Designing Digital Filters for Servo Systems

The aim of this work was to select an appropriate digital filter for a servo application and to filter the noise from the measurement devices. Low pass filter attenuates the high frequency noise beyond the specified cut-off frequency. Digital lowpass filters in both IIR and FIR responses were designed and experimentally compared to understand their characteristics from the corresponding step responses of the system. Kaiser Windowing and Equiripple methods were selected for FIR response, whereas Butterworth, Chebyshev, InverseChebyshev and Elliptic methods were designed for IIR case. Limitations in digital filter design for a servo system were analysed. Especially the dynamic influences of each designed filter on the control stabilityof the electrical servo drive were observed. The criterion for the selection ofparameters in designing digital filters for servo systems was studied. Control system dynamics was given significant importance and the use of FIR and IIR responses in different situations were compared to justify the selection of suitableresponse in each case. The software used in the filter design was MatLab/Simulink® and dSPACE's DSP application. A speed controlled Permanent Magnet Linear synchronous Motor was used in the experimental work.

Implementing theLean Manufacturing System

Tuottavuuden ja tehokkuuden parantaminen on keskeisimpiä menestystekijöitä glo-baaleilla markkinoilla. Yksi kehittämisen toimintamalli on lean manufacturing -ajattelutapa, joka perustuu imuohjaukseen. Sen lähtökohtana on asiakasarvo ja keskit-tyminen arvoa lisäävien toimintojen maksimointiin. Tutkimuksen tavoitteena oli parantaa Strömfors Electric Oy:n materiaalivirtauksia yhdellä tuotantolinjalla. Projektin oli tarkoitus olla pilotti lean-implementointiin koko tehtaalla. Projektissa otettiin käyttöön kanban-imuohjausjärjestelmä, jota varten teh-tiin analyysejä ja laskelmia arvovirtoihin, varastoihin ja ohjaukseen. Lean-ajattelutapaan ja -työkaluihin perustuvaa kirjallisuutta käytettiin pohjatietona pilotti-projektissa sekätulevien kehitysprojektien suunnittelussa. Pilottiprojektin tuloksena materiaalinohjaus tehostui ja keskeneräisen tuotannon va-rasto tasoittui käyttötarpeen mukaiseksi. Työntekijät ja työnjohtajat tutustuivat leanin perusteisiin osallistuessaan pilottiprojektiin. Pidemmän aikavälin suunnitelmissa ontoimitusvarmuuden ja laadun parantuminen ensin pilottiprojektia koskevalla linjalla ja myöhemmin koko tehtaalla imuohjauksen kokonaisvaltaisen käyttöönoton myötä.

Field Sales Management Control: Towards a Multi-Level Theory

The purpose of this dissertation is to increase the understanding and knowledge of field sales management control systems (i.e. sales managers monitoring, directing, evaluating and rewarding activities) and their potential consequences on salespeople. This topic is important because research conducted in the past has indicated that the choice of control system type can on the other hand have desirable consequences, such as high levels of motivation and performance, and on the other hand leadto harmful unintended consequences, such as opportunistic or unethical behaviors. Despite the fact that marketing and sales management control systems have been under rigorous research for over two decades, it still is at a very early stage of development, and several inconsistencies can be found in the research results. This dissertation argues that these inconsistencies are mainly derived from misspecification of the level of analysis in the past research. These different levels of analysis (i.e. strategic, tactical, and operational levels) involve very different decision-making situations regarding the control and motivation of sales force, which should be taken into consideration when conceptualizing the control. Moreover, the study of salesperson consequences of a field sales management control system is actually a cross-level phenomenon, which means that at least two levels of analysis are simultaneously involved. The results of this dissertation confirm the need to re-conceptualize the field sales management control system concept. It provides empirical evidence for the assertion that control should be conceptualized with more details atthe tactical/operational level of analysis than at the strategic levelof analysis. Moreover, the results show that some controls are more efficiently communicated to field salespeople than others. It is proposed that this difference is due to different purposes of control; some controls aredesigned for influencing salespersons' behavior (aim at motivating) whereas some controls are designed to aid decision-making (aim at providing information). According to the empirical results of this dissertation, the both types of controls have an impact to the sales force, but this impactis not as strong as expected. The results obtained in this dissertation shed some light to the nature of field sales management control systems, and their consequences on salespeopl

Converter-flux-based current control of voltage source PWM rectifiers - analysis and implementation

Pulsewidth-modulated (PWM) rectifier technology is increasingly used in industrial applications like variable-speed motor drives, since it offers several desired features such as sinusoidal input currents, controllable power factor, bidirectional power flow and high quality DC output voltage. To achieve these features,however, an effective control system with fast and accurate current and DC voltage responses is required. From various control strategies proposed to meet these control objectives, in most cases the commonly known principle of the synchronous-frame current vector control along with some space-vector PWM scheme have been applied. Recently, however, new control approaches analogous to the well-established direct torque control (DTC) method for electrical machines have also emerged to implement a high-performance PWM rectifier. In this thesis the concepts of classical synchronous-frame current control and DTC-based PWM rectifier control are combined and a new converter-flux-based current control (CFCC) scheme is introduced. To achieve sufficient dynamic performance and to ensure a stable operation, the proposed control system is thoroughly analysed and simple rules for the controller design are suggested. Special attention is paid to the estimationof the converter flux, which is the key element of converter-flux-based control. Discrete-time implementation is also discussed. Line-voltage-sensorless reactive reactive power control methods for the L- and LCL-type line filters are presented. For the L-filter an open-loop control law for the d-axis current referenceis proposed. In the case of the LCL-filter the combined open-loop control and feedback control is proposed. The influence of the erroneous filter parameter estimates on the accuracy of the developed control schemes is also discussed. A newzero vector selection rule for suppressing the zero-sequence current in parallel-connected PWM rectifiers is proposed. With this method a truly standalone and independent control of the converter units is allowed and traditional transformer isolation and synchronised-control-based solutions are avoided. The implementation requires only one additional current sensor. The proposed schemes are evaluated by the simulations and laboratory experiments. A satisfactory performance and good agreement between the theory and practice are demonstrated.

Production Control Principles in Printed Wiring Board Fabrication

Työn tavoitteena oli kuvata piirilevyvalmistaja Aspocomp Oy:n Espoon tehtaan tämän hetkinen tuotannonohjausperiaate ja tunnistaa siinä esiintyvät puutteet sekä kehittää vaihtoehtoinen tuotannonohjausperiaate piirilevyvalmistukseen. Vaihtoehtoisen ohjausperiaatteen lähtökohtana oli tuotannonohjauksen sopeuttaminen vaativaan ja jatkuvasti muuttuvaan liiketoimintaympäristöön. Työn teoreettinen osa keskittyi tuotannonohjauksen eri lähestymistapoihin. Kirjallisuuskatsauksessa esitetään eri tuotannonohjausperiaatteiden keskeiset sisällöt, jotka muodostavat rungon toimivalle tuotannonohjauskäytännölle. Työn kokeellinen osa keskittyi Espoon piirilevytehtaan tuotannonohjausperiaatteen selvittämiseen. Espoon piirilevytehtaan nykyisessä tuotannonohjausperiaatteessa havaittujen ongelmakohtien ja liiketoimintaympäristön vaatimusten perusteella kehitettiin vaihtoehtoinen tuotannonohjaustapa. Vaihtoehtoisen tuotannonohjaustavan päämääränä oli läpimenoajan lyhentäminen sekä tuotannon parempi hallittavuus. Vaihtoehtoinen toimintamalli tavoitteiden saavuttamiseksi perustuu pullonkaulateoriaan, jossa keskeisin muutos nykyiseen toimintamalliin oli puolivalmisteiden varastointi toimitusajan lyhentämiseksi sekä tuotantovolyymin heilahdusten vaikutusten vähentämiseksi. Työn kokeellisessa osassa ilmeni, että kysynnän muutokset ja kapasiteetin suunnittelun puute aiheuttivat ongelmia piirilevytehtaan tuotannonohjauksessa.

System Investigation for Hybrid Electric Vehicle

A hybrid electric vehicle is a fast-growing concept in the field of vehicle industry. Nowadays two global problems make manufactures to develop such systems. These problems are: the growing cost of a fuel and environmental pollution. Also development of controlled electric drive with high control accuracy and reliability allows improving of vehicle drive characteristics. The objective of this Diploma Thesis is to investigate the possibilities of electrical drive application for new principle of parallel hybrid vehicle system. Electric motor calculations, selection of most suitable control system and other calculations are needed. This work is not final work for such topic. Further investigation with more precise calculations, modeling, measurements and cost calculations are needed to answer the question if such system is efficient.

The effects of real time control of welding parameters on weld quality in plasma arc keyhole welding

Joints intended for welding frequently show variations in geometry and position, for which it is unfortunately not possible to apply a single set of operating parameters to ensure constant quality. The cause of this difficulty lies in a number of factors, including inaccurate joint preparation and joint fit up, tack welds, as well as thermal distortion of the workpiece. In plasma arc keyhole welding of butt joints, deviations in the gap width may cause weld defects such as an incomplete weld bead, excessive penetration and burn through. Manual adjustment of welding parameters to compensate for variations in the gap width is very difficult, and unsatisfactory weld quality is often obtained. In this study a control system for plasma arc keyhole welding has been developed and used to study the effects of the real time control of welding parameters on gap tolerance during welding of austenitic stainless steel AISI 304L. The welding tests demonstrated the beneficial effect of real time control on weld quality. Compared with welding using constant parameters, the maximum tolerable gap width with an acceptable weld quality was 47% higher when using the real time controlled parameters for a plate thickness of 5 mm. In addition, burn through occurred with significantly larger gap widths when parameters were controlled in real time. Increased gap tolerance enables joints to be prepared and fit up less accurately, saving time and preparation costs for welding. In addition to the control system, a novel technique for back face monitoring is described in this study. The test results showed that the technique could be successfully applied for penetration monitoring when welding non magnetic materials. The results also imply that it is possible to measure the dimensions of the plasma efflux or weld root, and use this information in a feedback control system and, thus, maintain the required weld quality.

Improving Cross Direction Basis Weight Profile in a Fourdrinier Paper Machine

The purpose of this study was to improve PM7’s basis weight CD profile in Stora Enso’s Berghuizer mill and to search mechanical defects which affect to the formation of the basis weight CD profile. In the theoretical part PM7’s structure was presented and the formation of the basis weight and caliper CD profiles was examined as well as disturbances which are affecting to the formation. The function of the control system was scrutinised for the side of CD profiles as well as the formation of the measured CD profiles. Tuning of the control system was examined through the response model and filtering. Specification of the response model and filtering was explained and how to determine 2sigma statistical number. In the end of the theoretical part ATPA hardware and a new profile browser were introduced. In the experimental part focus was in the beginning to search and remove mechanical defects which are affecting to CD profiles. The next step was to verify the reliability of the online measurements, to study the stability of the basis weight CD profile and to find out so called fingerprint, a basis weight CD profile which is unique for each paper machine. New response model and filtering value for basis weight CD profile was determined by bump tests. After a follow up period the affect of the new response model and filtering was analysed.

Simulating the performance of paper machine control

The topic of this thesis is the simulation of a combination of several control and data assimilation methods, meant to be used for controlling the quality of paper in a paper machine. Paper making is a very complex process and the information obtained from the web is sparse. A paper web scanner can only measure a zig zag path on the web. An assimilation method is needed to process estimates for Machine Direction (MD) and Cross Direction (CD) profiles of the web. Quality control is based on these measurements. There is an increasing need for intelligent methods to assist in data assimilation. The target of this thesis is to study how such intelligent assimilation methods are affecting paper web quality. This work is based on a paper web simulator, which has been developed in the TEKES funded MASI NoTes project. The simulator is a valuable tool in comparing different assimilation methods. The thesis contains the comparison of four different assimilation methods. These data assimilation methods are a first order Bayesian model estimator, an ARMA model based on a higher order Bayesian estimator, a Fourier transform based Kalman filter estimator and a simple block estimator. The last one can be considered to be close to current operational methods. From these methods Bayesian, ARMA and Kalman all seem to have advantages over the commercial one. The Kalman and ARMA estimators seems to be best in overall performance.

Modeling and Control of the Power Conversion Unit in a Solid Oxide Fuel Cell Environment

In this doctoral thesis, a power conversion unit for a 10 kWsolid oxide fuel cell is modeled, and a suitable control system is designed. The need for research was identified based on an observation that there was no information available about the characteristics of the solid oxide fuel cell from the perspective of power electronics and the control system, and suitable control methods had not previously been studied in the literature. In addition, because of the digital implementation of the control system, the inherent characteristics of the digital system had to be taken into account in the characteristics of the solid oxide fuel cell (SOFC). The characteristics of the solid oxide fuel cell as well the methods for the modeling and control of the DC/DC converter and the grid converter are studied by a literature survey. Based on the survey, the characteristics of the SOFC as an electrical power source are identified, and a solution to the interfacing of the SOFC in distributed generation is proposed. A mathematical model of the power conversion unit is provided, and the control design for the DC/DC converter and the grid converter is made based on the proposed interfacing solution. The limit cycling phenomenon is identified as a source of low-frequency current ripple, which is found to be insignificant when connected to a grid-tied converter. A method to mitigate a second harmonic originating from the grid interface is proposed, and practical considerations of the operation with the solid oxide fuel cell plant are presented. At the theoretical level, the thesis discusses and summarizes the methods to successfully derive a model for a DC/DC converter, a grid converter, and a power conversion unit. The results of this doctoral thesis can also be used in other applications, and the models and methods can be adopted to similar applications such as photovoltaic systems. When comparing the results with the objectives of the doctoral thesis, we may conclude that the objectives set for the work are met. In this doctoral thesis, theoretical and practical guidelines are presented for the successful control design to connect a SOFC-based distributed generation plant to the utility grid.

One chip solution for low-cost active magnetic bearing system

In this work the implementation of the active magnetic bearing control system in a single FPGA is studied. Requirements for the full magnetic bearing control system are reviewed. Different control methods for active magnetic bearings are described shortly. Flux and the current base controllers are implemented in a FPGA. Suitability of the con-trollers for a low-cost magnetic bearing application is studied. Floating-point arithmetic’s are used in the controllers to ease designing burden and improve calculation precision. Per-formance of the flux controller is verified with simulations.

Kaasupoljinohjeen toteuttaminen hybridilinja-auton säätöjärjestelmälle

Sähkö- ja hybridiajoneuvot yleistyvät tiukentuvien päästömääräysten seurauksena, koska sähkömoottoritekniikan avulla ajoneuvon kokonaishyötysuhdetta on mahdollista parantaa merkittävästi. Akkujen kapasiteettiin, kokoon, painoon ja latausaikoihin liittyvien ongelmien vuoksi sekä nestemäistä polttoainetta että sähköä hyödyntävä hybriditekniikka on toistaiseksi pelkkään sähkökäyttöön verrattuna usein toimivampi toteutus. Vanhojen hyötyajoneuvojen hybridikonversiot saattavatkin yleistyä, jos voidaan osoittaa, että konversio on toteutettavissa järkevin resurssein ja voidaan laatia konversion teknisiä haasteita helpottavia ohjeita. Syksyllä 2012 käynnistyi Lappeenrannan Teknillisen Yliopiston vetämä CAMBUS-projekti, jossa on tarkoitus kehittää kaupallisesti tarjolla olevia järjestelmiä pätevämpi hybriditekniikka linja-autokäyttöön. Tämä kandidaatintyö pyrkii kirjallisuuskatsauksen keinoin selvittämään, minkälainen kaasupolkimen toteutus olisi tätä hybridikonversiota ajatellen paras kuljettajan kontrolloiman säätöohjeen käytännön toteutukseen. Lähdemateriaalina on käytetty mm. Boschin ja Automobiltechnische Zeitschriftin ajoneuvoalan käsikirjoja ja oppikirjoja, Volkswagenin koulutuskäsikirjoja ja täydentävästi tieteellisiä artikkeleita ja patentteja. Niiden pohjalta on koottu yleisimmät tämänhetkiset tekniset toteutustavat, pohdittu tiedonsiirron ja sähkömagneettisen yhteensopivuuden haasteita, sekä kokonaissäätöjärjestelmän näkökulmasta säätöohjeen suuretta. Selvityksen perusteella polkimen asentotunnistuksen kannalta oleellista on turvallisuus, eli lähinnä mekaaninen kestävyys ja riittävä häiriösuojaus. Ajoneuvossa ilmeneviä voimakkaita magneettikenttiä hyvin sietävä digitaalinen väyläjärjestelmä voi hyvin toteutettuna myös yksinkertaistaa ajoneuvon sähköjärjestelmän muuta toteutusta. Aineistojen perusteella vääntömomentti on luonnollisin valinta ohjaussuureeksi. Vääntömomenttiohjeen avulla voidaan helposti luoda selkeä ja johdonmukainen tuntuma kuljettajalle voimanlähteiden turvalliseen hallintaan ja se helpottaa myös kommunikointia pidonhallintajärjestelmän ja muiden ajoneuvon hallintaan liittyvien järjestelmien kanssa.

Flexible multibody dynamics and intelligent control of a hydraulically driven hybrid redundant robot machine

The assembly and maintenance of the International Thermonuclear Experimental Reactor (ITER) vacuum vessel (VV) is highly challenging since the tasks performed by the robot involve welding, material handling, and machine cutting from inside the VV. The VV is made of stainless steel, which has poor machinability and tends to work harden very rapidly, and all the machining operations need to be carried out from inside of the ITER VV. A general industrial robot cannot be used due to its poor stiffness in the heavy duty machining process, and this will cause many problems, such as poor surface quality, tool damage, low accuracy. Therefore, one of the most suitable options should be a light weight mobile robot which is able to move around inside of the VV and perform different machining tasks by replacing different cutting tools. Reducing the mass of the robot manipulators offers many advantages: reduced material costs, reduced power consumption, the possibility of using smaller actuators, and a higher payload-to-robot weight ratio. Offsetting these advantages, the lighter weight robot is more flexible, which makes it more difficult to control. To achieve good machining surface quality, the tracking of the end effector must be accurate, and an accurate model for a more flexible robot must be constructed. This thesis studies the dynamics and control of a 10 degree-of-freedom (DOF) redundant hybrid robot (4-DOF serial mechanism and 6-DOF 6-UPS hexapod parallel mechanisms) hydraulically driven with flexible rods under the influence of machining forces. Firstly, the flexibility of the bodies is described using the floating frame of reference method (FFRF). A finite element model (FEM) provided the Craig-Bampton (CB) modes needed for the FFRF. A dynamic model of the system of six closed loop mechanisms was assembled using the constrained Lagrange equations and the Lagrange multiplier method. Subsequently, the reaction forces between the parallel and serial parts were used to study the dynamics of the serial robot. A PID control based on position predictions was implemented independently to control the hydraulic cylinders of the robot. Secondly, in machining, to achieve greater end effector trajectory tracking accuracy for surface quality, a robust control of the actuators for the flexible link has to be deduced. This thesis investigates the intelligent control of a hydraulically driven parallel robot part based on the dynamic model and two schemes of intelligent control for a hydraulically driven parallel mechanism based on the dynamic model: (1) a fuzzy-PID self-tuning controller composed of the conventional PID control and with fuzzy logic, and (2) adaptive neuro-fuzzy inference system-PID (ANFIS-PID) self-tuning of the gains of the PID controller, which are implemented independently to control each hydraulic cylinder of the parallel mechanism based on rod length predictions. The serial component of the hybrid robot can be analyzed using the equilibrium of reaction forces at the universal joint connections of the hexa-element. To achieve precise positional control of the end effector for maximum precision machining, the hydraulic cylinder should be controlled to hold the hexa-element. Thirdly, a finite element approach of multibody systems using the Special Euclidean group SE(3) framework is presented for a parallel mechanism with flexible piston rods under the influence of machining forces. The flexibility of the bodies is described using the nonlinear interpolation method with an exponential map. The equations of motion take the form of a differential algebraic equation on a Lie group, which is solved using a Lie group time integration scheme. The method relies on the local description of motions, so that it provides a singularity-free formulation, and no parameterization of the nodal variables needs to be introduced. The flexible slider constraint is formulated using a Lie group and used for modeling a flexible rod sliding inside a cylinder. The dynamic model of the system of six closed loop mechanisms was assembled using Hamilton’s principle and the Lagrange multiplier method. A linearized hydraulic control system based on rod length predictions was implemented independently to control the hydraulic cylinders. Consequently, the results of the simulations demonstrating the behavior of the robot machine are presented for each case study. In conclusion, this thesis studies the dynamic analysis of a special hybrid (serialparallel) robot for the above-mentioned special task involving the ITER and investigates different control algorithms that can significantly improve machining performance. These analyses and results provide valuable insight into the design and control of the parallel robot with flexible rods.

Adaptive control of Hydraulic Drive

Adaptive control systems are one of the most significant research directions of modern control theory. It is well known that every mechanical appliance’s behavior noticeably depends on environmental changes, functioning-mode parameter changes and changes in technical characteristics of internal functional devices. An adaptive controller involved in control process allows reducing an influence of such changes. In spite of this such type of control methods is applied seldom due to specifics of a controller designing. The work presented in this paper shows the design process of the adaptive controller built by Lyapunov’s function method for the Hydraulic Drive. The calculation needed and the modeling were conducting with MATLAB® software including Simulink® and Symbolic Math Toolbox™ etc. In the work there was applied the Jacobi matrix linearization of the object’s mathematical model and derivation of the suitable reference models based on Newton’s characteristic polynomial. The intelligent adaptive to nonlinearities algorithm for solving Lyapunov’s equation was developed. Developed algorithm works properly but considered plant is not met requirement of functioning with. The results showed confirmation that adaptive systems application significantly increases possibilities in use devices and might be used for correction a system’s behavior dynamics.

Stiffness based trajectory planning and feedforward based vibration suppression control of parallel robot machines

The dissertation proposes two control strategies, which include the trajectory planning and vibration suppression, for a kinematic redundant serial-parallel robot machine, with the aim of attaining the satisfactory machining performance. For a given prescribed trajectory of the robot's end-effector in the Cartesian space, a set of trajectories in the robot's joint space are generated based on the best stiffness performance of the robot along the prescribed trajectory. To construct the required system-wide analytical stiffness model for the serial-parallel robot machine, a variant of the virtual joint method (VJM) is proposed in the dissertation. The modified method is an evolution of Gosselin's lumped model that can account for the deformations of a flexible link in more directions. The effectiveness of this VJM variant is validated by comparing the computed stiffness results of a flexible link with the those of a matrix structural analysis (MSA) method. The comparison shows that the numerical results from both methods on an individual flexible beam are almost identical, which, in some sense, provides mutual validation. The most prominent advantage of the presented VJM variant compared with the MSA method is that it can be applied in a flexible structure system with complicated kinematics formed in terms of flexible serial links and joints. Moreover, by combining the VJM variant and the virtual work principle, a systemwide analytical stiffness model can be easily obtained for mechanisms with both serial kinematics and parallel kinematics. In the dissertation, a system-wide stiffness model of a kinematic redundant serial-parallel robot machine is constructed based on integration of the VJM variant and the virtual work principle. Numerical results of its stiffness performance are reported. For a kinematic redundant robot, to generate a set of feasible joints' trajectories for a prescribed trajectory of its end-effector, its system-wide stiffness performance is taken as the constraint in the joints trajectory planning in the dissertation. For a prescribed location of the end-effector, the robot permits an infinite number of inverse solutions, which consequently yields infinite kinds of stiffness performance. Therefore, a differential evolution (DE) algorithm in which the positions of redundant joints in the kinematics are taken as input variables was employed to search for the best stiffness performance of the robot. Numerical results of the generated joint trajectories are given for a kinematic redundant serial-parallel robot machine, IWR (Intersector Welding/Cutting Robot), when a particular trajectory of its end-effector has been prescribed. The numerical results show that the joint trajectories generated based on the stiffness optimization are feasible for realization in the control system since they are acceptably smooth. The results imply that the stiffness performance of the robot machine deviates smoothly with respect to the kinematic configuration in the adjacent domain of its best stiffness performance. To suppress the vibration of the robot machine due to varying cutting force during the machining process, this dissertation proposed a feedforward control strategy, which is constructed based on the derived inverse dynamics model of target system. The effectiveness of applying such a feedforward control in the vibration suppression has been validated in a parallel manipulator in the software environment. The experimental study of such a feedforward control has also been included in the dissertation. The difficulties of modelling the actual system due to the unknown components in its dynamics is noticed. As a solution, a back propagation (BP) neural network is proposed for identification of the unknown components of the dynamics model of the target system. To train such a BP neural network, a modified Levenberg-Marquardt algorithm that can utilize an experimental input-output data set of the entire dynamic system is introduced in the dissertation. Validation of the BP neural network and the modified Levenberg- Marquardt algorithm is done, respectively, by a sinusoidal output approximation, a second order system parameters estimation, and a friction model estimation of a parallel manipulator, which represent three different application aspects of this method.