fuzzy logic controller for one-way sma actuator - AGH

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104 * Department of Process Control, AGH University of Science and Technology, Krakow; [email protected], [email protected] MECHANICS Vol. 27 No. 3 2008 Ireneusz DOMINIK * , Janusz KWANIEWSKI * FUZZY LOGIC CONTROLLER FOR ONE-WAY SMA ACTUATOR SUMMARY Fuzzy logic controllers are well known and often used for their ability to control nonlinear objects in an easy and efficient way. In the article fuzzy logic controller was chosen to control displacement of one-way actuator where the movement in one-way was realized by SMA wire while an external load was responsible for the way back. The SMA wire is characterized by one of the highest in technology weight ratios, which describes the ratio of maxi- mum external load to its own weight. It allows for building miniature devices which are extremely efficient. Mostly SMA wires are applied as on-off actuators. Having built a test stand with SMA wire the research on selection of an appropriate method control was launched to control displacement. Eventually a fuzzy controller was implemented into PLC controller made by Omron. In that way in future it will be easier to emigrate from the PLC platform to a dedicated embedded microprocessor. The fuzzy controller was built as a task controller, where the specialized controllers for particular stages of the systems operation were distinguished. They allowed for accurate and fast SMA wire control. The design con- troller allows for position control with ±0.1% accuracy with time response below 0.4 s. Keywords: fuzzy controller, position controller, SMA wire, nonlinear object REGULATOR ROZMYTY DLA JEDNOSTRONNEGO AKTUATORA SMA Regulatory rozmyte s¹ dobrze znane i czêsto stosowane z powodu ich zdolnoci do sterowania obiektami nielinio- wymi w prosty i skuteczny sposób. W artykule regulator rozmyty zosta³ wybrany do sterowania pozycj¹ jednostron- nego aktuatora, gdzie za przemieszczenie w jednym kierunku odpowiada ciêgno ze stopu z pamiêci¹ kszta³tu (SMA), a za ruch powrotny odpowiada zewnêtrzne obci¹¿enie. Ciêgno SMA charakteryzuje siê jednym z najwiêk- szych wspó³czynników wagowych, które s¹ zdefiniowane jako stosunek maksymalnego zewnêtrznego obci¹¿enia do masy w³asnej aktuatora. Pozwala to na zbudowanie miniaturowych urz¹dzeñ, które s¹ wyj¹tkowo wydajne. Ogól- nie, ciêgna SMA s¹ stosowane jako obiekty dwustanowe. Po zbudowaniu stanowiska badawczego przeprowadzono szereg badañ w celu znalezienia sposobu regulacji, który w sposób zadowalaj¹cy bêdzie sterowa³ po³o¿eniem ciêgna. Ostatecznie regulator rozmyty zosta³ zaimplementowa- ny w sterowniku PLC firmy Omron. Pozwoli to w przysz³oci na stosunkowo ³atw¹ i szybk¹ emigracjê z platformy PLC do dedykowanego wbudowanego mikroprocesora. Regulator rozmyty zosta³ zbudowany jako regulator zadaniowy, gdzie zosta³y wyró¿nione wyspecjalizowane regula- tory dla odpowiednich etapów sterowania, czego efektem by³o dok³adne i szybkie sterowanie obiektem. Zaprojekto- wany regulator rozmyty pozwala na zrealizowanie sterowania pozycyjnego z dok³adnoci¹ ±0,1% dla czasu odpo- wiedzi poni¿ej 0,4 s. S³owa kluczowe: regulator rozmyty, sterowanie po³o¿eniem, ciêgno ze stopu z pamiêci¹ kszta³tu, obiekt nieliniowy 1. INTRODUCTION Modern technology sets increasingly new requirement for construction materials in the field of, inter alia: reliability, higher endurability or new, yet undiscovered, features, which may improve the parameters of the existing solutions. In order to meet these requirements a new group of the so called Intelligent Materials were created. One of the sub- groups are Shape Memory Alloys (SMA). Shape Memory Alloys SMA attract more and more inter- est and nowadays many research centers are working on developing more accurate and better applicable actuators (Nakatani 2005, Scheibe 2006, Tabrizi 2007). A tangible effect of using SMA materials is a considerable simplifica- tion of the presently used constructions which entails obvi- ous economic benefits. Along with an increase in the vol- ume of production and decrease in the costs of production, SMA materials become increasingly available on the con- sumer market. On the basis of the collected experiment data (Kwaniewski 2006) it was concluded that SMA wires are nonlinear and time variant. Thus, it was decided to use one of the methods from computation intelligence area to control them. The arti- cle presents the use of a fuzzy controller. The reason is that they are most widespread among these tools and regarded as the most trustworthy. The set value compared with the present value constitutes an error which amounts to the input signal of a fuzzy controller. The fuzzy controller was implemented in CJ1M controller produced by Omron (Omron 2007) from which voltage mani- pulated variable was transformed into current manipulated variable. The current flows through an SMA wire in the plant (the prototype of linear position actuator) causing the dis- placement of the load. The displacement measurement was realized by non-touch magnetic sensor produced by Balluff (Balluf 2005). So, displacement was the controlled variable. Block diagram control system for a prototype of linear position actuator was shown in Figure 1.

Transcript of fuzzy logic controller for one-way sma actuator - AGH

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Modern technology sets increasingly new requirement forconstruction materials in the field of, inter alia: reliability,higher endurability or new, yet undiscovered, features,which may improve the parameters of the existing solutions.

In order to meet these requirements a new group of the socalled Intelligent Materials were created. One of the sub-groups are Shape Memory Alloys (SMA).

Shape Memory Alloys SMA attract more and more inter-est and nowadays many research centers are working ondeveloping more accurate and better applicable actuators(Nakatani 2005, Scheibe 2006, Tabrizi 2007). A tangibleeffect of using SMA materials is a considerable simplifica-tion of the presently used constructions which entails obvi-ous economic benefits. Along with an increase in the vol-ume of production and decrease in the costs of production,SMA materials become increasingly available on the con-sumer market.

On the basis of the collected experiment data (�2�>�+�2�1+2006) it was concluded that SMA wires are nonlinear andtime variant. Thus, it was decided to use one of the methodsfrom computation intelligence area to control them. The arti-cle presents the use of a fuzzy controller. The reason is thatthey are most widespread among these tools and regarded asthe most trustworthy.

The set value compared with the present value constitutesan error which amounts to the input signal of a fuzzy controller.The fuzzy controller was implemented in CJ1M controllerproduced by Omron (Omron 2007) from which voltage mani-pulated variable was transformed into current manipulatedvariable. The current flows through an SMA wire in the plant(the prototype of linear position actuator) causing the dis-placement of the load. The displacement measurement wasrealized by non-touch magnetic sensor produced by Balluff(Balluf 2005). So, displacement was the controlled variable.

Block diagram control system for a prototype of linearposition actuator was shown in Figure 1.

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The tested element was a wire made of shape memoryalloys (SMA). During heating the contraction of the wirewas observed. The source of heating is the current flowingin the wire. There are two types of SMA wire actuators. Inthe one-way actuator the movement in one way is realizedby SMA wire while an external load or a spring is responsi-ble for the way back. Two-way actuator uses SMA wire tocreate the movement both ways. In our research we usedone-way actuator with an external load.

The peculiar character of the research led to the buildingof a dedicated power amplifier, shown in Figure 1 as a con-verter u/i. The built amplifier differs from the standart onesby ability to keep the constant current output value. It isvery important in the research of the SMA wire because itsresistance under temperature influences changes. The am-plifier allows to protect the wire against too high a currentvalue. This feature is very useful because of the wire currentlimitation. Otherwise, the wire loses its characteristics andeventually can be destroyed.

In the past an important problem, which made difficultthe creation of more sophisticated algorithms, was the lackof appropriate tools for building Function Blocks in PLC.The European Norm IEC 61131-3 solved this problem byintroducing standardized Structured Text (ST) language. It isbased on Pascal language which can be noticed in Figure 2.

Implementing the high-level programming language al-lowed for the development of advanced programs inacces-sible in PLC’s until now. They included, among others,fuzzy logic controllers, neuron networks or genetic algo-rithms.

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We can observe that in many cases highly complicated andundefined processes are well controlled by an experiencedoperator. Moreover, the control is based on defining thework strategy, it consists of a set of non precise, heuristicrules which are impossible to realise in a conventional con-trol system. An operator uses quantities of a linguistic vari-able, e.g. velocity in a descriptive form (labels): “a bit slow-er”, “faster”, “very fast”. They are not precise (fuzzy).However, a control system based on such activity worksproperly.

In the systems where fuzzy logic is applied, we deal witha three-phase process. In the first phase the measured vari-ables undergo fuzzification. It means that the continuousinput variable is assigned to a membership (affiliation)function, which allows determination of the degree of mem-bership. In the middle phase, in the fuzzy reasoning(approximate reasoning, generalised modus ponens) systembased on knowledge (e.g. model of a system), written asa set of rules IF-THEN, reasoning is realised mainly onqualitative reasoning. In the last phase defuzzification takesplace, i.e. crisp value is derived.

The second category of model is based on Sugeno rea-soning, known also as TSK because it was elaborated byTakagi, Sugeno and Kanga (Takagi 1985, Sugeno 1991). Inthis method the antecedent is fuzzy (linguistic), and the con-sequent is functional; it is a combination of fuzzy and crispmodels. This model integrates features of linguistic modelsfor representation of qualitative knowledge with the effi-ciency of quantitative information representation.

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The standard form of rules in the model reads as follows:

IF x is A AND u is B, THEN z = f (x, u) (1)

where A and B are sets of the linguistic labels defined ininput space x and u in the antecedent, whereas z = f(x, u) isa function in the consequent. This function is usually poly-nomial, and if the polynomial is of the first order we meanSugeno’s first order fuzzy set (�2�>�+�2�1+9<<9A5

The first controller used during the research was zero-orderTSK fuzzy logic controller. It had two inputs: present value PVand error e and one output: manipulated variable MV, whichwas the value of current flowing through the SMA wire.

The zero-order TSK fuzzy controller data are as follows:

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The singleton values were matched in a way that ensuredlack of overshooting. It was critical because just after heat-ing the SMA wire gives extra resistance which prolongs theresponse time. Thus, a much better solution was to selectappropriate singleton values (Fig. 5).

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The preliminary research proved that it is possible to usehigh value currents applied within short periods (hereinaf-ter referred to as acceleration impulse) in such a manner thatthe wire is displaced at high speed without being damaged.The following research aimed at determining the maximumcurrent value which can flow through the wire to maximizethe speed of its work. The next task was to find impulsewidth which in connection with the given value of currentintensity does not damage (overheat) the SMA wire. Inother words, such a surface area of the current impulse (itsintegral) was desired as to maximally increase the wires’work without damaging them at the same time.����������%�$�$E���/+"&��(#+%��@��(%�.+�"�#A

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There is a lack of data on this phenomenon in the litera-ture. Thus, a number of experiments were conducted usingdifferent diameter wires and different loads.

As a result of experimental data the general relationshipfor each SMA wire diameter was found: the maximum cur-rent value used to accelerate contraction equals the currentvalue where the position (error) to switch off the impulse isat the very most half of the set value. It means that ifa current is higher, the SMA wire position (error) to switchoff the impulse is higher than SV/2 value. As a result, theabove mentioned critical overshooting can appear.

For example, for an SMA wire of 0.20 mm diameter andfor error SV/2 = 4 mm where the impulse turns off, thecurrent value equals about 2 A. This is double the nominalcurrent value recommended by the producer (Dynalloy2004). For this values the SMA wire contracts in time 0.28 swithout overshooting. It is about 4 times faster than in stan-dard conditions. This is a really good result, especially thatthe wire remains stable (without oscillations) and the stepresponse experiment is repeatable. As an example, a com-parison of characteristic values of the acceleration impulseof the 0.20 mm wire obtained from diagrams similar to thediagram in Figure 6 are presented in Table 1.

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* Gwyl – error limit below which impulse turns off

The values Gwyl and G100% determine the borders forturning on and off the accelerating impulse. Above the errorG100% current value is about 2–3 times higher than the nom-inal value. Below the error Gwyl the impulse is turned off(Fig. 6).

During the research there were used both simple shapeaccelerating impulses (Fig. 7) as well as gradient impulses(Fig. 8). It appears that the impulse gradation hardly chang-es the response time so we decided to use a single (1 step)accelerating impulses.

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To control the above mentioned accelerating impulse a ze-ro-order TSK fuzzy controller Rimp was used. Its perfor-mance was not good enough for correct work in the steadystate so the separate steady state controller Rust was added.Together these two controllers constitute a zero-order taskfuzzy logic controller, which is illustrated in Figure 9.

Impulse turn-off error *

Gwyl [mm]

Current

I [A]

Response time

tr 5% [s]

Impulse duration timp [s]

0.75 1 1.07 1.02

1.70 1.25 0.62 0.56

3.10 1.5 0.42 0.37

4.05 1.75 0.28 0.25

5.10 2 0.25 0.17

5.65 2.25 0.24 0.14

5.64 2.5 0.2 0.11

5.64 2.75 0.2 0.11

5.64 3 0.2 0.1

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The controller Rust is sufficient to operate as an SMA ac-tuator for the whole displacement range. The controller Rimpserves only to accelerate displacement. It is superior to thecontroller Rust, so during their action the controller Rust doesnot work. In that way it additionally shortens the cycle time.

The steady state controller Rust was a fuzzy controllersimilar to the single controller described in chapter 1. Themembership function distributions for the set value (first in-put) was the same as for the single fuzzy logic controller(Fig. 3) for both the steady state controller Rust and theaccelerating impulse fuzzy controller Rimp. On the over hand,the error membership function (controller second input) waschanged and was dedicated to the particular task controllers.Figure 10 shows the error membership function distributionfor steady state controller Rust, whilst Figure 11 shows thesame distribution for the steady state controller Rimp.

Apart from changing the error membership function, therules for the controller Rimp were different, as shown in Fi-gure 12.

The rules create the relation matrix and for the controllerRimp it consists of 6 lines (according to 6 equal intervalseach 2 mm wide in set value membership function) whereevery line includes the same descriptions (but with differentvalues for every line).

The data in the matrix rows are as follows:

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The sample results of using a zero-order task fuzzy logiccontroller are illustrated in Figures 13 and 14.

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In order to compare the results the following performancecriteria of control were taken into consideration: responsetime 5L [s] and standard integral criterions: Integral of theAbsolute Error IAE (I1m) and Integral of Squared Error ISE(I2) (Tab. 2). These criteria are based on the measure oftransient states in a system.

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The comparison clearly indicates both the improvementof time response (4 times) and quality of control (20 timesfor SV = 10 mm).

In the future we plan to modify our controller in sucha way that it works in a more repetitive, predictable way.The controller we have designed allows for accurate workfor the changes in the set values when the actuator initialposition was 0 mm. Unfortunately, during changing inter-mediate set values e.g.: from 2 to 5 mm, about 20L of re-sponses have overshooting, which, as mentioned above, ishighly undesirable in controlling SMA actuators. This willbe the subject of future research.

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The research work was supported by the Polish governmentas part of the research programme No 3767/T02/2006/31conducted in the years 2006–2007.

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t 5% [s]

IAE ISE

Single fuzzy controller

SV = 4 mm SV = 10 mm

1.45 1.78

4.62 17.51

0.82 7.39

Task fuzzy controller

SV = 4 mm SV = 10 mm

0.340.38

0.59 0.87

0.19 0.38