position control of hybrid stepper motor

7/27/2019 Position Control of Hybrid Stepper Motor

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Position Control of HighPerformance Stepper

Motor

Presented By:

Aditya Chaudhary

GG9562/12-EEIM-136

Instrumentation & Control

M.Tech. III Sem.


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Key Features


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Key Features


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Agenda

Introduction

SMM-PWM Based Controller

Neural Network Based AdaptiveController


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Introduction

Hybrid Stepper Motor is the combination of permanent magnet andvariable-reluctance stepper motor.

Caused the reduction in weight and inertia of the rotor

But increase in the dynamics

Traditional Open loop control system of the stepper motor cant be

used because stepping may produce Mechanical resonances, Vibrations, Acoustic Noise, Aging

Reduction in control bandwidth

On comparing with other motors, hybrid stepper motor does nothave a clear equivalent circuit for analysis, in fact it has manyvariations in the stator-rotor teeth configuration. Thus, a controlsystem design for this is difficult.

Therefore, an Adaptive Controller is selected.

Otherwise, through DQ Transformation, a equivalent circuit isdeveloped and then a controller is applied.


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Smart Mixed Mode-PWMBased Controller


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SMM PWM Based Controller

This controller uses current feedback and micro-stepping, forcontrolling the Stepper Motor.

A Smart Mixed Mode (SMM) is the combination of the two level andthree level PWM techniques.

For this type of controller, we have to generate a mathematicalmodel.


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Stepper Motor Model

Hybrid stepping motor was originally designed as an ac two-phasesynchronous motor.

Neglecting the space harmonics, voltage equations on the rotatingdq frame are:

(1)

Flux linkage in the dq axes is expressed as

(2)


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Stepper Motor Model

Instantaneous torque T can be expressed as the sum of threecomponents:

1. the permanent-magnet torque Tm

2. the reluctance torque Tr

3. the detent (or cogging) torque Td.

The first two terms can be computed as the partial derivative of theco-energy Wcwith respect to the rotor angle, i.e.,

It turns out that

(3)

(4)


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Stepper Motor Model

The reluctance torque term depends on the variation of reluctancebetween the two axes and can be zeroed by keeping id=0.

The last torque term Td does not affect significantly the torqueproduced by the motor and can be neglected.

Thus the torque is

Equation (5) shows that to obtain a constant torque, a constant iqcurrent must be supplied.

Referring to a stationary reference frame, we obtain the statorcurrents

(5)

(6)


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Control Scheme


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Stepping Operation

(a) Full-Step Operation (b) Half-step operation


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Microstepping

In a traditional full-step operation,each phase is supplied separately.

In a half-step operation, anadditional rest position is introducedbetween two full steps by supplyingboth phases with equal currents.

A technique to smoothen shaftrevolution by reducing torque rippleis to create new intermediate rest

positions, reducing the step size. Thistechnique requires a dedicatedsupply waveform and is referred toas microstepping.


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Microstepping

Keeping ( + ) on a circle,i.e. supplying the stator withsinusoidal currents (6), aconstant torque in obtained.

Microstepping frequency as

requested by the regulator is:

=60.

where is the number of fullsteps per revolution and

is the number of microstepsper full steps.


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PWM Operation

DC/AC converter is the keyelement of the motor control

PWM is generated by operatingthe switches of the full bridgewith a suitable switch sequence.

Two Modulation techniques areused: (a) Two level PWM and (b)Three level PWM


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PWM Operation

Two Level PWM

(fast current decay)

Three Level PWM

(slow current decay)


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PWM Operation

In mixed mode operation, the two level PWM and three level PWMare mixed to obtain a SMM-PWM.

In SMM-PWM, Toffperiod in changed according to the two level andthree level PWM. This ensures the proper decay of the current,

reducing the current ripple, according to the need of the operation.

In fact, the MM-PWM is built by mimicking the two level modulationTon period and changing the Toffperiod, mixing slow and fast decayaccording to the percentage of the slow decay ks.

The MM-PWM will be characterized by stating its percentage of the

slow decay ks; obviously, the percentage of the fast decay is the 100%complement ofks.

For example, ks= 33% stands for a MM-PWM where the currentdecay is slow for 33% ofToffand fast for the remaining 67%.


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SMM-PWM


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Experimental Results

Peak-to-peak current ripple as a function of microstepping


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Experimental Results

Average copper loss as a function of switching frequency


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Pros and Cons

Pros:

Reduction of the losses.

Either of the optimal performance or minimum cost is chosen.

Cons:

Machine Parameters have to be known priorly.


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Neural Network Based

Adaptive Control


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Adaptive Controller

ANN Controllers used widely used in system identificationand non-linear control system because:oDo not require mathematical models

oOffers advantage of performance improvement through learning

using parallel and distributed processing.

Dynamic Back-propagation learning technique is used formultilayer networks.

This type of control is implemented using two individual

controllers.1. NN Identifier (NNI) { 4:5:1 }

2. NN Controller (NNC) {5:5:1 }


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NNC Architecture

Five inputs:1. Previous instants input

2. Present instants input

3. Previous two instants rotorangular speed

4. Previous instants rotorangular speed

5. Previous instants controlsignal

The parameters of the NNC are adjusted on the error between thereference model output (), and the actual output of the systemunder control ().

Control is approximated as:

= ( 1 , 2 , , 1 , 1 )


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NNI Architecture

Four Inputs

1. Actual control effort

2. Delayed control effort

3. Estimate of the rotor angularspeed at the previous twoinstants

4. Previous rotor angular speed

Parameters are adjusted on the error between, the actual motorspeed () and the output of the identification network ().

Estimated speed is approximated as: = ( 1 , 2 , , 1 )


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Learning Algorithm: Dynamic BackPropagation

The DBP learning algorithm is used to train both the NNI and NNC.

The algorithm is based on the principle of the minimization of a costfunction of the error between the desired output and the actualoutput of each network.

The minimization is achieved by varying the adjustable parameters ofthe NNI and NNC in the negative direction of the gradient of the costfunction.

The most important step in the employed algorithm is thecomputation of the partial derivatives of each of the outputs of the

network with respect to each of its adjustable parameters.


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Learning Algorithm: DBP Steps

1. Chose the number of hidden layers and the number of nodes perlayer( generally chosen on trial and error basis).

2. Assign weights and basis to every neuron and rearrange them in avector matrix . (Referred as adjustable parameters).

3. Appropriately chose T(update window size), so that all the adjustable

parameters can be changed and (learning rate).

4. Mapping of Inputs and Outputs is done by NNC and NNI.

5. An Error vector is found as:

This Error vector is the Cost function in the DBP algorithm. The Parameter is

updated as:


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Where

Training is terminated when < .

Number of partial derivate to be computed:

3 + 3 + 3 + 3 + 3 0 . And = .


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Overall Control Structure


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Performance Results

NNI Variation

NNC Variation


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Performance Results

NNC under step input signal


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Performance Results

NNC underexternaldisturbance

PID underexternaldisturbance


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Pros and Cons

Pros:

The Controller does variate with the fixed position

Any External Disturbance is easily compensated

Model of the Motor Drive and Load has not to be known

Cons:

Training time is much more

Huge number of Initial Values of the weights and bias has to be

placed manually Number of neurons in the hidden layer is known by hit and trial bases


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References

1. A. Rubaai, M. J. Castro-Sitiriche, M. Garuba, and L. Burge, III,Implementation of artificial neural network-based trackingcontroller for high performance stepper motor drives, IEEE Trans.Ind. Electron., vol. 54, no. 1, pp. 218227, Feb. 2007.

2. Alberto Bellini, Carlo Concari, Giovanni Franceschini, and AndreaToscani, Mixed-Mode PWM for High Performance SteppingMotors, IEEE Trans. Ind. Electron, vol. 54, no. 6, pp. 3167-3177,Dec. 2007

3. Ahmed Rubaai, Raj Kotaru, Online Identification and Control of a

DC Motor Using Learning Adaptation of Neural Networks, IEEETrans. Ind. Electron., vol. 36, no. 3, pp. 935-942, May/June 2000.


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ThankYou

position control of hybrid stepper motor

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