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EEL 841EEL 841Solid State Controllers of DrivesSolid State Controllers of Drives

Prof. Bhim SinghProf. Bhim SinghDepartment of Electrical Engineering Department of Electrical Engineering

Indian Institute of Technology, Delhi Indian Institute of Technology, Delhi Hauz Khas, New DelhiHauz Khas, New Delhi--110016, India110016, India

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Stepper Motor DrivesStepper Motor Drives

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Stepper MotorStepper MotorA stepper motor is an electromagnetic incremental actuator which converts digital pulse inputs to analogoutput shaft motion;The shaft of the stepper motor rotates in equal increments in response to a train of input pulses.When properly controlled, the output steps of a stepping motor are always equal in number to the number of input pulses.

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Advantages of Stepper MotorAdvantages of Stepper MotorA stepper motor is inherently a discrete motion device, therefore it is more compatible with modern digital control techniques;It is more easily adaptable for interfacing with other digital components;The positional error in a stepper motor is non-cumulative;It is possible to achieve accurate position and speed control with a step motor in an open loop system;Thus, avoiding the ordinary instability problems and elimination of feedback transducers;

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Advantages of Stepper MotorAdvantages of Stepper MotorPower consumption for intermittent operation is reduced during quiescent periods for a permanent magnet type stepper motor;Design procedure is simpler for a stepper motor control system

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Applications Applications of of

Stepper Motor DrivesStepper Motor Drives

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Applications of Stepper MotorApplications of Stepper MotorStepper motor applications may be divided into following classes:o Instrumentation (low torque applications);o Computer peripherals and office equipments

(medium torque, high performance, high volume applications);

o Numerical control of machine tools and robotics (high torque applications);

o Electro medical (high torque applications);o Miscellaneous applications.

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Applications of Stepper MotorApplications of Stepper MotorInstrumentation:o Quartz watches;o Synchronized clocks;o Camera shutter operation;o Mechanical converter (D/A).Computer peripherals:o Dot matrix and line printers;o Floppy disc drives;o Digital x-y plotter;o Magnetic tape transport;o Paper tape drive.

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Applications of Stepper MotorApplications of Stepper MotorOffice Equipments:o Electronic typewriter (serial printer);o Fax machine;Machine tool applications:o Numerically controlled (NC) milling machine;o Index table;o Robotics;Electro-medical Applications:o X ray machines;o Radiation therapy units.o CAT scanners;o Ultrasound scanners.

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Applications of Stepper MotorApplications of Stepper MotorMiscellaneous Applications:o Nuclear reactors;o Aerospace;o Solar panel tracking.o Constant flow hydraulic pumps;o Tele operated TV camera;o UV spectrometer etc.

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Classification Classification of of

Stepper Motor DrivesStepper Motor Drives

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Classification of Stepper MotorClassification of Stepper Motor

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Permanent Magnet Stepper MotorPermanent Magnet Stepper MotorIt has permanent magnet on the rotor and also known as can-stack motor;Due to its low manufacturing cost, it is employed in paper feed motor of printers or head drive motor of a floppy disc drive.

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Cutaway View of 2 ph PM Stepper MotorCutaway View of 2 ph PM Stepper Motor

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Variable Reluctance Stepper MotorVariable Reluctance Stepper MotorIt has no permanent magnet either on the rotor or the stator;The rotor carries no windings and has salient pole construction;Rotor and stator both are made of soft iron stampings.The stator also has salient poles and carry stator windings.The number of stator poles is an even multiple of the number of phases for which the stator windings are wound.The number of phases must be at least three for bidirectional control of stepper motor.It can have single stack or multi stack construction;The torque developed by the motor shall be more in multi stack motor.

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Variable Reluctance (VR) Stepper MotorVariable Reluctance (VR) Stepper Motor

6/4 pole6/4 pole 12/8 pole12/8 poleSingle StackSingle Stack

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VR Multi Stack Stepper MotorVR Multi Stack Stepper Motor

Cross Section Parallel to ShaftCross Section Parallel to Shaft

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VR Multi Stack Stepper MotorVR Multi Stack Stepper Motor

Cross Section Cross Section ParpendicularParpendicular to Shaftto Shaft

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VR Multi Stack Stepper MotorVR Multi Stack Stepper Motor

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Hybrid Stepper MotorHybrid Stepper MotorIt has permanent magnet mounted on the rotor;It provides détente torque with windings de-energized;Less tendency to resonate;Higher holding torque capability;Better damping due to the presence of rotor magnet;High stepping rate capability;High efficiency at lower speeds and lower stepping rates.It suffers from high inertia and weight due to presence of rotormagnets;Performance is affected by change in magnet strength.

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Hybrid Stepper MotorHybrid Stepper Motor

Cross Section Parallel to ShaftCross Section Parallel to Shaft

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Hybrid Stepper MotorHybrid Stepper Motor

Cross Section Perpendicular to ShaftCross Section Perpendicular to Shaft

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Operation of Hybrid Stepper MotorOperation of Hybrid Stepper MotorAs long as the stator winding A and B are energised in a particular manner, the rotor stays put in the corresponding position;The rotor will move further only when the pattern of energization of the stator windings is changed;Figures a – h in next slide represent programmed sequence;Figures a,c,e,g represent single phase energisation, however, b,d,f,g represent two phase energisation;These figures constitute 8 step sequence in which the rotor moves 45º per step;Here one or two phases are alternatively energised, therefore this sequence is known as hybrid or mixed or 1-2 sequence.

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Hybrid Stepper Motor operationHybrid Stepper Motor operation

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1.81.8ºº Rotation Hybrid Stepper MotorRotation Hybrid Stepper MotorIt carries a cylindrical permanent magnet sandwiched between two rotor discs;The stator and rotor both are made of soft iron stampings;Each rotor disc has 50 teeth and the stator has 8 poles with 5 teeth per pole;There are 40 poles on the stator which can be in perfect alignment or misalignment depending on the switching.

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1.81.8ºº Hybrid Stepper MotorHybrid Stepper Motor

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1.81.8ºº Hybrid Bifilar Stepper MotorHybrid Bifilar Stepper Motor

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Characteristics of Stepper Characteristics of Stepper MotorsMotors

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Static CharacteristicsStatic Characteristics

Torque Angle CurveTorque Angle Curve

Torque Current CurveTorque Current Curve Hybrid motor torque and detente Hybrid motor torque and detente torque profiletorque profile

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Dynamic CharacteristicsDynamic CharacteristicsPull in curve: corresponds to start-stop or single stepping mode;Pull out curve: corresponds to slewing mode;

Start Stop ModeStart Stop Mode

Torque speed characteristicTorque speed characteristic Slewing ModeSlewing Mode

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Dynamic CharacteristicsDynamic CharacteristicsStart-stop Mode: rotor comes to rest after one step;Slewing Mode: rotor still moves in response to previous pulse when next pulse arrives; Therefore motor can overrun by several steps before stopping.

Mid Frequency Resonance : Pull in curve of stepper motor suddenly dips very low in particular range of stepping rates;This phenomenon os a manifestation of instability of motor operation.

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Some DefinitionsSome DefinitionsStep angle (θs) : It is the angle through which an unloaded stepper motor rotates for every step of the energizationsequence; i.e. θs = 360º/ZSteps/revolution (Z) : For hybrid motor : Z=Nr.kws,

Kws = 4 for 4 step sequence (i.e. 1 ph on or 2 ph on)Kws = 8 for 8 step (i.e. 1-2 or hybrid) sequence of energization of stator winding;

For single stack VR stepper motor :Ns = Nr ± p where p is no. of teeth per phase (minimum 2)Z = p.m(m-1) for Ns > Nr; p.m(m+1) for Ns < Nr where Nr

and Ns are number of teeth in rotor and stator respectively; m is number of phases (minimum 3)

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Some DefinitionsSome DefinitionsHolding Torque (TH) : It is the maximum load torque which the energized stepper motor can withstand without slipping from equilibrium position;Detente Torque (TD) : It is the maximum load torque which the un-energized stepper motor can withstand without slipping;Détente torque is due to residual magnetism and is therefore present in PM or hybrid stepper motor only;Torque Constant (Kt) : It is the initial slope of the torque-current curve of the stepper motor, and also known as torque sensitivity;Pull-in Torque (TPI) : It is the maximum torque that the stepper motor can develop in the start-stop mode at a given stepping rate Fs (steps/sec), without losing synchronism;

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Some DefinitionsSome DefinitionsPull-out Torque (TPO) : It is the maximum torque that the stepper motor can develop at a given stepping rate Fs (steps/sec), in the slewing mode, without losing synchronism;Pull-in Rate (FPI) : It is the maximum stepping rate at which the stepper motor will start or stop, without losing synchronism, against a given load torque T.Pull-out Rate (FPO) : It is the maximum stepping rate at which the stepper motor will slew, without missing steps, against a load torque T.Response Range : It is the range of stepping rate at which the stepper motor can start or stop, without losing synchronism, at a given torque T. Response range spans stepping rates Fs ≤ FPI;

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Some DefinitionsSome DefinitionsSlewing Range : It is the range of stepping rate FPI ≤ Fs ≤ FPO at which the stepper motor can run in the slewing mode, against a given load torque T, without losing synchronism;Synchronism : This term means strict one to one correspondence between the number of pulses applied to the stepper motor and number of steps through which the motor has actually moved;Stiffness : It is the slope of the static torque / rotor position characteristic at the equilibrium position.

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Analysis of Stepper MotorsAnalysis of Stepper Motors

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Static Torque ProductionStatic Torque ProductionFor a motor with p rotor teeth and a peak static torque TPK at a rotor displacement θ from the step position, the torque developed by the motor is approximately T = - TPK sin pθ;When a load torque TL is applied the rotor is displaced from the demanded position by the angle θe, at which the load and motor torques are equal, i.e. TL = T = - TPK sin pθe;

The static position error is θe = {sin-1 (- TL /TPK)}/ p;Therefore, static position error can be reduced either by increasing the peak static torque or by increasing the number ofrotor teeth.A motor with high stiffness develops a large torque for a small displacement from equilibrium.

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Static Torque ProductionStatic Torque ProductionConsidering a 4 phase motor with two-phases-on excitation which gives approximately sinusoidal torque/position characteristic as shown;The first step command changes excitation to phases B & C and the static torque at the position θe then exceeds the load torque, so the motor accelerates in positive direction;

Assuming that the motor has moved to θ1 with phase BC excited, the average torque produced is:

( ) ( ) [ ]1

11 1

1 sin 2 sin sine

PKM PK e

e e

TT T p d p pp

θ

θθ π θ θ θ

θ θ θ θ= − − = −

− −∫

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Static Torque ProductionStatic Torque Production

( )

( )

2 2

2

p 1

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The equation of motion for the system inertia (J) is/ which, after solving, gives

/ ;After one period of escitation t the rotor is at position ,

therefore

/ or

M L

M L e

M L p e

T T Jd dt

T T t J

T T t J

θ

θ θθ

θ θ

− =

= − +

= − + [ ]

[ ]

1/ 21

1/ 2p 1

( ) /( )

So the starting rate for the four phase motor is approximately :

Starting rate = 1/t ( ) / ( )

p e M L

M L e

t J T T

T T J

θ θ

θ θ

= − −

= − −

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Converter Topologies for Converter Topologies for Stepper Motor DrivesStepper Motor Drives

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3 phase Uni-polar Drive Circuit

+Vs

1 2 3

Base Drive

Phase 1 control Signal

Forcing Resistance R

Free wheeling Resistance Rf

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Bipolar Drive Circuit (one phase)+Vs

Forcing Resistance R

Base Drive

Phase 1-

control Signal

Base Drive

Phase 1+

control Signal

Base Drive

Phase 1+

control Signal

Base Drive

Phase 1-

control Signal

Phase 1 winding

T1 D1

T3 D3

T2D2

T4D4

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Uni-polar Drive Circuit for one phase of Bifilar Wound Stepper Motor

+Vs

1

Base Drive

Phase 1+

control Signal

RRf

Base Drive

Phase 1-

control Signal

Rf

•

•

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Uni-polar Bilevel Drive (one phase)Circuit Phase Current

H

L

1

2

1

2

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Uni-polar Chopper Drive Circuit (one phase)

VH

1

T1

T2

D1

D2

Rc Vc

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Control Schemes for Stepper Control Schemes for Stepper Motor DrivesMotor Drives

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Microprocessor based Open Loop Control for Stepper Motor

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Constant Stepping Rate Open Loop Control

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Closed Loop Control for Stepper Motor

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Micro stepping Control of Micro stepping Control of Stepper MotorsStepper Motors

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Micro Stepping ControlMicro Stepping Control

Micro stepping control enables the stepper motor to move through a tiny micro step of size ∆θ << θs in response to input pulse;This overcomes the limited resolution and mid frequency response problems;The pull out curve of micro stepping control is shown

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Micro Stepping ControlMicro Stepping ControlIn micro stepping control, the stator magnetic field is made torotate through a small angle θ << 90º in response to an input pulse;This is achieved by modulating currents through windings B2and A1 in such a way that IB2 = IR Cos θ, while IA1 = IR sin θ;The resulting stator magnetic field will be at an angle θº(elect.) w.r.t. the positive real axis;The phasor diagram and the sequence table for micro stepping control is given in next slides.The torque developed is same as developed under one-phase-on sequence, as the resultant current remains IR;However, if the torque required is as under two-phase-on sequence then the magnitudes of the currents should be such that IA

2 + IB2 = 2.

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Micro Stepping Principle

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Circuit for Micro Stepping Control

Power supply

Phase A

IA

1 2

Current Controller

A

Phase B

IB

3 4

Current Controller

B

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Micro Stepping Table

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Block Diagram of Micro-stepping Controller

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Block Diagram of Micro-Friend II Kit

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Advantages of Micro SteppingAdvantages of Micro SteppingImprovement in resolution by the factor MSR (micro stepping ratio) i.e. MSR = θs /∆θ in as much as the smallest angle through which the motor rotates per input pulse is : ∆θ = (1/MSR). θs usual values of MSR are 5, 10, 125 and powers of 2 up to 128;

Rapid motion at a micro stepping rate MFs = MSR.Fs where Fs

is full stepping rate;

DC motor like smooth performance;

Elimination of mid frequency resonance.

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ReferencesReferences1. A.C. Leenhouts, “The art and practice of step motor control,” Intertec

communications Inc., 1987.2. B.C. Kuo, “theory and applications of step motors,” west publishing co., 1974.3. P.P.Acarnley, “Stepping Motors : a guide to modern theory and practice,”

Peter Peregrinus Ltd., 1982.4. V.V. Athani, “ Stepper Motors: fundamentals, applications and design”, New

age international (P) ltd. publishers, New Delhi, 1997.