Proceedings of the 2009 IEEEInternational Conference on Mechatronics and Automation

August 9 - 12, Changchun , China

Double closed-loops Control Application in HighFrequency Chopped Wave Cascade Speed Control System

»:N,

'--+-.... INVERTOR

i , POWER i,~ -

Zhang Junwei'<, Wang Bingshu' r' Wan Jun3 and Jiang Ping"

1.College ofControl Scien ce and Engineer ing;2. North China Baoding Electric Power VOC.&TECH. CollegeI.North China Electric Power University;3. Converter and Power Control Technique Institution;4. Hebei University

Baoding, Hebei Province, China

Zhangjunwei213@163.com; Wangbingshu@163.comAbstract - The high frequency chopped wave cascade speed part connected with rotors is three-phase uncontrolled rectifiedcontrol system has an overt advantage on less controlling voltage, circuit, which changes three AC phase from rotors into directI~wer controlli~~ po~er, simp~e structure and I.ittle te~hni.que current leaded to the chopped main circuit. The right part isdifficulty, thus It IS widely used m more and more industrial sites, active reverse circuit made up of thyristors which forms theespecially the energy saving and improvement of high voltage, dditi I tIt ti f Th iddl ti .h ., bl d t S it i t t tal rona coun er e ec romo rve orce. e mr e sec IOn ISuge power Ian ower an wa er pump. 0, I IS impor an o. . .analyse and study the dynamic characters about this system. In the typical boost. chopp~d wave CIrcUIt. Th~ ~ou~dthis paper, the principle about it is firstly introduced. Then, the asynchronous motor IS used m the system. In the mam cIrCUIt,basic relationship between the input and output parameters of the inductances LI and L2 play a role in flatting wave andthe main circuit is analysed by means of state-space averaging energy reserving. The capacitance C stores energy , filtersmethod. Subsequently, the simplified math model is derived. On higher harmonic and stabilizes voltage.the base of it, the simplified dynamic model of the high-frequencychopped wave cascade speed control system is deduced.According to this mathematical model, the dynamiccharacteristic structure graph is presented. At last, thecorresponding current loop and speed loop are designed bymeans of using the model-optimizing engineering method andharmonic vibration peak minimum guide, and the double loopsdesign is verified by the simulation model constructed in thesimulink software. The controlling results acquired fromsimulation are satisfied.Index Terms - cascade speed control; chopped wave; duty ratio;double closed-loops; state-space averaging method

I. INTRODUCTION

Different from other AC speed control system, savingenergy and controlling speed for the high frequency choppedwave cascade speed control system is achieved by means ofcontrolling the slip power leaded from rotors sides to powersystem or the feedback windings of the inner feedback motor .This control method not only has the same advantages of lesscontrolling voltage, lower controlling power, simple structureand more efficient energy saving as the traditional cascadespeed control mode, but also has obvious improvements onpower factor , harmonic suppression and security andreliability . So it is paid more and more attention s by peopleand used more and more widely in industry site. While atpresent, open loop control ways is adopted to the most ofactual high-frequency chopped wave cascade speed controlsystem s, which is not provided with current limiting and proneto over-current protection. Thus it is very necessary to analysisthe dynamic characters of system in depth and adopt doubleclosed loops controlling ways to improve the applicationproperties of this speed control system.

II. STR UCTURE AND PRI NCIPLE OF THE CHOPPED WAVE

CASCADE SP EED CONTROL SYSTEM

Fig.l shows typical structure of high frequency choppedwave cascade speed control system. According to it, the left

Fig. I Structure of high frequency chopped wave cascade speed system

IGBT works in on-off state, which opens and closes in thelight of the given duty ratio . When it turns on, the additionalcounter electromotive force is shorted, and while it turns off,the additional counter electromotive force is connected in themain circuit. So, while the duty ratio is changed, the averagevalue of counter electromotive force added to the main circuitin one on-off period could be adjusted. Thus, the current fromthe rotors and the electromagnetic torque of motor are bothchanged with duty ratio changing. Therefore, the motor speedis controlled smoothly and conveniently.

III. MODELING OF CHOPPED WAVE CASCADE SP EED CONTROL

SYST EM

A. State-space Averaging Method Analysis of the MainCircuit

Know from fig. I, the main circuit of system is a typicalboost chopped wave structure. The DC commutated voltagefrom the rotors side and the counter electromotive force fromthe inverter are the input parameters, and the current flowingthrough two inductances and the voltage of the capacitance arethe output ones , which are determined by the input parameters,the structure parameters and the duty ratio. According toFourier decomposition, the AC component of commutatedvoltage from rotors side and the counter electromotive forcefrom inverter side are mainly based by six integral multiple,

978-1-4244-2693-5/09/$25.00 ©2009 IEEE 487

(7)

(3)

(5)

(8)

(4)

(6)

o

o,B 2 = 0

o

oR

one chopped period), the state equation is

o

ratio, and Ts is

listed similarly:

di L (I)

dldi (I)

dldU c (I)

dl

- ~L]

2) . In second topology structure of one chopped wave

period (when IGBT is oft), I k$. I $. t k + d'I'; cd is the duty

Both sides of expression (8) are divided by Ts ' thus the even

value of state var iables in one period could be gained, if

In view of inductance current and capacitance voltage as

state variables being continuous, nam ely on condition that the

initial value in second state is the final value in first state, the

solution of the system state variables in k on-off periods.X (I k+l) = e[A,d +A2(I -d )]7; X(tk) + e A2(I -d )T, AI-I .

(e A, d"I~ _ I)Bp + A ;I[e A2(l - d) 7; - I]B2U

Because one on-off period of the high frequency chopped

wave is very short, In the above calculation, exponential

format eAT could be substituted approximately with its linear

format eAT == 1 + AT, and the higher order term of~ is

omitted further. Thus, the system solution at the end of one

on-off period could be expressed as :

X(lk+,) - X(lk ) =[A,d +A2(l -d)JT:X(lk)+

[d~ +(l-d)B2JT,U

L 2

1

C CSeen from the above analysis, expression (1) and (3) are thecontinuous state equations. If state variables of system are

defined as:XV) =[diJf)!dt d(f)!dt dl..lW!dqT, the solutions of

equations under first and second topology structure areexpressed respectively:

X(t) =eA ](t - ld X(tk

) +A,-' (e A](t -Id - I)B,UX(I) = e A2[1- ( lk+dT,l)X (t k +dTs) +

A;' (eA2[1-(lk+d7; l] - I)B2U

.defining X(t) = [X(tk+l) - X(tk wi..The standard solution of

state equations cou ld be listed as : X =AX + BU , and thecoefficient matrix of new state equation is the linearconstitution of two subsystems' coefficient matrix.

A = [dA, + (1 - d)A 2 J (9)

(I)

E

R

R1 0 0 0L] L]

R 1 (2)A - 0 , B ] = 0]-

L2 L2 L2

01

00 0

-C

Fig.2b Equivalent Circuit when IGBT turns off

Among the matrix, R1 and L 1 represent the resistance andinductance of the rectified side; in like manner, R, L2represent the resistance and inductance of the inverted side .

Fig.2a Equivalent Circuit when IGBT turns on

and the amplitude of which are a little relative to the DCcomponent. In addition, considering the restraint to harmonicsingredients from inductances, to simplify calculation, the DCcomponent of both commutated voltage from rotors andcounter electromotive force from inverter are only adopted inthe whole analysis.

According to the non-matrix converter modelling theory,the main circuit in continuous mode cou ld be expressed bytwo non-linear time-varying states, which corresponds to twoswitch states in one chopped wave period (referred to fig .2).

L1 R1 RI'YV"V,"",

1) In first topology structure of one chopping per iod (when

IGBT is on), I k $. I $. Ik + dTs (d is the duty ratio, and 1~ is

one chopped period), the state equation is listed as below:

di L (I)

dldi(/)

dldUc(1)---

dl

Among the above expression, i f- represents the current

flowing through inductance L 1; i represents the current

though inductance L2; Uc represents the voltage of capacitance

C; U and E represents the commutated voltage from rotors sideand the counter electromotive force from inverter respectively;the coefficient matrix Al and B

Iis respectively:

488

(19)

equivalent resistance as s =1; nl is the synchronous speed.

According to documents [10,13], the electromagnetic torque

of the chopped wave cascade speed control system:

t, = _1 (2.34E20

- 3XD Id

) old (18)WI 1C

side; According to the above mentioned about the maincircuit, the basic electrical equation could be listed as thebelow:

4:~+~ old =234 [sE;o-(I-D)E;'2 oCOS!t.iJ (14)

~=~~/1t+2Rn+~ +(1_~2 ·(3XrIRr+2Rr+~) (15)

4. =2LD +~ +(1-D)2 ·(L2+2LT ) (16)

I d represents the average value of load direct current in one

chopped cycle. Substitute S = nl - n/ nl with the slip ratio of

expression (14) and take laplace transformation at both sides ofit, the transfer function about input and output parts of themain circuit could be derived as the below:

Id(s) = ~n (17)

2.34·[~0(1-n(s)/~)-(1-D)Erz cosfJJ ~~+1In expression (17), Lr. is the time constant;

TLn 3XR -~r. nn,

1 is proportional gain; Rr. is the

R _ 3X D nr.

itn,

To is the electromagnetic torque at the steady work

point; I dO is the load direct current at the steady work point.

Supposed.- =~(2 34E _ 6XD 1 ) ,put the expanded formo • 20 dO

UJ1 Jr

after taken taylor expansion on the electromagnetic torque andload torque expression according to the expression (19) intothe electromechanical motion equation and arrange to gain thebelow:

C (1 _ 1 ) - GD2

dn (20)o d dL - 375 dt

In this equation, 1dL is the load direct current decided to load

torque. Take laplace transform at both sides of it, expression(20) could be deduced to the below form:

n(s) 1 (21)

1d(s)-1dL ( S ) ~s

In this expression,~ is synchronous angular velocity. Take

the taylors expansion at the steady work point determined

together by the given speed n* and the load torque TL .

Considering the quadratic term and higher order term ofexpanded formula are too small to be ignored. So theexpression only expanded to its first order derivative is:

1 ( "'l 6XD ) ( )T, = To+- 2.-,4Ezo---Ido I d - I do~ 1C

(10)

(11)

o

Ro

d

C

Solving the group of differential equations described by

expression (11), the relationship of current iL and the input of

system could be gained:d3~ d2~

CL1L2 dt 3 + (CL2R1+RC~) dt2 +(L1+ (12)

d'' L2 + R1CR) diL + (R1+ d" R)iL = U - Edt

As the orders of magnitude about capacitance,inductance and resistance in actual applications are usuallyvery small, and after omitting small coefficient term, thesolution could be simplified as the below:

u, +d'2~) ~~ +(R] +d'2R)iL=U-aE (13)

So, the dynamic relationship about the even values ofduty ratio, structure parameters, input parameters and load

direct current iL in one on-off period could be gained. The

magnitude of rotors' current is determined by the load direct

current iL ' and which further determine the torque and speed.

B. Chopped Wave Cascade Speed Control system SimpleDynamic Modeling and Double Closed loops DynamicStructure Figure

The commutated voltage from rotor side and the counterelectromotive force from inverter side are respectively

2.34sE20and 2.34ETZ CoSflrnin' among which, £20 and E r 2 are

rotor no-load electromotive force and inverter transformer

secondly side effective voltage. fJmin is the minimum inverter

angle, which equals to 30° r-.J 35° degrees approximately.Considering the equivalent commutation resistances3sX D / Jr and 3Xr /1! caused by the commutated overlapping

angle r of rotor rectification side and inverter second side, and

the equivalent resistances RD and R: transformed into rotor

side and inverter transformers secondly side, of which, X D

and X T are respectively equivalent leakage reactance

translated to rotor side and inverter transformers secondly

B = [dB l + (1 - d)B2 ]

Known from the equation, the contributions to systemresponse from each state are described with respectiveactuation duration. Then the state space expression about theeven values of input and output in one on-off period could begot. Generally speaking, it is equivalent to gain the stateequation by means of sampling system state variables withsuch step as one on-off period. Put the above two coefficientsmatrix showed by expression (2) and (4) into expression (9)and (10), the new state equation could be listed as:

diL _ RI 0 d 1 0

dt ~di

dtd~

dt

489

Among this expression, T = GD2

• GD2 is the total momentI 375Co

inertia of motion parts. Thus, the system dynamic math modelcould be built by means of the middle clement, namely thedirect load current, which describes the impact from inputparameters of the system on the speed in different duty-ratio.

The delay resulted from thyristors out of control of therectification could be described approximately by the inertial

element, of which the proportional gain is Kv,and the time

constant isT,' If the given filtering element and the feedback

filtering element are both considered, and combined with theexpression (17) and (21), the double closed-loops dynamicstructure figure could be painted as the below drawing :

2.34E20

Fig. 3 Dynamic structure diagram of double closed loops control in high frequency chopped wave cascade speed control system

(22)

IV. DOUBLE CLOSED Loops CONTROLLING SYSTEM D ESIGN

A. Current Inner Loop DesignKnown from the dynamic structure figure, the current

inner loop matches to the typical second order engineeringoptimization conditions, because the controlled object of theinner loop is made up of one big inertial element( T =TLn )

and two little inertial elements( T = Tai,T,). For control

capability, the current loop should accomplish good trackingproperties, little overshoot and certain anti-disturbance ability .So the typical I-type system method could be used to design it.

r--~... I d(s)

a

~(S)I' KK ~ T' /JCR. . In I ,

~ ""H'X'i."b

FigA Dynamic structure diagram of current inner loop in high frequencychopped wave cascade speed control system

Because current response is more and more faster thanspeed response, during current transient changing, the impacton the current resulting from disturbance2.34E20/n) .n(s) could be neglected. Thus, the current inner

loop could be equivalently converted into unit negativefeedback form showed as the figure 4a. Because the timeconstants of current feedback filtering element and rectifierdevice amplification clement arc both far less than Trn, take

small inertia clements approximate processing,set Tr.i = T, +Tai . The form as the figure 4b showed could be

gained .

490

Supposing the transfer function of current PI adjustor is

expressed as:WACR

(s) = K , . T iS +1, in order to cancel the poleTiS

point corresponding to the time constant of big inertia clementof controlled object, set t, =TLn • Thus, like the format of open

loop anticipated transfer function about the typical I-typesystem, the below expression could be presented:

KiKvKLJJ K

1"is(Tr.iS+1) seTs+1)In the light of optimal mode engineering design principles,when amplification coefficient K and inherent time

constant T meets KT =0.5, the damping coefficient ofsystem ~ equals to 0.707, which satisfies property index of

second-order engineering optimal system. So the expression ofthe amplification coefficient is gained as: K , Tf."

2KVK f."flTr.;

B. Speed Out Loop DesignAt first, write down the closed loop transfer function

about the current inner loop. Because the current loop isdesigned by virtue of second-order engineering optimalsystem and its transfer function could be listed by expression(22) , which is one small inertia clement, thus the speed outloop could be simplified as fig.5a showed . According to thedrawing, the controlled objects includes two small inertiaelements and one integrating element, which is the typicaltype II system. So its dynamic parameters should be calculatedby the third-order engineering optimization method, whichcould improve the anti-disturbance ability of the system on theone hand, endow the speed out loop with good trackingfeatures on the other hand ':" .

bFig.S Dynamic structure diagram of speed out loop in high frequency

chopping cascade speed control system

According to the rules of resonance peak M r minimum,

when mid-frequency band width h = 5 , the dynamiccharacters of system is optimal. To simplify the system, furthertake the small inertia elements approximate treatments,

setTDI = 2TD + T;m ' the dynamic structuredrawing about unity

negative feedback system of speed closed loop could bedescribed as fig.5b. Supposing the transfer function of the

speed PI adjustor is expressed as:WASR (s) = Kn . "n S +I . Thus,

"ns

according to the format of open loop anticipated transferfunction about the typical Il-type system, the belowexpression could be presented:

«; Tn +1 X a/(fJTJ) = ~(1S + I) (23)TnS s(T}:ns + I) s (Ts +1)

Expression (24) and (25)could be derived from the definitionabout rand K of the minimum M r method.

t; =T=hT=hTDI (24)

K _ K n a _ h + I (25)- fJT r - 2h 2T 2

I n

Substitute h = 5 to expression (24) and (25), these below

expression could be gained:

Tn =5TDI (26)

K = (h + l)fJT f = O.6fJTf (27)n 2 haT x» aT t n

Known from the expression (23), one zero point rs +1existsin the closed loop transfer function. To cancel with it in orderto avoid causing large overshoot, the inertia element with timeconstant being 1S should be added to the front of the closedloop. Thus, the transfer function of given filtering elementbefore the speed out loop should be:

IW n(s)= (28)

g (5x Tr.n +Ton)s + I

V. SIMULATION ANALYSIS

The 1# slag pump technological reconstruction projectof Qinhuangdao Power company Ltd. undertaken byBaoding HuaFang Electrical Control company Ltd. is madeas the example to design its double closed loops controlling

491

device, and is simulated to verify the effect of controllingaccording to the model from document". The systemparameters are known as below:

Motor rated power: 560KW; stator rated linevoltage:6KV; stator rated line current:65.1A; rotor openedcircuit voltage:977V; rotor rated line current:354A; rated

speed: 742r/min; GD 2 =130Kg . m 2 .overload

multiples: A. = 2.0 ;efficiency: '7= 94.21% ;rated power

factor: cos¢ = 0.804 ;inverter transformer secondary side

line voltage:626V; inverter transformer secondary side linecurrent:213A; filtering inductance L1:2.1mH; filteringinductance L2:5.1mH; capacitance :2400 IJF ;full-speed

load power:408KW;speed-regulating range:358-742r/min,active application range: 465-742 r/min; maximum givenvoltage of speed out loop and current inner loop are bothlOY; the filtering time constant of feedback elements arerespectively: Ton = 0.0 ls and To; =0.002s ; the maximum load

direct current is 800A. Based on the above parameters, thePI adjustors' parameters of two loops are respectively:x, =0.8467 , 1; =0.0233 , «, =12 , T; =0.087 . The time

constant on given filtering element of the speed loop:T

g= 0.097 .With a view to less speed range, unsteady

proportion coefficient IS calculated by the speedwhen s =0.25.

Table!. Main dynamic characters index while given speed descent from therated speed

nCr/min) 600r/min 550r/min 500r/min 450r/min 400r/min

t5 ( %) 5.83 4.9 4.36 3.78 3

Is(s) 0.785 0.98 1.22 1.5 1.88

Simulation work conditions: start asynchronous motorconnected with water resistance, when the speed reaches to therating speed and become steady, regulate to the given speed.Table.l lists overshoot and adjustment time under differentspeed descended from rating speed 742r/min. Known from theabove data, overshoot t5 is less than or equal to 6%; andadjustment time when control deviation band is within 2% isless than or equal to 1.88s. Fig. 6a displays the dynamicchanging process of the current and speed when speed isadjusted to 500r/min from rating speed. Figure 6b displays thesimulation result that the load TL=4300N.m is added to themotor suddenly after speed tends to stabilize at 500r/min.Known from it, the system dynamic maximum speed descentis 27r/min and recover time is 0.38s. Obviously, the systempossesses good anti-disturbance ability after added to thedouble closed loops. Meanwhile, the load direct current iseffectively limited, which prevents from over-current andadvance the security.

Fig 6a. Simulation result of current and speed when stabilized to 500r/minfrom rated speed

Fig 6b. Dynamic process resuming to given speed after suddenly added byload disturbance 4300N.m when 4.2s

VI CONCLUSION

The mathematical model of the main circuit of highfrequency chopped wave cascade speed control system isfounded by means of the state-space averaging method, andbased on which, the dynamic model about the system is built.According to the second-order and the third-order engineeringoptimum method, double closed loops controlling ways isdesigned. Relative to the open loop controlling ways, doubleclosed loops control improves not only the security, stronganti-disturbance features and dynamic and static properties ofsystem but also effectively restrain the load busbar current,avoiding excessive current protection, which is verified by thesimulation results . The modelling theory and the designmethods about closed loops control are important and helpfulto the engineering design and application of the highfrequency chopped wave cascade speed control system. Butthe impact on controlling effect among the whole speedgoverning process and definite method about non-constantdynamic parameters are expected to be discussed furtherly .

492

REFERENCES

Pl. Jiang Youhua, Ning Yu, Wu Guoxiang. Study on Digital Dual Closed­loop Chopper Inner-feed Cascade Variable Speed Drive System Based onSate-space Averaging Model and Its Application[J]. Control Theory andApplications, 2007.24(1) : 109-112.[2].Jiang Youhua, Cao Yilong, Gong Youmin. Application of ChopperDouble-close-loop in Inner Feedback Motor Cascade Speed Drive System[J].Electric Drive, 2006.36(6): 16-18.[3]. Xu Chang, Wang Bingshu, Lv Lixia, Zhang Xiaodong, Xin Liang.Simulation Study of High Frequency Chopping Motor Speed Control byStatic Slip Power Recovery[J]. Electric Power Science and Engineering,2006.27(3):

[4]. POWALEE, YIMSHU, LEECHENG. Steady-state analysis of aninterleaved boost converter with coupled inductors[J]. IEEE Trans onIndustrial Electronics, 2000, 47(4):787 -795.

[5].Wang Fuqing. Engineering Design about Double Closed LoopsControlling in Cascade Speed Control Drive System.[J]. Xian Metallurgicaland Architecture College Journal , 1992.24(1): 104-110.[6].Wang Qingling. Analysis of the Main Circuit with Chopper of CascadeSpeed Control System[J]. Power Electronics , 1990(2):26-30.[7].Xu Shuque. Static-state Calculation and Dynamic-state Design of CascadeSpeed Control System with Double Closed Loops[J]. Electric Drive,1984.(4):9-16.[8].lhao Yingchang, Sun Zechang. Closed Loop Control Structrue andDynamic Characters Comprehensive Analysis of Cascade Speed DriveSystem[J]. Electric Drive, 1981.(3):1-10.[9].lhang Xijing, Tao Weiqing. Computer Comprehensive Analysis aboutDynamic response of Double Closed Loops Cascade Speed ControlSystem[J]. Engineering Technology College Journal , 1986.5(1):101-116 .[lO].Wei Zeguo. Principle and Application of SCR Cascade Speed ControlSystem[M] ,First Edition .Beijing: Metallurgical Industry Press, 1985.[11].Chen Boshi. Automatic Control System of Electric Drive (MotionControl System)[M], Third Edition. Beijing : Machinery Industry Press,2003.[l2].Chen Jianye. Computer Simulation of Power Electronic Circuit[M], FirstEdition. Beijing: Tsinghua University Press, 2003.[13].Wang Junyan. AC Speed Drive[M], First Edition.Beij ing:HigherEducation Press,2003.[14].Hong Naigang. MATLAB Simulation of Power Electronics and ControlSystem of Electric Drive[M], First Edition. Beijing: Machinery IndustryPress,2006.[15].Ye Bin. Application Technology of Power Electronics[M], First Edition.Beijing : Tsinghua University Press, 2006.