Embedded Systems September 2000 Vol13_10

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SPECTRA 8 torque, however. The only torque it does produce results from the motion of the flux to the next indexed step. The second current is 90 degrees out of phase with the first and is called the iq, or quadrature, current. This current produces a flux that either leads or trai ls the stator flux . If it u·ails the stator motion, the moto r is a gen- erato r. If it leads, we have torque, and thus, a motor. The amount of i1 cur- rent conu·ols the amount of torque we have. For more torque, you need more i,r For more rotor flux, you need more id. Knowing these two values, you can solve for the vector that represents the amount of torque in a motor. By feed- ing i, " iq, and your command values to your PID conu·oller, you can generate result values that may be used to cor- rect the motion of position, velocity, or torque in your device. But there's a catch ... Unfortunately, the motor is static; it's not in motion. The stator flux is con- stantly moving when the motor is in motion. In a three-phase motor these values are consta ntly cha ngin g. Even if the motor is simply movi ng in a sin- gle direction at a constant speed with no acceleration or decele ration, the currents in each winding are con- stantly changing according to the angular position of the rotor in each electrical revolutio n . This does not mean that the iq and id change. (You will see in the following mathematical expression that they will be constant.) It means that in order to keep the flux moving at a constant rate, the currents in each winding must vary continuo usly. At this poin t, let's go back and look those at three-phase currents. Remember, these transforms go both ways. We must use the forward trans- form to convert the curren ts and posi- tion for input to the PID conu·oller and as reverse transforms to convert them back to individual phase values for output to the amplifie r. The Clarke transform We have two sources of information about the motor that we can use in our PID conu·oller. One consists of the position of the rotor returned from the encoder or a similar device and the other is the current in the wind- in gs. Both are important. In order to produce values we can use to control or correct the motors operation, we need to know the curren t status. We need the curre nts and position. Because trying to control th e motor using the individual phase cur- re nts is a complicated affair, we use the Clarke transform to change tl1e refer- ence of the three-phase currents, ia(t), ib( t), and ic(t) to currents in the two- phase orthogonal stato• This conversion is illustrated in Figure l. Now, referring to the star-connected motor in Figure 2, we have: · axis: ia and ifJ . PCM·9550F Features B" x 5.75" - Intel low power Pentium"MMX'" processor - Supports Video-in and Wout (PCM-9550FM) - 8 digital inputs and 8 digttal outputs - Supports XGA & 36-btt LCD - 30 audio & 1 00 Mbps Ethernet - One PC/104+ & one mini PCI socket (Type Ill) AD\-\NTECH Embedded Computing ~.~v::~.~~~~~~~no~~x~i::;.~~~-7!79 1-800-866-6008 E-mail' EP(; www. a dva n tee h .com I e pc Visit us at Embedded Systems Conference 2000, Booth #5069 180 SEPTEMBER 2000 Embedded Systems Programming EBX Form Factor No Cooling Fan Digital I/O Long-term Supply which denote currents, voltages, and flux linkages. Please note that the final relationship maintains the balance of currents, voltages, or flux linkages as explained by Kirchoffs Law, tl1at is, their sum will be zero. Anytime the re is a current, voltage, or flux in one phase there must be corresponding currents, voltages o r fluxes in the other two to balance it. Both the fo r- ward and reverse Park and Clarke transforms may be applied to currents, voltages, or linkages in exactly the

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