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Prepared by AMIRIX Systems Inc., 77 Chain Lake Drive, Halifax, Nova Scotia, Canada B3S 1E1

Tel: (902) 450-1700 Fax: (902) 450-1704 Web: www.amirix.com / products / mopro.shtml Email: motionpro@amirix.com

Prepared by AMIRIX Systems Inc., 77 Chain Lake Drive, Halifax, Nova Scotia, Canada B3S 1E1
Tel: (902) 450-1700 Fax: (902) 450-1704 Web: www.amirix.com / products / mopro.shtml Email: motionpro@amirix.com
1. Introduction
Induction motors are very common because they are inexpensive and robust, finding use in everything from industrial applications such as pumps, fans, and blowers to home appliances. Traditionally, induction motors have been run at a single speed which was determined by the frequency of the mains voltage and the number of magnetic poles in the motor. Controlling the speed of an induction motor is far more difficult than controlling the speed of a DC motor since there is no linear relationship between the motor current and the resulting torque as there is for a DC motor. A technique called vector control can be used to vary the speed of an induction motor over a wide range. In the vector (also called field oriented) control scheme, a complex current is synthesized from two quadrature components, one of which is responsible for the flux level in the motor, and another which controls torque production in the motor. Essentially, the control problem is reformulated to resemble control of a DC motor. Vector control offers a number of benefits including speed control over a wide range, precise speed regulation, fast dynamic response, and operation above base speed. Vector control techniques have been reported in the technical literature for quite some time, but up until now they have only been available in the form of expensive vector drives. Now, with the availability of low cost digital signal processor (DSP) such as the Analog Devices ADMC331 or ADMCF326, vector control for induction motors can be implemented at low cost. The ADMC331 and ADMCF326 are single chip motor controllers consisting of a 16 bit DSP core and a peripheral set carefully chosen to match the requirements of motor control. Because the ADMC331 / F326 are optimized specifically for motor control, several benefits result: · Few external components are required, resulting in lower system bill of materials and assembly costs,
Low code overhead to generate pulse width modulation (PWM) waveforms. Far more software overhead is required to create the PWM switching signals when using a general purpose microcontroller, or even other motor control DSPs. Synchronization of PWM switching cycles and the onchip analog digital converter (ADC) sampling means that digitized currents and voltages are cleaner than if an external ADC was used.
This application note presents some of the ideas that are contained in the MOTIONPRO AC331 and AC326 AC Induction Motor Development Kits. The kits contain a complete reference design, including both hardware and software, of an induction motor controller. More information on the kits is available at www.amirix.com / products / mopro.shtml. All algorithms discussed in this application note are included in source code form in the MOTIONPRO development kits. The ADMCF326 is very similar to the ADMC331 with the major differences being: · 28 pin package (SOIC or DIP) · 11 programmable I / O pins as opposed to 24 on the ADMC331 · 4Kx24 bit on-chip FLASH program memory The references and bibliography in section 5 contain some excellent sources for more information.
DSP is a good fit for motor control because of the processing power available and the low cost of DSPs such as the Analog Devices ADMC331 or ADMCF326. Vector control requires some intensive numeric processing to which microcontrollers are not well suited. With the compute power of the DSP at hand, other benefits such as sensorless operation are possible which can further reduce system cost. Simpler control techniques such as V / F control are possible with microcontrollers however, their performance is lower as well.
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2. Hardware
Figure 1 gives a simplified view of the hardware environment for induction motor control using the ADMC331 or ADMCF326. The AC mains are rectified and stored on DC bus capacitors. A three phase IGBT voltage source inverter then chops the DC bus voltage using pulse
width modulation (PWM) techniques to produce the three motor phase voltages. The inverter is controlled by three pairs of PWM signals from the DSP (AH, AL, BH, BL, CH, and CL in the diagram). The on-chip analog digital converter (ADC) on the DSP is used to digitize two of the motor phase currents (IB and IC in the diagram).
Vdc Single Phase Rectifier
Voltage Source Inverter a
Motor
230V AC 60 / 50 Hz input b
N c Three Phase Y-Connected Load
ADMC331 or ADMCF326 DSP
Figure 1: Hardware Overview
3. Algorithm
The second fundamental idea is that of reference frames. The idea of a reference frame is to transform a quantity that is sinusoidal in one reference frame to a constant value in a reference frame which is rotating at the same frequency. Once a sinusoidal quantity is transformed to a constant value by careful choice of reference frame, it becomes possible to control that quantity with traditional proportional integral (PI) controllers.
3.1 Algorithm Overview The basic structure of the DSP software is illustrated in Figure 2. The figure shows that two of the motor phase currents and the DC bus voltage are digitized by the ADC. Then the third current is calculated using the fact that for the Y connected motor, the phase currents sum to zero. The three phase currents, called Ias, Ibs, and Ics are then transformed to a two phase system using a forward Clarke
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Then, four independent Proportional Integral (PI) controllers are used to regulate the speed and flux by regulating the quadrature and direct currents and voltages. The resulting quadrature and direct voltages (Vqs, Vds) are transformed back to the stationary reference frame using a reverse Park transform. Finally, a reverse Clarke transform is used to get back to a three phase (variable) system. The forward and reverse Park transforms are the boundary between a stationary reference frame and a rotating reference frame. To the right of the Park transforms, all variables are in the stationary reference frame, and are sinusoidal. To the left of the Park transforms, all variables are in a reference frame which is rotating synchronous with the stator flux. These variables in the synchronous reference frame are constant quantities which can be regulated using PI controllers. The motor speed is estimated using the motor back EMFs and stator fluxes. As well, speed is calculated using pulses from a tachometer.
Synchronous Reference Frame
Stationary Reference Frame
Speed Reference + / PI
IqsRef + / PI
Vqs P A R K (rev) Vys
Flux Reference
Vas Vbs Vcs PWM Timers
Stator Flux angle estimate
Stator Flux magnitude estimate
Flux Estimation by integrating back EMF
EMF, Flux Speed Estimator PIO from Tachometer
Figure 2: Vector Control Algorithm Overview
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3.2 Vector Transforms The Park and Clarke vector transforms are one of the keys to vector control of induction motors.
The Clarke transform can also be understood using a vector diagram as shown in Figure 3. In the figure, A, B, and C are the axes of a three phase system, each offset 120° from the other. X and Y are the axes of a two variable system where X is chosen to be coincident with A. To perform the Clarke transform of a three variable system (iA, iB, iC), iX is equal to iA and iY is the scaled projection of iB and iC onto the Y axis. The scaling is necessary to preserve the signal magnitudes through the transform.
3.2.1 Clarke Transform The forward Clarke transform does a magnitude invariant translation from a three phase system into two orthogonal components. Since the variables in a three phase system (A, B, and C) sum to zero there is redundant information. Therefore, the system can be reduced to two variables, called X and Y. The Clarke transform is given by:
where:
iA, iX
Using the fact that the three phase currents are balanced, i.e.:
and the fact that:
Figure 3: Clarke Transform Vector Diagram The following Matlab code can be used to illustrate the operation of the forward Clarke transform. A balanced three phase variable system is created for 3 cycles of a 60 Hz signal sampled at a 1 ms period. These variables, Ia, Ib, and Ic are then Clarke transformed to produce the two variables Ix and Iy. All the variables are plotted in Figure 5. It can be seen that the Clarke transform is magnitude preserving and that Ix and Iy are in quadrature.
the equation for ixs(t) can be written as:
Thus, the Clarke transform can be simplified to:
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1 0.5 0 -0.5 -1 Ia Ib Ic
1 0.5 0 -0.5 -1 Ix Iy
1 0.5 0 -0.5 -1 Ia Ib Ic
Figure 4: Forward Clarke Transform Input and Output The reverse Clarke transform converts a two variable system back to a three phase system using the following system of equations:
Figure 5: Reverse Clarke Transform Input and Output
3.2.2 Park Transform The Park transform is a vector rotation which rotates a vector (defined by its quadrature components) though a specified angle. The Park transform function implements the following set of equations:
where:
The operation is illustrated using the following Matlab code:
where is the angle to rotate the vector through. A reverse vector rotation can be accomplished simply by changing the sign on the sin() input value. The vector rotation is illustrated by Figure 6.
Y ISTATOR D iQ
The results are plotted in Figure 5.
Figure 6: Park Transform Vector Diagram
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Some references describe the Park transform as a combination of the Park and Clarke transforms presented here. Breaking it into a three-variable-to-two transform (i.e. the Clarke transform) and a vector rotation is done for efficiency of calculation: with separate Park and Clarke transforms, only two trigonometric calculations are required as opposed to 6 in the traditional Park transform. The DSP implementation actually avoids doing any trigonometric functions: it uses division to calculate sine() and cosine() instead of using an arctan function to calculate an angle, and then calculating the sine and cosine of that angle. The following Matlab code defines an Ixs, Iys vector pair, and rotates them through a 30° angle.
3.3 Flux Estimation An estimation of motor flux is performed as part of the control algorithm for two reasons: 1. The flux magnitude is needed for input to the flux PI controller. In a sensorless (i.e. only voltage and current sensing) system, the flux angle is needed to transform between the stationary and synchronous reference frames using the forward and reverse Park transforms. In systems with shaft position sensors (e.g. resolvers or encoders), the sensor output can be used as the rotor flux angle.
The motor flux is estimated by first calculating the motor back-EMF which is equal to:
where Vx, y is the requested motor voltage (corrected for any drops in the DC bus voltage), Rs is the stator resistance of the motor, and Ix, y are the stator currents (in the two variable system following the forward Clarke transform). Then the stator flux is found by integrating the back EMF:
The challenge with flux estimation is to perform a numerical integration which does not grow without bound when a DC offset is present on its input, or which does not have an offset produced by an initial non-zero phase. Integration can be represented in the Laplace domain as a multiplication by 1 / s:
Figure 7 plots the results of this calculation. It can be seen that the Istator vector is the resultant (i.e. vector sum) of either Ix and Iy or Id and Iq. In other words, (Ix, Iy) and (Id, Iq) are representing the same vector quantity (Istator) in two different reference frames.
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 Istator Ix Iy Id Iq
The addition of a feedback term removes the DC offset and initial condition problems from the pure integrator.
Figure 7: Calculated Park Transform Vectors
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3.4 PI Controllers
Error
The vector control algorithm includes four Proportional Integral (PI) controllers to control speed, flux, Iqs (torque producing current), and Ids (flux producing current). A continuous time PI controller can be represented by the following equation:
Kp Request Sum Proportional Gain Ki Integral Gain Sum2 Sum1
Output
Scope
1 z Unit Delay
Error Kp Request Sum Proportional Gain Ki Integral Gain 1 s Integrator Sum1 Output
Figure 9: Discrete Time PI Controller One problem with this implementation is numeric overflow when the integral term grows too large. A common variation on the classic PI controller is to limit the amplitude of the integral term. This is shown in Figure 10.
Error Kp Request Sum Proportional Gain Ki Integral Gain Sum2 Saturation Sum1 Output
Scope
1 z Unit Delay
Scope
Figure 10: Discrete Time PI Controller with Integral Term Limit
Figure 8: Continuous Time PI Controller The discrete time difference equations which implement the PI controllers are as follows:
3.5 Speed Estimation The motor shaft speed can be estimated from terminal quantities (voltages and currents) 2. This can remove the need for expensive speed feedback components such as optical encoders. The rotor speed is equal to the difference between the electrical frequency and the slip frequency:
The electrical frequency is given by:
Back EMF, x Back EMF, y Flux, x Flux, y Magnitude of stator flux squared
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And the slip frequency is given by:
5. Bibliography and References
1. J. Hu, B. Wu, New Integration Algorithms for Estimating Motor Flux Over a Wide Speed Range, IEEE Power Electronics Specialist Conference, June 22-27, 1997, vol. 2, pp. 1075-1081 2. X. Xu, D.W. Novotny, Implementation of Direct Stator Flux Orientation Control on a Versatile DSP Based System, IEEE Transactions on Industrial Applications, JulyAugust 1991, Vol. 27, No. 4, pp. 694-700 3. Sensorless Control of AC Motor Drives, edited by K. Rajashekara, et al., 1996, IEEE Press, ISBN 0-7803-1046-2 4. G.F. Franklin, J.D. Powell, M. Workman, Digital Control rd of Dynamic Systems, 3 edition, 1997, Addison-Wesley, ISBN 0-201-82054-4 5. R. Valentine, Motor Control Electronics Handbook, 1998, McGraw-Hill, ISBN 0-07-066810-8 6. Chee-Mun Ong, Dynamic Simulation of Electric Machinery, 1997, Prentice-Hall, ISBN 0-13-723785-5
where:
ds iqs
4. Conclusion
This application note has described a sophisticated variable speed control technique for AC induction motors which can now be implemented on low cost DSPs such as the ADMC331 and ADMCF326 from Analog Devices. The DSP code to implement the algorithms discussed here is available in the form of a development kit to get users started quickly with the technology.
AMIRIX offers consulting and development services to get your application designed and to market quickly and cost effectively. For more information, contact us at: AMIRIX Systems Inc. 77 Chain Lake Drive Halifax, Nova Scotia Canada B3S 1E1 Tel: (902) 450-1700 Fax: (902) 450-1704 Email: motionpro@amirix.com Or visit us at: www.amirix.com / products / mopro.shtml
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