的猪胆液加适量小苏打、洗衣粉,能防治茄子立枯病、辣椒炭疽病,能驱赶长豆角、四季豆、瓜类等蔬菜上的蚜虫、菜青虫、蜗牛等多种害虫。稀释液可保持10天有效。 6.大蒜、番茄叶巧杀红蜘蛛用大蒜(捣烂成泥状)2份,水1份混拌均匀,取其滤液喷治。或用新鲜的番茄叶(捣烂成浆)加清水2倍并浸泡5小时然后取滤液喷洒果树、花木或蔬菜,都可有效将红蜘蛛杀死。 7.糖醋、烂果诱捕金龟子选用熟烂酸臭的无花果、烂西瓜等,与糖醋液(红糖、醋、水比为1:3:16),一起放入陶钵,支撑分布在果园或菜园中,每2—3天收集钵中的金龟子即可。 8.三合板涂漆聚捕微型害虫在较大的三合板两面涂上橙黄色油漆,干后再涂一层机油、黄油混合油,分布挂在果园或菜园中,蚜虫、白粉虱、美洲斑潜蝇等害虫就会自投罗网。1周后更换涂刷油漆、混合效果更好。

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