Long Stroke Linear Switched Reluctance Actuator Displacement With a Fuzzy Logic Controller

Espírito Santo A., Calado, M. R. A., C. M. P.Cabrita * Departamento de Engenharia Electromecânica

Universidade da Beira Interior Calçada Fonte do Lameiro, Covilhã, PORTUGAL

e-mail: aes@ubi.pt

Abstract – Linear switched reluctance actuators (LSRA) possess simple construction due to the absence of windings on either the stator or translator parts, being those windings concentrated. That windings structure makes the LSRA to become an actuator with a fail-save system. However, usage of this kind of actuator is difficult because of their demanding control. The machine control difficulty results from the fact that the actuator is highly dependent on its complex magnetic circuit, which is also complex to model and simulate. Observing actuator force maps, one can conclude that the developed traction forces depend on both relative stator to translator positions and coils excitation current. Thus, some well-chosen positions can be considered as optimal positions to trigger a specific actuator phase. This paper proposes a method, based on fuzzy logic control strategy, to determine automatically the best positions to perform the switching of converter connected with the actuator phases. This proposed converter switching sequence allows the control of the LSRA for long distance displacement.

I. INTRODUCTION

The linear switched reluctance actuators (LSRA) are counterparts of rotary SRMs [1]; the linear configuration can be obtained from the rotary configuration, i.e., cut radially and unrolled. Thus, the LSRA develops force (thrust) and motion by the tendency of a secondary to assume a position where the inductance of the dc excited primary is maximised.

This kind of linear electric machine is not compatible with machine conventional design or control methodologies. In fact, the classical empirical parameters used in those approaches are, in this case, unknowns, as

well as the magnetic flux density distribution and, consequently, the actuator performance [2]. The most difficult task in controlling this device is related with the knowledge the proper time and at wish position, a particular actuator coil phase must be turned on or off.

This paper uses an already designed and analysed, trough both defined analytical and numerical methods, actuator developed by the authors, to verify the actuator dynamical behaviour response to the proposed fuzzy logic control strategy [3]. Control main goal is the selection of proper actuator phase that, when active, will contribute for the correct actuator displacement from an initial position to a predefined final position. Actuator control actions can be separated in long stroke action, and in short stroke action. The first kind of control action, proposed in this paper, is used for actuator long range movement. While the second is used for short range precision movement. Precision movement can be obtained with simultaneous excitation of two phases, allowing that the developed force can be balanced between both phases.

As well known, the LSRA as two physical structures. The first one is a stationary part, made of magnetic material, composed by a set of teeth without coils. The second one is a moving part, also made of magnetic material, with a yoke form. Also, the minimum number of stator yokes is equal to three, in order to achieve a bi-directional displacement. A yoke and respective coil constitute an actuator phase. Each phase is independent from another, fact that brings two major advantages: (1) flux will be completely independent for each phase; and (2) increasing the number of phases, the movement resolution will be also increased.

Figure 1. Single phase actuator topology FEM flux density (tesla) distribution

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Figure 1 shows finite elements (FEM) flux density distribution, obtained from a commercial package software usage, for the actuator with a single-phase mover, being the excitation coil of 640 Amp/ Turn.

II. ACTUATOR CHARACTERISATION

Each actuator phase behaviour is completely described by a three-dimensional map where co-energy W’(i,x) is function of current i and relative position x. Co-energy map is obtained collecting data from several FEM analysis performed with primary actuator at different static positions. For each one, a set of excitation coil’s currents is simulated.

Differentiate the obtained co-energy map, with respect to direction, will give device traction force map F(i,x)showed in Fig. 2. If differentiation is made with respect to current, is possible to obtain device flux linkage map (i,x),and, with it, device inductance map L(i,x).

-0.015 -0.01 -0.005 0 0.005 0.01 0.0150

2

4-150

-100

-50

0

50

100

150

Position [m]Current [A]

Trac

tion

Forc

e [N

]

Figure 2. Actuator traction force map for different positions and currents

Actuator non-linearity characteristic can be observed from the obtained device maps. From them, is visible that both L(i,x) and F(i,x) will differ not only with position, but also with current. If these maps are used for device modelling, then, simulation will take into account actuator non-linearity’s. For phase n = {1,2,3}, expression (1) describes electromagnetic behaviour, where Rn is the coil resistance and vn the supplied voltage. Mathematical expression (2) describes actuator mechanical behaviour where a is the device acceleration, M the mass, F the produced traction force, and Fa the frictional force.

( , ) ( )( )

( , ) ( , )( , ) ( ) ( )

1( )

n nn n n

n n nn n n

a

dL i x i tv R i tdt

di L i x L i xdxL i x i t Ri tdt i dt x

a F FM

(1)

(2)

Applying the proposed analysis method is possible to obtain a device dynamic numerical model based on the co- -energy map. With it is possible to observe, and validate, the control strategy under development. This model can be

used as a black box, where inputs are the phase voltages, and outputs are the position, force, phase currents, velocity or even others parameters.

It can be said that this kind of machine exhibits a cyclic characteristic. Knowing the relative position of phase with respect to the stator tooth, as also to the coil current, is possible to characterise the yoke force performance.

III. FUZZY LOGIC CONTROLLER DESIGN

Traditional control methodologies adjust actuator process parameters based on results obtained from the analysis of system mathematical model [4],[5]. Real world applications are nonlinear and are described by a set of differential equations. This situation turns difficult to apply conventional control techniques. Fuzzy logic control is based on fuzzy sets and fuzzy logic theory. Process control parameters are adjusted as a result of inference on a human model of the process stored in a knowledge database. Control design does not need a precise mathematical model that describes the system nonlinearities. Human process expert operator know-how is enough to describe, in a linguistic base, all system information, and design the controller to properly adjust system control parameters.

Proposed fuzzy controller, shown in Fig. 3, uses as inputs the actuator position error (ErroPosicao) and the normalized actuator zone position (ZonaForca). The controller outputs will give information to be used in the definition of each coil voltage power status (Fase1, Fase2,Fase3).

Fuzzification DefuzzificationInference

KnowladgeBase

(Rules)Fuzzy Controller

ZoneNormalization

Xref

X

ErroPosicaoFase1

V1 V2 V3

V1 V2 V3

+

Fase2 Fase3ZonaForca

Figure 3. Fuzzy logic controller and actuator interface

Zone normalization uses the actuator cyclic characteristic to know the force that each phase will produce if its respective voltage coil is turned on. Note that the actuator phase 1 is used as the reference phase. Using position X from actuator phase 1 is possible to know relative position for the others phases. Fig. 4 exhibits normalized zone division and, also, is possible to observe the traction force produced by actuator phase. Is important to observe that traction force will be zero for the alignment and unalignment positions; maximum traction force is obtained with actuator phase near positions {10,-10}.

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Figure 4. Normalized zones

The domain of normalized zones is between {-15,15}. The language parameter of the ZonaForca is

ZonaForca = {A, B, C, D, E, F, G}

-15 -10 -5 0 5 10 15

0

0.2

0.4

0.6

0.8

1

ZonaForca

Deg

ree

of m

embe

rshi

p

A B FC D E G

Figure 5. Input membership function for ZonaForca

The domain of position error is between {-15,15}. The language parameter of the ErroPosicao is

ZonaForca = {N, Z, P }

-15 -10 -5 0 5 10 15

0

0.2

0.4

0.6

0.8

1

ErroPosicao

Deg

ree

of m

embe

rshi

p

N Z P

Figure 6. Input membership function for ErrorPosition

The domain of coils voltage is between {0,12}. The language parameter of Fase_n (n=1,2,3) is

ZonaForca = {N, Z, P }

0 2 4 6 8 10 12

0

0.2

0.4

0.6

0.8

1

Fase1

Deg

ree

of m

embe

rshi

p

N Z P

Figure 7. Output membership function for Fase_n

The obtained values for outputs Fase1, Fase2 and Fase3 are used to decide when power on or power off the correspondents phase coils. That control decision is taken using the function:

12 _ 6.1{1, 2, 3}

0 _ 6.1n

Fase nV n

Fase n

The fuzzy controller uses minimum operator for AND operation, being the used Defuzzification method the Centre of Gravity

( ).

_ {1, 2, 3}i i

i

ii

x xFase n n

x

TABLE I. CONTROLLER RULES

ErroPosicao ZonaForca Fase1 Fase2 Fase3 P A Z Z P P B Z Z P P C Z P Z P D Z P Z P E P Z Z P F P Z Z P G Z Z P Z A Z Z Z Z B Z Z Z Z C Z Z Z Z D Z Z Z Z E Z Z Z Z F Z Z Z Z G Z Z Z N A Z P Z N B P Z Z N C P Z Z N D Z Z P N E Z Z P N F Z P Z N G Z P Z

A collection of control rules, used by the fuzzy controller, and defined as conditional statements of the type if…then…., that uses antecedent and consequent data can be found on Tab. I.

Finally, the control surface obtained from the application of this method, and for actuator phase 1, is shown in Fig. 8.

1180

-10

0

10-15

-10-5

05

1015

6

7

8

9

ZonaForcaErroPosicao

Fase

1

Figure 8. Control surface for Fase1

IV. ACTUATOR CONTROL SIMULATION

The actuator numerical model, together with the proposed fuzzy logic controller are used to construct a software application in MatLab, that allows the validation of the actuator dynamical response, with the main goal of displace the mover from one position to another.

Simulation begins with actuator parameters characterization: weight, coil resistance, voltage, actuator traction force and inductance maps. Control is executed every time that actuator’s mover changes its position, so is also required the specification of the “amount” of displacement x that will trigger the controller. While simulation process is running, position error and normalized zone determination tasks are executed, being this information given to the fuzzy logic controller that, in turn, will return each actuator coil power state. This information, together with actuator position InitPositionand velocity InitVelocity, is used to construct numerical model initial state vector

uev = {InitPosition, InitVelocity, V1, V2, V3} (8)

Actuator numerical model receives uev and runs simulation till mover had displace the quantity x.Displacement, velocity and phase currents data obtained from simulation are returned in matrix

u = {position, velocity, I1, I2, I3} (9)

The final state of the actuator’s system is used in next x simulation period. This process is running till final

position is reached. Fig. 9 shows an example of simulated control process.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

Time [sec]

Dis

plac

e [m

]

Figure 9. Simulation results

V. CONCLUSIONS

Linear switched reluctance actuators are a new kind of actuators that own a high liability because of there simple construction. The major problem concerns the control operation, in order to know when and at which positions each actuator phase must be powered on or off. This paper proposes a fuzzy controller that, applied with base on an already proposed actuator numerical model, allows to validate actuator performance.

Proposed fuzzy controller uses as inputs the position error and normalized force zone. This last parameter takes advantage from actuator cyclic characteristics. Output data from controller is used to decide when to turn on or of power applied to each coil. Fuzzy logic control can easily be implemented to run on a microprocessor in real time. Triangular membership function storage demands low memory resource. Also, chosen conjugation and defuzzification operations implementation require a very low processing capabilities.

REFERENCES

[1] Calado, M. R., Actuador Linear de Relutância Variável Comutado. Modelização, Dimensionamento, Construção e Ensaio, PhD Thesis (in Portuguese), July 2002, Universidade da Beira Interior, Covilhã, Portugal.

[2] Maria R. A. Calado, António E. Espírito-Santo, Carlos M. P. Cabrita, “Performance Analysis of a Linear Switched Reluctance Actuator. A Basis to the Control Design”, WSEAS Transactions on Circuits and Systems, Issue 7, Volume 4, July 2005.

[3] A. Espírito Santo, M. R. A. Calado, C. M. P. Cabrita, “VariableReluctance Linear Actuator Dynamics Analysis Based on Co-energy Maps for Control Optimization”, Linear Drives for Industry Application, Kobe-Awaji, 2005.

[4] C.C. Lee, “Fuzzy Logic in Control Systems: Fuzzy Logic Controller - Part I”, IEEE Transactions on Systems, Man and Cybernetics, vol. 20, nº 2, Março/Abril 1990

[5] C.C. Lee, “Fuzzy Logic in Control Systems: Fuzzy Logic Controller - Part II”, IEEE Transactions on Systems, Man and Cybernetics, vol. 20, nº 2, Março/Abril 1990.

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