Servo Plant Compensation Techniques potx

There area number of control techniques that can be applied to compensate formachine structural resonances that are both low in frequency and inside theposition servo loop.. This simple

11.1 DEAD-ZONE NONLINEARITY

Stiction, sometimes referred to as stick-slip, occurring inside a positioningservo, can result in a servo drive that will null hunt The definition of a nullhunt is an unstable position loop that has a very low periodic frequency such

as 1 Hz or less with a small (a few thousandths) peak-to-peak amplitude(limit cycle) The most successful way to avoid stiction problems is to useantifriction machine way (rollers or hydrostatics) or use a way linearmaterial that has minimal stiction properties If stiction-free machine slideways cannot be provided, the use of a small dead-zone nonlinearity placedinside the position loop, preferably at the input to the velocity servo, has

had some success in overcoming a null hunt problem However the deadzone must be very small (e.g., 0.001 in.); otherwise, the servo drive will have

an instability from too much lost motion A simple analog dead-zonenonlinear circuit is shown inFigure 2.The same function can be providedwith a digital algorithm in computer control of machines

in a turning machine application At feed rates below 0.01 ipm, therequirement for a smooth surface may not be easily attainable because theservo drive may have a cogging problem at these low federates Increasingthe forward loop gain to the velocity drive can overcome the lowfeedcogging problem but will result in an unstable servo drive As a compromise,

a change in gain nonlinear circuit can be used to improve the low-feed-ratesmoothness and still have a stable servo drive The object is to have a highforward-loop gain in the velocity servo (which is inside a position loop) Fornormal operation, the high servo loop gain is reduced by the change-in-gaincircuit at a low velocity to its normal gain, thus maintaining a stable servodrive This type of nonlinear circuit has been used successfully for smooth

Fig 2 Dead-zone nonlinearity

feed rates down to 0.001 ipm The analog version of a change-in-gainnonlinearity is shown in Figure 3 With digital controls a digital algorithmcan be used.

11.3 STRUCTURAL RESONANCES

Structural resonances or machine dynamics, as it often referred to, iscertainly not a new subject However, on the morning of November 7, 1940,the nation awoke to the destruction of the Tacoma Narrows Bridge A

42 mile-per-hour gale caused the bridge to oscillate thus exciting thestructural resonances of the bridge to a final destruction frequency of about

14 Hz and a peak-to-peak amplitude of 28 ft The destruction of the bridgewas a wake-up call to the importance of dynamic analysis in structural

Fig 3 Change-in-gain nonlinearity

design in addition to static analysis and design Some sixty years later thetechnology of dynamic analysis is now well known.

To further investigate machine resonances, a typical linear industrialservo drive can be represented as in Figure 4 The mechanical components

of this servo drive are referred to as the servo system plant The servo plantmay have a multiplicity of resonant frequencies resulting from a number ofdegrees of freedom In actual practice there will be some resonantfrequencies that are high in frequency and far enough above the servodrive bandwidth so that they can be ignored In general there will be apredominant low resonant frequency that could possibly be close enough tothe servo drive bandwidth to cause a stability problem Therefore a singledegree of freedom model as shown in Figure 5 can represent thepredominant low-resonant frequency, where:

BL¼ viscous friction coefficient (lb-in.-min/rad)

T¼ driving torque, developed by the servo motor (lb-in.)

K¼ mechanical stiffness of the spring mass model (lb-in./rad)

JM¼ inertia of the motor (lb-in.-sec2

)

JL¼ inertia of the load (lb-in.-sec2

)

S¼ laplace operatorFrom Newton’s second law of motion, the classical equations for this servoplant (industrial machine system) can be written In most industrialmachines it can be assumed that the damping BL is zero Therefore the

Fig 4 Block diagram of a machine feed drive

motor equation is:

Further solving for yM and yL by combining Eq (11.3-4) and (11.3-6):

s

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiKðJMþ JLÞ

of hydraulic fluid resonance, which can be a limiting factor of stability Thehydraulic resonance or can be observed as a typical second order response

in the Bode frequency response ofFigure 6.For hydraulic drives having alow damping factor dh, the resonant peak may be higher than 0 dB gain,which will result in a resonant oscillation There are a number of methods tocompensate for this resonant oscillation First, a small cross-port dampinghole of about 0.002 in can be used across the motor ports Secondly, thevelocity loop differential compensation can be varied, which quite ofteneliminates the oscillation Lastly, the velocity loop gain could be lowered,which can also lower the velocity servo bandwidth As an index ofperformance (I.P.) the hydraulic resonance should by proper sizing be above

200 Hz, and the separation between the velocity servo loop bandwidth oc

and the hydraulic resonance oh should be three to one or greater Brushless

DC electric drives do not usually have velocity loop resonance problemsunless a more compliant coupling is used internally in the motor to couple aposition transducer to the motor shaft

Both hydraulic and brushless DC electric drives can have resonance(stability) problems if the machine is included in the position servo loop.This is an ongoing problem with industrial machines, in spite of all theavailable technology to minimize stability problems A typical positionservo Bode frequency response is shown inFigure 7.As a figure of merit theseparation between the velocity loop bandwidth oc and the position-loopvelocity constant Kv (gain) should be two to one or greater The machine

resonance or should be at least three times greater than the velocity servobandwidth oc However in actual practice the machine resonance inside theposition loop is often quite low (such as 15 Hz) The resonant peak in thiscase should be above 0 dB gain, resulting in a resonant oscillation There are

a number of control techniques that can be applied to compensate formachine structural resonances that are both low in frequency and inside theposition servo loop The first control technique is to lower the position-loopgain Kv(velocity constant) Depending on how low the machine resonance

is, the position-loop gain may have to be lowered to about 0.5 ipm/mil (8.33/sec) This solution has been used in numerous industrial positioning servodrives However, such a solution degrades servo performance For verylarge machines this may not be acceptable The I.P that the servo loop gain(velocity constant) should be lower than the velocity servo bandwidth by afactor of two, will be compromised in these circumstances

A very useful control technique to compensate for a machineresonance is the use of notch filters These notch filters are most effective

Fig 6 Hydraulic velocity servo

when placed in cascade with the input to the velocity servo drive Thesenotch filters should have a tunable range from approximately 5 Hz to acouple of decades higher in frequency The notch filters are effective tocompensate for fixed structural resonances If the resonance varies due tosuch things as load changes, the notch filter will not be effective Since most

of these unwanted resonant frequencies are analog sinusoidal voltages, anotch filter can effectively remove these frequencies

In digital control the algorithm for the notch filter can be used Asimple analog notch filter is shown inFigure 8as it appeared in ElectronicsMagazine, December 7, 1978 This filter is equivalent to a twin T-notch filterbut it is an active filter versus passive networks, so there are no signal losses.The frequency of the notch is set by the selection of resistor R For a1-microfarad (mF) capacitor (C), the values for R versus the notch frequencyare shown in Figure 9

The depth of the notch is adjusted by varying the potentiometer P1.Frequency responses of the notch filter for values of R ranging from 40 Kohms to 200 ohms are shown inFigure 10 A 40-Hz notch filter frequencyresponse is shown inFigure 11with a number of potentiometer settings to

Fig 7 Position loop frequency response

show the change in the depth of the notch filter as the potentiometer isvaried.

A few case histories are of interest In a hydraulic servo valve feeddrive, pump pulsations of 500 Hz traveled through the machine piping to theservo valve, the hydraulic motor, and finally the feedback tachometer of thevelocity loop The high sensitivity of the tachometer (100 V/1000 rpm)sensed the 500-Hz vibration and generated this voltage into the servo driveelectronics, where it was amplified through the entire drive, causing anundesirable vibration A 500-Hz notch filter at the tachometer output feed

to the servo amplifier eliminated the vibration problem

In another case, the switching frequency of a numerical control(125 Hz) beat with the single-phase, full-wave DC SCR drive frequency(120 Hz) producing a 5-Hz signal that appeared in the machine servo drive,causing what appeared to be a 5-Hz instability Using a notch filterfrequency of the control switching frequency, the 5-Hz beat frequency signalwas eliminated

In another case history a 45-Hz resonance existed in an air bearing of arotary position feedback transducer Once this resonance was excited it wasamplified through the electronics drive and the machine slide vibrated at

Fig 9 Notch filter resistance nomogram.

Fig 10 Notch filter characteristics.

Fig 11 Depth of notch filter characteristics

signal frequencies appear in industrial servo drives This simple notch filtercan readily be used to eliminate all kinds of undesirable signals.

11.4 FREQUENCY SELECTIVE FEEDBACK

Another technique that has been very successful with industrial machineshaving low-frequency machine resonances, is known as ‘‘frequency selectivefeedback’’ In abbreviated form it requires that the position feedback belocated at the servo motor eliminating the mechanical resonance from theposition servo loop, resulting in a stable servo drive but with significantposition errors These position errors are compensated for by measuring theslide position through a low-pass filter; taking the position differencebetween the servo motor position and the machine slide position; andmaking a correction to the position loop, which is primarily closed at theservo motor

Compensator Operation

The complete control circuit has more complexity than comparing twoposition transducer outputs Figure 12 can be used to discuss the actualoperation of the compensating system This particular compensating schemeused an instrument servo to perform the compensating function A softwarebased frequency selective feedback system will also be discussed For thiscompensating system, the machine-feed servo drive uses a positionmeasuring feedback resolver (1) connected electrically in series with acorrection resolver (5) Any correction required during positioning isintroduced into the numerical control feedback circuit with the correctionresolver (5)

The compensator circuit includes the positioning servo-motor positionmeasuring resolver called a compensator feedback resolver (2), a machineslide linear position measuring transducer (3), and an instrument typecorrection servo drive The difference between the feed servo-drive motorposition and the machine slide position is measured with the compensatorfeedback resolver (2) and the linear resolver (3) However, an additionalcorrection resolver (4) is included in the circuit Therefore, the instrumentcorrection servo error is a function of three resolver positions This is shown

in the block diagram ofFigure 13.The resolver positions are shown as angle

y The total correction error is shown as a function of the three resolverpositions

Fig 13 Simplified block diagram for frequency selective feedback.Fig 12 Analog block diagram for frequency selected feedback.

As a position error is developed between the feed servo-drive motorposition ym and machine slide position ys, an error is developed at theinstrument servo drive(Figure 13).The error is also a function of yc.

ye¼ ym
yc
ys¼ ðym
ysÞ
yc (11.4-2)

It is significant to note that the bandwidth of the instrument correctionservo must be a low frequency such as 1.5 Hz This is required to eliminatethe machine structural dynamics from the machine slide feedback position

ðysÞ and is the key to the frequency selective feedback control function

A correction yc is developed at the output of the instrument servodrive, which is a function of:

The correction ycis added to the main-feed servo drive by means of resolver(5) The correction yccauses the feed servo drive to move by the amount ofthe correction Therefore both ym(at the motor) and ys(at the machine slide)move by the amount of the correction yc The correction can be shownmathematically to be approximately a function ofðym
ysÞ as follows:Since: yc¼ Gl½ðym
ysÞ
yc from Eq: (11.4-3)

From another point of view the instrument servo-drive error must bereduced to zero after the correction is made From Eq (11.4-2) the error is:

Assuming the initial condition at the start of the correction is such that the

machine slide position ys is short of the correct position (assume 10 in.) by0.01 in and that the location of ym and ys are as follows:

ym¼ a related distance of 10 in

ys¼ a related distance of 9:99 in:

After correction the related positions will be—

ym¼ a related distance of 10:01 in:

ys¼ a related distance of 10 in:

The relation between ymand ysis the same but the machine position yshasmoved to the correct position

Fig 14 Correction diagram for frequency selective feedback

Meanwhile the correction yc(which was equivalent to 0.01 in.) had to

be included in the error of the instrument servo Since the relation ofðym

ysÞ remains constant, a correction must be made in the instrument servoloop to reduce the error to zero:

Software version of frequency selective feedback

The software version for the correction is shown in Figure 15 This versioncan be added to a machine axis that exhibits a structural resonance problem.The drive is assumed to be a typical commercial electric servo drive with acurrent loop and a velocity loop inside a position servo loop

The difference between the motor position and the machine slideposition is used as an input to a low-pass digital filter This filter has a verylow bandwidth of about 1.5 Hz The reason for this is to remove structuraldynamic frequencies from the correction process

Fig 15 Software version of frequency selective feedback

The machine axis prior to adding frequency selective feedback, isassumed to have a position transducer on the machine slide To addfrequency selective feedback, an instrument gearbox must be added to therear of the servo motor A position transducer such as a resolver will begeared to the motor shaft with a ratio determined by the resolution of themachine slide feedback transducer.

11.5 FEEDFORWARD CONTROL

The problem of developing an industrial servo drive with high-performancecapabilities for accurate positioning is a subject of much importance Onmultiaxis industrial machine servos using classical type 1 servo control, it is

a requirement that each machine axis have matched position-loop gains tomaintain accuracy in positioning Quite often this means that all machineaxis servo drives must have their position-loop gains Kv adjusted to thepoorest performing axis Consider the basic approach to the design of apoisoning servo drive illustrated in Figure 16

This is the classical type 1 servo, which exhibits characteristic errors e

in position that are well known for various inputs yi.Consider a simplified block diagram of the system where GðsÞ is theservo drive and inner-loop transfer function typically of the following form: