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yMotion Control Basics

Itodctio Pag 4

Comparison of approaches; the role of speed, torque, inertia, and accuracy

Stp moto tcology Pag 4

Open-loop control; what makes a step motor a step motor; distinguishing

qualities of different types of step motors; understanding step motor makeup

Fdback cotol ad cotol toy Pag 6

The functions and limitations of a closed-loop servosystem; feedback and

control loops; types of linear systems; stability of linear systems; Nyquist

and Routh

Stp spos Pag 10

The ve basic parameters: delay, rise time, time to peak, overshoot, and

settling time; what step response says about a systems dynamics

y Sample Questions

Level One Page 12

Level Two Page 12

Level Three Page 12

Level Four Page 13

Level Five Page 13

tableof ContentS

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Stepmotortechnology open-loopcontrol

All motion controls aim to maneuver loads

down paths with a regulated motion. Open-

loop designs rely on their predened setup(and not feedback) to output target motion

tasks. In contrast, if movements are achieved

by comparing actual load motion to target mo-

tion and then making corrections, the system

is closed loop.

No matter what control type is used, it

must account for four design parameters:

Speed. How fast does the controlled de-

vice have to move? This parameter is typicallyspecied in rpm, inches per minute, or the

time it takes to get from A to B.

Torque. How hard does the motion

control device have to work to move the load?

This is expressed in rotational units as a

force through a lever arm, lb-ft, or lb-force for

linear systems.

Inertia. How much torque is required

to change the speed of the moving parts?

Inertia denes the resistance of all physical

parts to changes in speed or direction. The

smaller and lighter the parts, the easier it is

to change the speed.

Accuracy. How close to the ideal motion

path must the motion control come when mov-

ing or coming to rest? This is often expressed

as an error in degrees or inches betweenactual and target position.

Stp moto tcology

Step motors serve as a way to position a

load without using position-feedback devices

and their associated circuitry. Motor position

is controlled through adjusting the electrical

current running through the phase windings.

Thus step motors typically run open-loop;there are no sensors for position, velocity or

acceleration. Nor is there a feedback loop to

correct for errors between the commanded

load position and its actual position.

The variable reluctance (VR) step mo-

tor is one of the oldest types. It contains no

permanent magnets and consequently can be

designed to operate over a rather large tem-

perature range. More recently, the variable-reluctance design began serving as the basis

for switched reluctance-type motors.

Energization of coils wound on the sta-

tor teeth of the motor causes magnetic ux

that crosses an air gap between the rotor and

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stator. The teeth on the rotor are oriented

so that at any given time, some of the teeth

dont line up exactly with stator teeth. Whenthe teeth dont line up, some of the ux cross-

ing the air gap is at an angle that is not per-

pendicular with the tooth surfaces. Torque

then results until the rotor rotates to a stable

equilibrium position. All in all, the torque vs.

position relationship of the rotor is a function

of the phase winding current. A rising cur-

rent in the stator winding has no effect when

the stator and rotor teeth are aligned. (It

does, however, result in more motor stiffness.)

Thus the step motor rotor rotates by selec-

tively energizing stator teeth. The step mo-

tors step angle is the difference between the

spacing of the stator teeth and rotor teeth. For

example, if stator teeth are spaced every 40

and the rotor teeth are every 65, the motor

step angle is 25.

The positional resolution of a step motor

is proportional to the number of rotor teeth,

or the polecount of the motor. Motors with

high polecounts also tend to produce torque

vs. position qualities that are more sinusoi-

dal than those having few teeth. Step motors

also exhibit a cyclic torque happening at the

same per-revolution rate as the polecount.

Each torque cycle also contains a positive and

negative maximum holding torque and two

zero-torque points.

Further, the holding torque of the motor

rises in proportion to the square of the cur-

rent amplitude when winding currents are

relatively low. At higher currents the teeth

go into saturation and torque rises progres-

sively less steeply as current rises.

The equivalent circuit of a motor phase

winding is the series connection of a wind-

ing resistance and a position-dependent

inductance driven from a voltage. The voltageacross the phase winding is thus equal to the

IR drop through the winding, plus the induc-

tive voltage, plus the electromotive force of the

motor.

A type of step motor called a hybrid step

motor has a construction that resembles a

high-resolution variable-reluctance motor.

The main differences are in how the rotor is

constructed and the winding interconnections.

A VR step motor has rotor teeth running

straight along the length of the rotor lamina-

tion stack. In contrast, hybrid step motors

have rotors that contain both magnets and

some teeth that on some segments of the rotor

are offset by a half-tooth pitch from those on

the other segments. The magnets separate ro-

tor sections and are magnetized axially. The


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overall torque produced by one phase in the

hybrid step motor tends to be proportional to

the product of winding current and magnet

strength.

Another kind of commonly used step motor

is called the canstack motor. Sometimes, it

is called a tin can motor or claw-type perma-

nent-magnet step motor. Each phase winding

consists of a bobbin-

wound coil and the stator

is typically stamped.The rotor is typically

a cylindrical ferrite or

rare-earth molded mag-

net bonded to the shaft.

Rotor bearings are often

sintered bronze sleeve

bearings.

Torque in a canstack

step motor arises when

the eld generated by

winding currents deects

the magnetic eld produced by the magnet.

Its basic torque and electrical equations are

the same as those for a hybrid step motor. The

main difference in operation is that there are

higher eddy current losses because of the how

the stator is constructed.

Most canstack motors have nominal step

angles of 15 and 7.5. The result-

ing stiffness is appreciably less

than that of hybrid step motors

having 50 poles.

Fdback cotol

A feedback control system

takes the difference between a

reference input and some aspect

of the system being controlledto generate an error signal. The

controller uses the error signal

to generate an output used to

drive the system toward the de-

sired state. In the case of motion

controllers, the reference input is

usually either a commanded po-

sition or a commanded velocity.

The term servomotor implies that a motor will be used in a con-

trol system with eedback in a closed-loop system. The basic

principles o servomotors are similar to other ac and dc motors,

but: Rotor size and weight are reduced to minimize inertia. Heat

buildup within the motor is also minimized with ns and high-

temperature materials. All servomotors accommodate feedback

devices (such as encoders and resolvers) that are typically mount-

ed inside the motor housing.

Closed loop and the definition of servomotor

A scale can provide

feedback.

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cloSed-loopandfeedbackcontrol

The feedback is usually the position or the ve-

locity of the load, respectively. The controller

uses the difference between the sensed state

of the load and the commanded state to deter-

mine how much signal to send to the actuator

in order to reduce the error toward zero.

The process just described is that of a ser-

vomechanism. Another type of feedback con-

trol system is called a regulator. Regulators

primarily maintain the controlled variable

or system output almost exactly equal to a

desired value despite any disturbances. Also,

a regulator usually contains no integrating

elements in its feedback loop.

All control systems that manage physical

parameters are nonlinear but if the time-

varying parameters are slow and the non-lin-

earities are small, designers typically analyze

such systems using linear xed-parameter

analysis.

The most important property of a lin-

ear system is that superposition will apply.

Thus in linear systems the shape of the time

response is the same regardless of how big or

small the size of the input or initial condition.

Linear systems can also be described by lin-

ear constant coefcient differential equations.

Control systems are nonlinear when

control elements exhibit properties such as

saturation, limiting, backlash, or hysteresis.

Superposition does not hold in such cases.

The response of the system will depend on the

size of the input and on the initial conditions.

It is typically difcult to solve such systems

with nonlinear differential equations, so the

typical practice is to use numerical or graphi-

cal methods.

Linear control systems are often cat-

egorized by the nature of their steady state

performance. Type-0 systems are typically re-

ferred to as regulator systems. The zero refers

to the value of the exponent of the Laplace S

parameter in the denominator of the transfer

function. Type-1 systems are typically ser-

vocontrol systems. For reference inputs that

change with time at a constant rate, a con-

stant error is necessary to produce a steady

state rate of the controlled variable. Type-1

systems are also referred to as zero-displace-

ment-error systems. In type-2 systems, a

constant acceleration of the controlled vari-

Servocontrol ast acts

Most closed-loop systems are servosystems, making

corrections on the fy. The word servo (an abbreviation o

servomechanism) is dened as an automatic device for

controlling large amounts of power by means of very small

power, and automatically correcting mechanism performance.

Electric, hydraulic, pneumatic, and even pure mechanical

servosystems exist. Most common are electric varieties: Theseconsist of servomotor, comparator, amplier, feedback device,

and trajectory or command generator.

The comparator (via a eedback device) monitors motor shat

position and compares this against what the motor should be

doing as dened by the system command signal. The output

rom the comparator is the dierence between the two and is

called position error.

If there is error, the amplier or drive converts the low-level

comparator error-signal output into high-current signals which are then applied to the motor windings to cause rotation

in the direction that will minimize position error.

The command generator provides the target or command

position signal that tells the motion control system how to move

the servomotor and load.

Single-axis servo motion controls combine these parts;

sophisticated controllers provide these servo capabilities plus

PLC logic and more.


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able demands a constant error under steady

state conditions. These systems maintain

a constant value of the controlled variablespeed with no actuating error. Consequently

they are sometimes called zero-velocity-error

systems.

A linear control system is unstable when

it has an unbounded response to any bounded

signal. In a Laplace analysis, the stability ofthe system depends on the location of poles or

zeros in the complex S plane plot of the con-

trolled variable divided by the reference input,

written with Laplace operators. Poles are

dened by S=0 in denominator, zeros by S=0

in the numerator.

There are several ways of determining

stability. Among the most widely used are

the Routh-Hurwitz Criterion, Nyquist Sta-bility Criterion, and Root-locus methods.

The Nyquist criterion considers a system

for which the open loop transfer function

is given by G(s). Adding feedback H(s) al-

lows construction of a closed loop with the

transfer function given by G/(1 + GH). Most

stability investigations start with the case

where H=1. Then the characteristic equa-

tion, used to predict stability, becomes G + 1

= 0. Stability can be determined by examin-

Bode plots represent system transer unctions.

Today, software and dynamic signal analyzers

automate their use or comparison o input-output

signals. Multiplying input by a systems Bode plot

predicts output. Conversely, by working backward

from plots generated experimentally, one can

determine a Bode plot and reveal load eects,

machine resonances, and suitable electrical

compensation techniques.

Bodes notation leverages the fact that, for a

given sinusoidal input, resulting output is always

sinusoidal, and usually at the inputs frequency.

However, systemic storage and release of energy

often warp magnitude and phase. The twin charts of

a Bode diagram reveal these distortions.

10

-10

-20

-40

180

90

-90

-180

0

20

40

0

5t t10t

10

v

vn

= 0.1

= 0.2

= 0.3

= 0.5

= 0.7

= 1.0

t

0.1 0.2 0.4 0.6 0.8 1

Lag

Lead

Phase(degrees)

Magnitude(dB)

1 1 1

2 4 6 10

Frequency ratio into quadratic factors (rad)

Frequencyv into rst order factors (rad)

Frequencyv into integral and derivative factors (rad)

Frequency v into gain factor (rad)

8

0.1 0.2 0.4 0.6 0.8 1 2 4 6 108

0.1 0.2 0.4 0.6 0.8 1 2 4 6 108

6

t

4

t

2

t

1

2.5t

G(s)=[1+2z(

)+(

)2]-1

G(s)=K

G(s)=(jv)-1

G(s)=(1+jvt)-1

jvvn

jvvn

A first order action acts as low-passfilt er to eliminate noise. The larger the

time constant t, the slower t he response.

A proportional action reduces disturbanceerror (providing for system stiffness)but never completely gets rid of it.

-20

A differential action provides early correction(or system damping). Because it responds to t herate of change of error, it cannot be used alone.

A quadratic action reflects behavior atnatural frequencies. Decreased damping increases

system response_

at the risk of overshoot.G(s) = (jv)

An integral action eliminates steady-stateerrors. However, because it is the areaunder the actuating signal's error curve,it can induce an oscillatory response.

Setting the gain usually improvessteady-state system response, but often at

the cost of stability. Adustmentswith lag and lead compensators help.

Bode plots: Visualization of control building blocks


9/13


ing the roots of this equation using the Routh

array, by examining the open-loop transfer

function using its Bode plots (see previous

page) or the polar plot of the open-loop trans-

fer function using Nyquist criterion.

Any Laplace domain transfer function can

be expressed as the ratio of two polynomials,

usually written as T(s) = N(s)/D(s). Zeros of

the T(s) are the roots of N(s) = 0. Poles of the

T(s) are roots of the D(s) = 0. For stability,

the real part of every pole must be negative.

If T(s) is formed by closing a negative unity

feedback loop around the open-loop transfer

function G(s)=A(s)/B(s), then the roots of the

T(s) denominator (also called the characteris-

tic equation) are also the zeros of 1 + G(s), or

simply the roots of A(s) + B(s).

Stp spos

Controls are often characterized by how

they respond to a step function. In the case of

a motion system, the step is usually a com-mand to change position or speed.

Step-response dynamics consist of ve

basic parameters delay, rise time, time

to peak, overshoot, and settling time. These

factors are indicative of the inertia, damping,

and spring forces present in most systems, as

well as the dynamic limitations of the control-

ler, drive, motor, and mechanical components

themselves. Often, one of the major challengesin designing motion controls is determining

how much deviation in the step response is

acceptable for a given application.

Rise time is how long it takes feedback

to initially reach 90% of the target value.

Overshoot is the maximum deviation

of feedback in the inverse direction of value.

When evaluating step responses, note that

although overshoots seem serious, they can-

not be in positioning. Minimizing overshoot

can severely affect tracking ability, but it can

safely be done in moderation by proling the

reference command.

Settling time is the time it takes to

reach nal stabilization, with a small toler-

ance about the target.

Note: It is not easy to achieve a clean

step response for evaluation. Small step

responses may be severely distorted by me-

chanical friction, sensor quantization, and

other non-linear phenomena such as cogging.

For high-gain feedback systems, a power

Servo limitations

Closed-loop motion controls make no distinction

between shaft disturbances and command signal

changes. Both cause the motor shaft to move to the

commanded position so if the command signal

is changed to any position, the system responds by

moving the motor shaft accordingly. That said, real-

world motion control exhibits compromised output.

1. I the load on the motor shat or speed ex-

ceeds the maximum motor and amplier torque and

speed, the system will exhibit position error.

2. Feedback devices cannot detect shat position

changes that are less than the sensor resolution.

3. All servosystems are limited in how rapidly

they respond to changes so motor shafts can to

respond imprecisely to rapid command sequences

or changes in load. In extreme cases, the system

can become unstable; response may be so slow,

that by the time it responds, the motor shat may

already be moving in a different way. This is called

instability, oscillation, or hunt, and can actually

cause a system to never come to rest ... or hunt or

the commanded position indenitely.

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acloSerlookatStepreSponSe

amplier saturates with very small tracking

steps. Large step responses are less affected

by friction, but are highly distorted by ampli-

er saturation.

How do time constants relate to settling

time?

Both are a measure of response speed.

Time constants gauge how quickly a response

builds, while settling time indicates how long

it takes the output (in the event of oscilla-tions) to settle within a given band around

the nal value. The most general term to

describe response speed is hertz the

maximum frequency at which the system can

respond without exceeding a given amount of

lag between the input and output.

What are the sources of inertia,

damping, and spring force?

System inertia includes rotor and load

inertia; damping (a resisting torque propor-

tional to speed) includes friction, drag, and

motor cogging; spring forces originate in the

magnetodynamics of the motor and in the

twisting of couplings, shafts, and other me-

chanical components.

How does motion control improve

response?

Increasing controller gain boosts system

stiffness, which gives faster response. Increas

ing damping can also improve speed because

it reduces the tendency to ring or hunt.

Let us revisit the inherent instability of po

sition control systems. Consider a closed-loop

The response to a step command

reveals a motion systems dynamics.In it youll nd measures of a systems

ability to overcome inertia, damping,

and spring forces. Delay is the time to

reach 50% of the nal value; rise time

the time it takes to go from 10 to 90%

and settling time is the time it takes

the output to settle within a specied

tolerance band (expressed in percent

around the nal value.

Output(%f

inalvalue) 140

120

100

80

60

40

20

Rise time

Overshoot

Settling timeTime to peak

Delay

Tolerance band

Time

Step response: A systems dynamic fingerprint

Error correction example

Assume that a system is on, and that its motor

shaft and command generator are both at 0. The

system is at rest. Position error is zero.

Now, some outside orce or torque moves the

motor shaft 1 clockwise. The comparator detects

this difference and responds by commanding the

amplier to produce counterclockwise torque and

turn the motor shat. System activity is continuously

monitored, so the comparator senses the shafts

counterclockwise direction and responds by de-

creasing its signal position error to the amplier. As

the motor rotates back to its 0 position, position

error decreases until the motor shaft is at 0. Finally,

the comparators output returns to zero. In fact, the

same sequence o events can occur in the other

direction: Closed-loop servosystems are bidirec-

tional and provide equal response or clockwise and

counterclockwise moves.

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acloSerlookatStepreSponSe

system, and suppose that the motor starts at

10 and must stop at 0. The system gener-

ates a current proportional to the error, which

energizes the motor windings and produces a

torque that accelerates the shaft toward 0.

As the motor approaches zero, position er-

ror and acceleration decreases. Velocity, how-

ever, continues to increase so by the time

the motor reaches its intended destination, its

going too fast to stop, and may overshoot the

position by as much as 10. This sets up the

reverse process, causing the motor to go back

and forth indenitely. Stabilizing compensa-

tion is needed.

In fact, theres similarity between position

controls and a simple pendulum. Both behave

according to the same dynamic equations, evi-

denced by sinusoidal motion. Submerging the

pendulum in viscous damping

oil stops its oscillation. A similar

opposing force, if proportional torotor velocity, can be applied to

a motor to stabilize a positioner.

Because motor position is

known, a differentiator is all thats

needed to nd velocity.

Now when the control loop is

closed, two operations are per-

formed: The rst generates a

corrective signal proportional to

the error. Its dynamic effect is like

that of the force of gravity on the

pendulum. The second operation,

based on the derivative, has an ef-

fect analogous to viscous damping.

Working together, the two opera-

tions cause the motor to stably

move, like a damped pendulum,

to the target position. The propor-tional and derivative terms give

this control technique its name: PD compensa-

tion.

Deadband

Once stability is established, deadband must be addressed.

Consider a motor that stops near (but not exactly at) a command

position of zero. The resulting torque produced by the small position

error may be insufcient to overcome friction and move the motor

the rest o the way.

The range of positions at which the motor may stop short of its

destination is called the deadband, and is a refection o system ac-

curacy. To correct such position errors, an integrator can be added

to the compensation algorithm. With an integrator, the drive signal

continues to increase as long as there is a position error. Thus, even

a small error eventually spurs corrective action. It may take 20 msec

or so, but with PID compensation, positioning systems are more ac-

curate than those without it.

Defnitions

Bandwidth: the frequency range 0< v


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13/13

SaMplequeStionS

If the phase winding current through a step motor rises while the motor

shaft is at a rest position, the result is?

Low-pass lters designed for servo positioning systems typically have trans-

fer functions with poles placed to?

LeveL FOur

A three-phase synchronous generator is operating at 1200 rpm, at 60 Hz.

What is the number of poles in the generator?

When a torque is applied across a compliant coupling, the resulting

deection is?

Electric motors have long been thermally characterized using whats

generally called the ___-parameter thermal model.

If a linear motion system is running at 250 degrees C, what temperature

coefcient should be applied to life calculations?

A motion system consisting of a motor moving a load through a pulley has an

idler pulley X times larger than the motor pulley. The reected inertia of the

idler pulley at the motor is?

LeveL FIveWhen a load couples to a motor through a compliant coupling material such

as polyurethane, the resulting damping torques are proportional to . . .?

Step motor control schemes that compare rotor position to the estimated

direction of the phase current vector are known as . . .?

In the Bode attenuation-phase plot of a simple system, a 20 dB/decade gain

rate of change corresponds to a phase shift of . . .?

When a nonlinear feedback system exhibits sudden discontinuities in the

input/output amplitude ratio and in phase angle as a function of frequency,

it is said to exhibit?

The rotor in a typical hybrid step motor is characterized by?

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