Design Notes on Precision Phase Locked Speed …

1 U-113 APPLICATION NOTEDESIGN Notes ON Precision Phase Locked SPEEDCONTROL FOR DC MOTORSABSTRACTT here are a number of high volume applications for DCmotors that require Precision control of the motor s Locked loop techniques are well suited to providethis control by Phase locking the motor to a stable andaccurate reference frequency. In this paper, the small sig-nal characteristics, and several large signal effects, ofthese loops are considered. Models are given for the loopwith Design equations for determining loop bandwidth andstability.

2 Both voltage and current motor drive schemesare addressed. The Design of a loop for a three phasebrushless motor is LOCKING GIVES Precision SPEEDCONTROLThe precise control of motor Speed is a critical function intoday s disc drives. Other data storage equipment, includ-ing 9 track tape drives, Precision recording equipment,and optical disc systems also require motor Speed the storage density requirements increase for thesemedia, so does the Precision required in controlling thespeed of the media past the read/write mechanism.

3 Oneof the best methods for achieving Speed control of a mo-tor is to employ a Phase Locked a Phase Locked loop, a motor s Speed is controlledby forcing it to track a reference frequency. The referenceinput to the Phase Locked loop can be derived from a pre-cision crystal controlled source, or any frequency sourcewith the required stability and accuracy. A block diagramof the Phase Locked loop is shown in Figure Figure 1, a Precision crystal oscillator s frequency isdigitally divided down to provide a fixed reference frequen-cy.

4 Alternatively, the motor could be forced to track a vari-able frequency source with zero frequency error. The mo-tor Speed is sensed by either a separate Speed windingor, particularly in the case of the DC brushless motor, aHall effect device. The two signals, motor Speed and ref-erence frequency, are inputs to a Phase detector. The de-tector output is a voltage signal that is a function of thephase error between the two inputs. The transfer functionof the Phase detector, K+, is expressed in volts/radian.

5 A1/s multiplier accounts for the conversion of frequency tophase, since Phase is the time integral of the Phase detector is the loop filter. This blockcontains the required gain and filtering to set the loop soverall bandwidth and meet the necessary stability output of the loop filter is the control input to the mo-tor drive. Depending on the type of drive used, voltage orcurrent, the driver will have respectively, a VOUT/VINtransfer characteristic, or an louT/Vr~ first glance, it seems that the motor has simply re-placed the VCO (voltage controlled oscillator), in the clas-sic Phase Locked loop.

6 In fact, it is a little more complicat-ed. The mechanical and electrical time constants of themotor come into play, making the transfer function of themotor more than just a voltage-in, frequency-out block. Inorder to analyze the loop s small and large signal behav-ior it is essential to have an equivalent electrical model forthe SIMPLE ELECTRICAL MODEL FOR A DCMOTORF igure 2 is an electrical representation of a DC motor. Theterms used are defined here:LM Motor winding inductance in henrysHM Motor winding resistance in asJTotal moment of inertia of the motor in Nm-set?

7 (Note: 1 Nm = oz-in)KT Motor torque constant in Nm/AmpKv Voltage constant (back EMF) of motor in voltage-sec/radFigure 1. Precise motor Speed control is obtained by Phase lockingthe motor to a Precision reference frequency.(Note: Kv = KT in SI units)3-132 APPLICATION NOTEU-113 NODE VOLTAGEEQUATES TOMOTOR BACK EMF*N = Number of Speed sensecycles per motor revolutionFigure 2. This simple electrical model is useful for determining thesmall and large signal characteristics of the motor.

8 Capacitor, CM is used to model the mechanical energystorage of the this model the winding inductance and resistance ele-ments correlate directly with the corresponding physicalparameters of the motor, with values taken directly off themanufacturer s data sheet. The capacitor, CM, models themechanical energy storage of the motor. Current into thecapacitor equates, via motor constant KT, to motor torque,and the voltage across the capacitor is equal to the motorback EMF. The back EMF voltage equates to motor ve-locity through the inverse of Kv.

9 In the model, the term Nis simply a multiplier equal to the number of feedback cy-cles obtained per revolution of the motor. For example, ina 4 pole brushless DC motor the commutation Hall effectdevice outputs will be at twice the rotational frequency ofthe motor, making N equal to equation for the capacitor, given in Figure 2, has theunits of Farads if J and KT are expressed in SI units. Inmodeling the overall transfer characteristic, it is importantthat the moment of inertia of the load on the motor beadded to the moment of inertia of the motor is worthwhile to note that the current into the motor, mi-nus idling current, is proportional to acceleration of themotor.

10 This is easily seen from the model by realizing thatthe time derivative of the capacitor voltage relates directlyto acceleration. The effects of loads on the motor can bemodeled by including a current source across the capaci-tor for constant torque loads, or a resistor for loads thatare linearly proportional to motor FUNCTIONS FOR VOLTAGE ANDCURRENT DRIVEN MOTORSU sing the electrical model, the small signal transfer func-tion of the motor is easily derived. Equations 1a and 1bgive the small signal frequency response for both the cur-rent and voltage driven cases transfer function given in equation (1a) describes thesmall signal response of motor Speed , OM(s), to changesin the drive current.