Prepared AMIRIXSystems Inc., Chain Lake Drive, Halifax, Nova Scotia, C

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Prepared AMIRIXSystems Inc., Chain Lake Drive, Halifax, Nova Scotia, Canada
Tel: (902) 450-1700 Fax: (902) 450-1704 Web: Email: motionpro@amirix.com
Induction motors very common because they inexpensive robust, finding everything from industrial applications such pumps, fans, blowers home appliances. Traditionally, induction motors have been single speed which determined frequency mains voltage number magnetic poles motor. Controlling speed induction motor more difficult than controlling speed motor since there linear relationship between motor current resulting torque there motor. technique called vector control used vary speed induction motor over wide range. vector (also called field oriented) control scheme, complex current synthesized from quadrature components, which responsible flux level motor, another which controls torque production motor. Essentially, control problem reformulated resemble control motor. Vector control offers number benefits including speed control over wide range, precise speed regulation, fast dynamic response, operation above base speed. Vector control techniques have been reported technical literature quite some time, until they have only been available form expensive vector drives. Now, with availability cost digital signal processor (DSP) such Analog Devices ADMC331 ADMCF326, vector control induction motors implemented cost. ADMC331 ADMCF326 single chip motor controllers consisting core peripheral carefully chosen match requirements motor control. Because ADMC331/F326 optimized specifically motor control, several benefits result: external components required, resulting lower system bill materials assembly costs,
code overhead generate pulse width modulation (PWM) waveforms. more software overhead required create switching signals when using general purpose microcontroller, even other motor control DSPs. Synchronization switching cycles onchip analog digital converter (ADC) sampling means that digitized currents voltages cleaner than external used.
This application note presents some ideas that contained MOTIONPROAC331 AC326 Induction Motor Development Kits. kits contain complete reference design, including both hardware software, induction motor controller. More information kits available algorithms discussed this application note included source code form MOTIONPROdevelopment kits. ADMCF326 very similar ADMC331 with major differences being: package (SOIC DIP) programmable pins opposed ADMC331 4Kx24 on-chip FLASH program memory references bibliography section contain some excellent sources more information.
DSP?
good motor control because processing power available cost DSPs such Analog Devices ADMC331 ADMCF326. Vector control requires some intensive numeric processing which microcontrollers well suited. With compute power hand, other benefits such sensorless operation possible which further reduce system cost. Simpler control techniques such control possible with microcontrollers; however, their performance lower well.
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Hardware
Figure gives simplified view hardware environment induction motor control using ADMC331 ADMCF326. mains rectified stored capacitors. three phase IGBT voltage source inverter then chops voltage using pulse
width modulation (PWM) techniques produce three motor phase voltages. inverter controlled three pairs signals from (AH, diagram). on-chip analog digital converter (ADC) used digitize motor phase currents diagram).
Single Phase Rectifier
Voltage Source Inverter
Motor
230V 60/50 input
Three Phase Y-Connected Load
ADMC331 ADMCF326
Figure Hardware Overview
Algorithm
vector control algorithm based fundamental ideas. first, flux torque producing currents, introduced above. induction motor modelled most simply (and controlled most simply!) using quadrature currents rather than familiar three phase currents actually applied motor. These currents, called direct (Id) quadrature (Iq) responsible producing flux torque respectively motor. definition, current phase with stator flux, right angles. course, actual voltages applied motor resulting currents familiar three phase system. problem then becomes moving between stationary reference frame reference frame which rotating synchronous with stator flux. This leads second fundamental idea behind vector control.
second fundamental idea that reference frames. idea reference frame transform quantity that sinusoidal reference frame constant value reference frame which rotating same frequency. Once sinusoidal quantity transformed constant value careful choice reference frame, becomes possible control that quantity with traditional proportional integral (PI) controllers.
Algorithm Overview basic structure software illustrated Figure figure shows that motor phase currents voltage digitized ADC. Then third current calculated using fact that connected motor, phase currents zero. three phase currents, called Ias, Ibs, then transformed phase system using forward Clarke
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transform. resulting currents called Iys. requested motor voltages (Vxs Vys) scaled down using measured value voltage account droop under heavy motor loads. resulting voltages, called Vdc_xs Vdc_ys, inferred stator voltages. These quantities together with stator currents then used estimate motor flux. flux estimated first calculating motor back which equal applied voltage (Vdc_xs, minus stator currents (Ixs, multiplied stator resistance. back then integrated arrive estimate motor flux. motor flux variables (Flux_xs Flux_ys) then used calculate stator flux angle magnitude. flux angle used rotate frame currents reference frame stationary with flux using forward Park transform. outputs this operation currents, responsible motor's flux level, Ids, responsible motor's torque level, Iqs.
Then, four independent Proportional Integral (PI) controllers used regulate speed flux regulating quadrature direct currents voltages. resulting quadrature direct voltages (Vqs, Vds) transformed back stationary reference frame using reverse Park transform. Finally, reverse Clarke transform used back three phase (variable) system. forward reverse Park transforms boundary between stationary reference frame rotating reference frame. right Park transforms, variables stationary reference frame, sinusoidal. left Park transforms, variables reference frame which rotating synchronous with stator flux. These variables synchronous reference frame constant quantities which regulated using controllers. motor speed estimated using motor back EMFs stator fluxes. well, speed calculated using pulses from tachometer.
Synchronous Reference Frame
Stationary Reference Frame
Speed Reference +/PI
IqsRef +/PI
(rev)
Flux Reference
IdsRef +/PI +/PI
(rev)
Timers
(for)
(for)
Ias=-Ibs-Ics
Stator Flux angle estimate
Stator Flux magnitude estimate
Flux Estimation integrating back
Vdc_Vxs Vdc_Vys
Vdc_xs=Vxs*(Vdc/Vdcmax) Vdc_ys=Vys*(Vdc/Vdcmax)
EMF, Flux Speed Estimator from Tachometer
Figure Vector Control Algorithm Overview
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Vector Transforms Park Clarke vector transforms keys vector control induction motors.
Clarke transform also understood using vector diagram shown Figure figure, axes three phase system, each offset 120° from other. axes variable system where chosen coincident with perform Clarke transform three variable system (iA, iC), equal scaled projection onto axis. scaling necessary preserve signal magnitudes through transform.
3.2.1 Clarke Transform forward Clarke transform does magnitude invariant translation from three phase system into orthogonal components. Since variables three phase system zero there redundant information. Therefore, system reduced variables, called Clarke transform given
cos( cos(2 sin( sin(2
where:
120°
iA,iX
Using fact that three phase currents balanced, i.e.:
fact that:
Figure Clarke Transform Vector Diagram following Matlab code used illustrate operation forward Clarke transform. balanced three phase variable system created cycles signal sampled period. These variables, then Clarke transformed produce variables variables plotted Figure seen that Clarke transform magnitude preserving that quadrature.
create balanced three phase system (0:0.001:1/60*3); sin(2*pi*60*t); sin(2*pi*60*t+(120/360*2*pi)); sin(2*pi*60*t+(240/360*2*pi)); perform Clarke transform 1/sqrt(3)*(Ib-Ic);
cos(
cos(
equation ixs(t) written
cos( cos( )iCs
Thus, Clarke transform simplified
sin(
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Figure Forward Clarke Transform Input Output reverse Clarke transform converts variable system back three phase system using following system equations:
Figure Reverse Clarke Transform Input Output
3.2.2 Park Transform Park transform vector rotation which rotates vector (defined quadrature components) though specified angle. Park transform function implements following equations:
where:
cos( sin( cos( sin(
cos( sin( sin( cos(
operation illustrated using following Matlab code:
Reverse Clarke transform example create phase quadrature system (0:0.001:1/60*3); sin(2*pi*60*t); sin(2*pi*60*t+(90/360*2*pi)); perform reverse Clarke transform gamma 2*pi/3; cos(gamma)*Ix sin(gamma)*Iy; cos(2*gamma)*Ix sin(2*gamma)*Iy;
where angle rotate vector through. reverse vector rotation accomplished simply changing sign sin() input value. vector rotation illustrated Figure
ISTATOR
results plotted Figure
Figure Park Transform Vector Diagram
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Some references describe Park transform combination Park Clarke transforms presented here. Breaking into three-variable-to-two transform (i.e. Clarke transform) vector rotation done efficiency calculation: with separate Park Clarke transforms, only trigonometric calculations required opposed traditional Park transform. implementation actually avoids doing trigonometric functions: uses division calculate sine() cosine() instead using arctan function calculate angle, then calculating sine cosine that angle. following Matlab code defines Ixs, vector pair, rotates them through angle.
Park transform example 0.25; 0.6; mag_xy sqrt(Ix^2 Iy^2); rotate through degrees angle -30; degrees theta angle/360*2*pi; calculate park transform cos(theta)*Ix sin(theta)*Iy; sin(theta)*Ix cos(theta)*Iy; mag_dq sqrt(Id^2 Iq^2);
Flux Estimation estimation motor flux performed part control algorithm reasons: flux magnitude needed input flux controller. sensorless (i.e. only voltage current sensing) system, flux angle needed transform between stationary synchronous reference frames using forward reverse Park transforms. systems with shaft position sensors (e.g. resolvers encoders), sensor output used rotor flux angle.
motor flux estimated first calculating motor back-EMF which equal
BackEMF
where Vx,y requested motor voltage (corrected drops voltage), stator resistance motor, Ix,y stator currents variable system following forward Clarke transform). Then stator flux found integrating back EMF:
BackEMF
challenge with flux estimation perform numerical integration which does grow without bound when offset present input, which does have offset produced initial non-zero phase. Integration represented Laplace domain multiplication 1/s:
Figure plots results this calculation. seen that Istator vector resultant (i.e. vector sum) either other words, (Ix, (Id, representing same vector quantity (Istator) different reference frames.
-0.1 -0.2 -0.1 Istator
MOTIONPROdevelopment implements integration algorithm from which uses feedback techniques overcome offset problem. Essentially, y=x/s integration operation factored into components follows:
addition feedback term removes offset initial condition problems from pure integrator.
Figure Calculated Park Transform Vectors
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Controllers
Error
vector control algorithm includes four Proportional Integral (PI) controllers control speed, flux, (torque producing current), (flux producing current). continuous time controller represented following equation:
Request Proportional Gain Integral Gain Sum2 Sum1
Output
Scope
Unit Delay
CO(t
where: CO(t) controller output time proportional constant e(t) error signal time integral constant Figure shows continuous time controller simulation model.
Error Request Proportional Gain Integral Gain Integrator Sum1 Output
Figure Discrete Time Controller problem with this implementation numeric overflow when integral term grows large. common variation classic controller limit amplitude integral term. This shown Figure
Error Request Proportional Gain Integral Gain Sum2 Saturation Sum1 Output
Scope
Unit Delay
Scope
Figure Discrete Time Controller with Integral Term Limit
Figure Continuous Time Controller discrete time difference equations which implement controllers follows:
Speed Estimation motor shaft speed estimated from terminal quantities (voltages currents) [2]. This remove need expensive speed feedback components such optical encoders. rotor speed equal difference between electrical frequency slip frequency:
where: integral constant I(k+1) integral error integral constant I(k) previous integral error integral constant e(k+1) error iteration proportional constant U(k+1) controller output Note that these equations notation where represents current iteration represents previous. Some references represent same quantities. These notations equivalent. discrete time controller shown block diagram form Figure
rotor elec -slip
electrical frequency given
elec
where: EMFx EMFy
(EMF
(EMFx
Back EMF, Back EMF, Flux, Flux, Magnitude stator flux squared
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slip frequency given
Bibliography References
Integration Algorithms Estimating Motor Flux Over Wide Speed Range, IEEE Power Electronics Specialist Conference, June 22-27, 1997, vol. 1075-1081 D.W. Novotny, Implementation Direct Stator Flux Orientation Control Versatile Based System, IEEE Transactions Industrial Applications, JulyAugust 1991, Vol. 694-700 Sensorless Control Motor Drives, edited Rajashekara, al., 1996, IEEE Press, ISBN 0-7803-1046-2 G.F. Franklin, J.D. Powell, Workman, Digital Control Dynamic Systems, edition, 1997, Addison-Wesley, ISBN 0-201-82054-4 Valentine, Motor Control Electronics Handbook, 1998, McGraw-Hill, ISBN 0-07-066810-8 Chee-Mun Ong, Dynamic Simulation Electric Machinery, 1997, Prentice-Hall, ISBN 0-13-723785-5
slip
where:
Total leakage factor= Rotor time constant Differential operator Stator inductance Stator current, quadrature (torque producing) component Stator flux, direct component Stator current, direct (flux producing) component
Conclusion
This application note described sophisticated variable speed control technique induction motors which implemented cost DSPs such ADMC331 ADMCF326 from Analog Devices. code implement algorithms discussed here available form development users started quickly with technology.
Need support with your motor control application?
AMIRIX offers consulting development services your application designed market quickly cost effectively. more information, contact AMIRIX Systems Inc. Chain Lake Drive Halifax, Nova Scotia Canada Tel: (902) 450-1700 Fax: (902) 450-1704 Email: motionpro@amirix.com visit
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Prepared AMIRIXSystems Inc., Chain Lake Drive, Halifax, Nova Scotia, C

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