`
`
`
`

`

`51DM f\N
`
`DC MOTORS
`
`SPEED CONTROLS
`
`SERVO SYSTEMS
`
`AN ENGINEERING HANDBOOK
`by
`" ,;) §<] g I ( g ~o~~c~~:~~~~~k~•:;n~~~~~:~~~-~:
`
`

`

`ELECTRO-CRAFT CORPORATION
`
`REGIONAL SALES OFFICES
`
`Corporate, Midwestern and Overseas Sales Office:
`
`Electro-Craft Corporation
`1600 Second Street South
`Hopkins, Minnesota 55343
`612/935-8226
`TWX: 910-576-3132
`
`Western Sales Office:
`
`Electro-Craft Corporation
`30961 West Agoura Rd., Suite 211
`Westlake Village (L.A.), Calif. 91361
`213/889-3631
`TWX: 910-494-4832
`
`Eastern Sales Office:
`
`Electro-Craft Corporation
`401 Old Colony Road
`Norton (Boston) , Mass. 02766
`617 /226-0206
`TWX: 710-391-6514
`
`© Electro-Craft Corporation
`First Edition October, 1972
`Second Edition October, 1973
`Third Edition, October, 1975
`All Rights Reserved
`
`. ii.
`
`FC
`
`Cf(cid:173)
`SY
`
`1.1
`
`1.2
`
`1.3
`
`CH
`
`AN -
`
`2.1 ,
`
`H1s·
`
`co~
`
`LA\tl
`IND
`
`MA(
`
`Mag
`
`Mag
`
`Magi
`
`Pern
`
`Magi
`
`WOR
`VOL.
`
`Volt
`
`

`

`curve (if acceleration rate is within the tor(cid:173)
`que capacity of the system), it may not
`follow the deceleration curve unless the
`load conditions and the dynamic braking
`capacity allow.
`If this is not the case, then
`a bidirectional system (servo system) must
`be used where continuous velocity tracking
`is necessary.
`
`Another circuit with linear features is shown
`in Fig. 3.3.13 . This is a ramp generator
`which produces linear, independently ad(cid:173)
`justable slopes.
`
`The circuits discussed above have been
`shown as manually operated devices.
`In
`many applications, they can be operated
`by various logic circuits, thereby taking
`their place
`in modern process controls.
`
`SWITCHING AMPLIFIERS
`
`While the linear amplifier discussed above
`performs excellently in high-performance
`speed controls, it has the problem of heat
`generation in the output stage, requiring
`forced-air cooling in amplifiers over 100 to
`200 W (depending on ambient temperature
`and heat sink design). The switching am(cid:173)
`plifiers overcome this problem by letting
`its output stage rapidly switch from a non(cid:173)
`conductive state to a fully conductive state,
`thereby minimizing operation of the output
`stage in the high dissipation region.
`
`Three basic methods are used to control
`power in switching amplifiers: pulse-width
`modulation (PWM), pulse-frequency modu(cid:173)
`lation (PFM), and silicon controlled rectifier
`
`O>----
`
`v--[
`'1
`
`a,
`
`b
`
`c
`
`Fig.
`tiers
`
`tern, it is clear that they are sensitive to
`variations in both load and friction torque.
`
`In cases where it is desirable to have the
`acceleration and/or deceleration under ve(cid:173)
`locity control, several methods can achieve
`the desired results.
`
`The simple RC circuit of Fig. 3.3.11 can be
`employed to control acceleration. First,
`assume that the switch is initially in the A
`position so that the command voltage V c
`is zero. The speed control is, therefore,
`holding the motor at rest. With the switch
`set in the B position, capacitor C is charged
`through voltage divider R1 , R2 . The volt(cid:173)
`age Vr will
`follow an exponential
`rise
`(Fig. 3.3.12) until the Zener voltage Vz
`is achieved, at which point the reference
`voltage Vr (as also the command voltage
`Ve) is stabilized.
`
`As the switch is returned to A, the voltage
`will decline in an inverse exponential fash (cid:173)
`ion.
`
`It should be noted that while the speed
`control system will follow the acceleration
`
`Yr.
`- - - -
`
`v,
`
`t
`
`/
`I
`I
`I
`I
`I
`
`/
`
`---
`
`-
`
`1
`
`0l
`
`-11 _J
`
`Fig. 3.3.12. Turn-on and turn-off characteristics
`of the RC circuit in Fig. 3.3.11.
`
`3-20
`
`

`

`+15V
`
`-15V
`
`l~ ~ ____.t
`
`Vo
`
`Amplitude
`adjust
`
`Fig. 3.3.13. Ramp generator with independently adjustable slopes.
`(SCR) controls. Their principal differences
`are shown in Fig. 3.3.14.
`
`_J[__
`
`Vin
`
`v- -
`
`The PWM system usually utilizes a DC sup(cid:173)
`ply, and the amplifier switches the supply
`voltage on and off at a fixed frequency and
`at a variable "firing angle" a (see Fig.
`3.3.14a) so that an adjustable average volt(cid:173)
`age across the load is established. The
`amount of power transferred to the load
`(motor) will depend on switching rate and
`In many of the PWM
`the load inductance.
`circuits, the pulse frequency is allowed to
`shift over a given range -
`in some cases for
`a good purpose.
`
`The PFM system has a fixed firing angle and
`a variable repetition rate (Fig. 3.3.14b),
`achieving essentially the same results as the
`PWM, but when used in motor control cir(cid:173)
`cuits, the widely variable pulse frequency
`required causes dissipation problems which
`makes the PWM more attractive.
`Inciden(cid:173)
`tally, a PWM circuit with a variable pulse
`rate is really a hybrid between the two.
`
`3-21
`
`'tJ -l~J--
`,_ -~----l----i-------
`OJ-L~ J" j-[~
`l-t,
`
`a, pulse-width modulated (PWM) system
`
`j,2~
`
`b, pulse-frequency modulated (PFM) system
`
`L ~~--t~} __ _
`
`c, SCR control system
`
`Fig. 3.3.14. Voltage waveforms in switching ampli(cid:173)
`fiers.
`
`

`

`The SCR circuit for DC control is usually
`used with a rectified AC supply voltage,
`although a rectification circuit can be placed
`before or after the control section of the
`amplifier. Fig. 3.3.14c shows a full-wave
`rectified supply voltage of a fixed frequency.
`The firing angle can be varied to cover a
`portion from 0 to 180 Oel of a half-wave.
`The average output voltage is not propor(cid:173)
`tional to the firing angle, and this part
`requires special attention in the control
`design.
`
`In the following discussion only PWM and
`SCR circuits will be covered, since the pure
`PFM is not particularly suited to motor con(cid:173)
`trol applications.
`
`PULSE-WIDTH MODULATED
`AMPLIFIERS
`As already mentioned, the PWM amplifier
`generally is powered by a DC supply.
`It
`
`can be designed using either transistors or
`SCR's as switches.
`Actually, the SCR
`amplifier is a PWM in spirit; but the func(cid:173)
`tional differences, the output voltage fre(cid:173)
`quency and wave shapes are different
`enough to warrant a separate discussion.
`
`Then what about SCR's powering a PWM?
`Since PWM's are based on a continuously
`available DC power source, and since SC R's
`cannot "turn off" current conduction by
`themselves as transistors can, they must be
`provided with a separate "turn-off" circuit.
`The problem associated with such circuitry
`has limited the use of SCR's in PWM sys(cid:173)
`tems to high current, low switching rate
`applications, such as lift truck and vehicle
`traction controls. Due to the unique nature
`
`Command
`v€
`
`DC to pulse
`width converter
`
`f1Jl
`
`Feedback
`compensation
`
`-~Load
`'C_j_)
`
`M --
`
`-
`
`Fig. 3.3.15. Elementary block diagram of a PWM speed control system.
`
`3-22
`
`

`

`of these controls, they are not discussed
`here.
`
`VP
`
`Voltage
`
`Today,
`PWM
`transistor-operated
`then,
`switching amplifiers are used in most high(cid:173)
`performance, high power speed control sys(cid:173)
`tems and servo sytems.
`
`A typical block diagram of a PWM speed
`is shown in Fig. 3.3.15.
`control system
`
`The pulse repetition rate is usually above
`1 kHz (often about 10 kHz), and this fre(cid:173)
`quency is mainly dictated by the required
`system response bandwidth, motor induc(cid:173)
`tance and motor high frequency loss charac(cid:173)
`teristics. At times audio noise emissions
`through wiring, heat sinks and motor frame
`components can be loud enough to be
`disturbing, and in such applications one can
`raise the pulse frequency to a point where
`the noise is not audible.
`
`In examining voltage and current character(cid:173)
`istics of a PWM system, we can first look at
`the ideal motor and its behavior in a PWM
`system. This motor equivalent circuit is
`shown in Fig. 3.3.16.
`~TIJUl
`
`"Free wheeling"
`diode
`
`'.{"
`
`1 av
`
`Current
`
`Fig. 3.3.17. Current and voltage relationship in a
`PWM control system.
`
`The waveform of the motor current during
`the switching mode is dependent not only
`on the switching rate, but on the motor
`speed n, the total inductance L, motor
`resistance R and the current level in the
`last cycle. Fig. 3.3.17 shows a steady-state
`relationship of current and voltage.
`
`Since the supply voltage is being switched
`on and off at a high frequency, we should
`evaluate the power losses in the motor. The
`power losses in such a system may be due
`to a host of factors, depending on the de(cid:173)
`sign of the motor: eddy current losses,
`hysteresis
`losses, armature commutation
`losses, viscous friction losses and armature
`resistance losses. But considering modern
`permanent magnet servomotors with small
`electrical time constants and minimal high
`frequency losses, a first approximation to
`evaluate motor power losses due to the
`armature resistance can be expressed by:
`
`PL = Rl~MS
`
`(3.3.9)
`
`-=-
`Fig. 3.3.16. Equivalent circuit of a DC motor in a
`PWM control system.
`
`In order to relate RMS current to average
`current in such cases, an expression relating
`
`3-23
`
`

`

`the two has been established, called the
`form factor (k):
`
`I RMS
`k =--
`-
`1av
`
`(3.3.10)
`
`The average motor current will determine
`the motor torque produced:
`
`(3.3.11)
`
`Substituting (3.3.10) into (3.3.9), the motor
`losses under PWM conditions are:
`
`(3.3.12)
`
`and we see that the armature losses depend
`on average current, form factor, and arma(cid:173)
`ture resistance. Another way of looking at
`the sources of the losses is to substitute
`(3.3.11) into (3.3.12). Then
`
`(3.3.13)
`
`Here it is clear that losses are due to severa l
`factors; the motor constants R and KT
`inherent in a given design, the form factor,
`and the output torque of the motor. Thus,
`the form factor has a strong influence on
`motor heating.
`In the case of a k = 1, the
`heating effect of a linear amplifier from
`the previous section is :
`
`P = Rt 2
`L
`av
`
`(3.3.14)
`
`But for a form factor k = 2, we have an
`armature power
`loss of four times the
`
`3-24
`
`I
`
`~ ---
`
`I_.......... v--
`
`_,/
`
`/
`
`/
`
`.. .. .. 2 20
`I/
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`" c
`5 I
`.,, .,,
`
`500
`
`200
`
`100
`
`£: 50
`I
`
`cf
`
`2
`
`I
`
`1.2
`
`1.4
`Form fac t or
`
`1.6
`
`1.8
`
`Fig. 3.3.18. Relationship of additional armature
`losses in a servomotor with form factor.
`
`amount shown above. Thus, we can con(cid:173)
`struct a graphical solution of the increase
`in armature loss due to form factor. This is
`shown in Fig. 3.3. 18.
`
`The form factor greatly influences armature
`losses, as for example a k = 1.2 will increase
`losses by 44%.
`
`in speed
`Since servomotor performance
`control systems is often limited mainly by
`power dissipation, it is important to in(cid:173)
`vestigate the form factor of a given ampl i(cid:173)
`fier source.
`In the case of a PWM amplifier
`the form factor will depend on the pulse
`frequency, on the electrical t ime constant
`of the motor and on any associated series
`inductances.
`
`The net result of using a PWM circuit is
`usually that the power dissipation in the
`amplifier is vastly decreased, and the tota l
`
`

`

`-
`
`system dissipation is improved; but in some
`cases the motor power dissipation may be
`higher than if a linear (class A) amplifier
`is used. One should also check the applica(cid:173)
`tion to see if the audio noise (if any) will
`be of consequence. This may be particular-
`ly irritating if the pulse frequency is sh ifting
`greatly with load variations. Another factor
`to consider in using a PWM system is the
`electrical noise generation, which can be
`transmitted into low level circuitry if care
`is not taken to properly shield and ground
`the high current portion of the system.
`
`SCR CONTROLS
`
`SCR speed control systems are nearly al(cid:173)
`ways based on power line frequency (50-60
`Hz). This limits the control bandwidth of
`the system from 2-3 Hz for a half-wave,
`single- phase system to about 25-30 Hz for
`a three-phase, full-wave system . This trans(cid:173)
`lates into a speed control range of 5: 1 for a
`half-wave control to 20: 1 for a full -wave
`control with tachometer feedback.
`
`WhiletheSCR control system is not capable
`of controlling as wide a speed range as is
`the linear transistor amplifier, it has a high
`power conversion efficiency due to its
`switching mode and the low forward con(cid:173)
`duction voltage drop . The relative simplic(cid:173)
`ity of its circuitry further adds to the
`positive features of the SCR control. The
`popularity of the SCR control for limited
`speed range DC motor control in the frac(cid:173)
`integral horsepower sizes has
`tional and
`been largely due to these features, and to
`the fact that SCR's can operate directly
`
`the power line without AC-to-DC
`from
`power conversion.
`
`One serious problem of operating motors
`from SCR controls is the high form factor,
`which may cause serious derating of the
`motor. The form factor depends on the
`type of control used (half-wave, full-wave,
`three-phase), on the conduction angle and
`on motor inductance; therefore, it is diffi(cid:173)
`cult to obtain form factor values without a
`detailed knowledge of the applicat ion.
`
`In the case of high-performance servomotors
`with low inductance, an appropriate deter(cid:173)
`mination of the form factor can be made
`on the assumption that the load is resistive.
`The graph in Fig. 3.3.19 shows the fo rm
`factor versus conduction angle for resist ive
`loads. The power dissipation in a motor is
`
`Half wave
`
`/
`
`r -Full wave
`
`ii ti
`.....
`
`~ 4
`~ g
`'; 3
`~
`
`2
`
`1..!-~-.-~-.-~~~---.-====;::::==;_._~
`0
`[0eij
`30
`90
`60
`150
`120
`180
`
`Conduction 01'19le
`
`Fig. 3.3.19. Form factor vs. conduction angle for
`resistive loads in SCR control circu its.
`
`3-25
`
`