Active du/dt Filtering for Variable-Speed AC Drives

An oscillating overvoltage has become a common phenomenon at the motor terminal in inverter-fed variable-speed drives. The problem has emerged since modern insulated gate bipolar transistors have become the standard choice as the power switch component in lowvoltage frequency converter drives. Theovervoltage phenomenon is a consequence of the pulse shape of inverter output voltage and impedance mismatches between the inverter, motor cable, and motor. The overvoltages are harmful to the electric motor, and may cause, for instance, insulation failure in the motor. Several methods have been developed to mitigate the problem. However, most of them are based on filtering with lossy passive components, the drawbacks of which are typically their cost and size. In this doctoral dissertation, application of a new active du/dt filtering method based on a low-loss LC circuit and active control to eliminate the motor overvoltages is discussed. The main benefits of the method are the controllability of the output voltage du/dt within certain limits, considerably smaller inductances in the filter circuit resulting in a smaller physical component size, and excellent filtering performance when compared with typical traditional du/dt filtering solutions. Moreover, no additional components are required, since the active control of the filter circuit takes place in the process of the upper-level PWM modulation using the same power switches as the inverter output stage. Further, the active du/dt method will benefit from the development of semiconductor power switch modules, as new technologies and materials emerge, because the method requires additional switching in the output stage of the inverter and generation of narrow voltage pulses. Since additional switching is required in the output stage, additional losses are generated in the inverter as a result of the application of the method. Considerations on the application of the active du/dt filtering method in electric drives are presented together with experimental data in order to verify the potential of the method.

Uso de hardware de código fonte aberto "Arduino" para acionamento de dispositivo solenoide em sistemas de análises em fluxo

This paper describes the use of the open source hardware platform, denominated "Arduino", for controlling solenoid valves for solutions handling in flow analysis systems. System assessment was carried out by spectrophotometric determination of iron (II) in natural water. The sampling rate was estimated as 45 determinations per hour and the coefficient of variation was lower than 3%. Per determination, 208 µg of 1-10-phenanthroline and ascorbic acid were consumed, generating 1.3 mL of waste. "Arduino" proved a reliable microcontroller with low cost and simple interfacing, allowing USB communication for solenoid device switching in flow systems.

DISPOSITIVO PARA EXTRAÇÃO LÍQUIDO-LÍQUIDO EM SISTEMAS DE ANÁLISES EM FLUXO

AbstractA device comprising a lab-made chamber with mechanical stirring and computer-controlled solenoid valves is proposed for the mechanization of liquid-liquid extractions. The performance was demonstrated by the extraction of ethanol from biodiesel as a model of the extraction of analytes from organic immiscible samples to an aqueous medium. The volumes of the sample and extractant were precisely defined by the flow-rates and switching times of the valves, while the mechanic stirring increased interaction between the phases. Stirring was stopped for phase separation, and a precise time-control also allowed a successful phase separation (i.e., the absence of the organic phase in the aqueous extract). In the model system, a linear response between the analytical response and the number of extractions was observed, indicating the potential for analyte preconcentration in the extract. The efficiency and reproducibility of the extractions were demonstrated by recoveries of ethanol spiked to biodiesel samples within 96% and 100% with coefficients of variation lower than 3.0%.

Thermal modelling of semiconductor switches in three-level Neutral Point Clamped Medium Voltage DTC-inverter

The aim of this thesis is to investigate the thermal loading of medium voltage three-level NPC inverter’s semiconductor IGCT switches in different operation points. The objective is to reach both a fairly accurate off-line simulation program and also so simple a simulation model that its implementation into an embedded system could be reasonable in practice and a real time use should become feasible. Active loading limitation of the inverter can be realized with a thermal model which is practical in a real time use. Determining of the component heating has been divided into two parts; defining of component losses and establishing the structure of a thermal network. Basics of both parts are clarified. The simulation environment is Matlab-Simulink. Two different models are constructed – a more accurate one and a simplified one. Potential simplifications are clarified with the help of the first one. Simplifications are included in the latter model and the functionalities of both models are compared. When increasing the calculation time step a decreased number of considered components and time constants of the thermal network can be used in the simplified model. Heating of a switching component is dependent on its topological position and inverter’s operation point. The output frequency of the converter defines mainly which one of the switching components is – because of its losses and heating – the performance limiting component of the converter. Comparison of results given by different thermal models demonstrates that with larger time steps, describing of fast occurring switching losses becomes difficult. Generally articles and papers dealing with this subject are written for two-level inverters. Also inverters which apply direct torque control (DTC) are investigated rarely from the heating point of view. Hence, this thesis completes the former material.

Multilevel converter modulation: implementation and analysis

Multilevel converters provide an attractive solution to bring the benefits of speed-controlled rotational movement to high-power applications. Therefore, multilevel inverters have attracted wide interest in both the academic community and in the industry for the past two decades. In this doctoral thesis, modulation methods suitable especially for series connected H-bridge multilevel inverters are discussed. A concept of duty cycle modulation is presented and its modification is proposed. These methods are compared with other well-known modulation schemes, such as space-vector pulse width modulation and carrier-based modulation schemes. The advantage of the modified duty-cycle modulation is its algorithmic simplicity. A similar mathematical formulation for the original duty cycle modulation is proposed. The modified duty cycle modulation is shown to produce well-formed phase-to-neutral voltages that have lower total harmonic distortion than the space-vector pulse width modulation and the duty cycle modulation. The space-vector-based solution and the duty cycle modulation, on the other hand, result in a better-quality line-to-line voltage and current waveform. The voltage of the DC links in the modules of the series-connected H-bridge inverter are shown to fluctuate while they are under load. The fluctuation causes inaccuracies in the voltage production, which may result in a failure of the flux estimator in the controller. An extension for upper-level modulation schemes, which changes the switching instants of the inverter so that the output voltage meets the reference voltage accurately regardless of the DC link voltages, is proposed. The method is shown to reduce the error to a very low level when a sufficient switching frequency is used. An appropriate way to organize the switching instants of the multilevel inverter is to make only one-level steps at a time. This causes restrictions on the dynamical features of the modulation schemes. The produced voltage vector cannot be rotated several tens of degrees in a single switching period without violating the above-mentioned one-level-step rule. The dynamical capabilities of multilevel inverters are analyzed in this doctoral thesis, and it is shown that the multilevel inverters are capable of operating even in dynamically demanding metal industry applications. In addition to the discussion on modulation schemes, an overvoltage in multilevel converter drives caused by cable reflection is addressed. The voltage reflection phenomenon in drives with long feeder cables causes premature insulation deterioration and also affects the commonmode voltage, which is one of the main reasons for bearing currents. Bearing currents, on the other hand, cause fluting in the bearings, which results in premature bearing failure. The reflection phenomenon is traditionally prevented by filtering, but in this thesis, a modulationbased filterless method to mitigate the overvoltage in multilevel drives is proposed. Moreover, the mitigation method can be implemented as an extension for upper-level modulation schemes. The method exploits the oscillations caused by two consecutive voltage edges so that the sum of the oscillations results in a mitigated peak of the overvoltage. The applicability of the method is verified by simulations together with experiments with a full-scale prototype.

Parallel-Operating Three-Phase Voltage Source Inverters – Circulating CurrentModeling, Analysis and Mitigation

The maximum realizable power throughput of power electronic converters may be limited or constrained by technical or economical considerations. One solution to this problemis to connect several power converter units in parallel. The parallel connection can be used to increase the current carrying capacity of the overall system beyond the ratings of individual power converter units. Thus, it is possible to use several lower-power converter units, produced in large quantities, as building blocks to construct high-power converters in a modular manner. High-power converters realized by using parallel connection are needed for example in multimegawatt wind power generation systems. Parallel connection of power converter units is also required in emerging applications such as photovoltaic and fuel cell power conversion. The parallel operation of power converter units is not, however, problem free. This is because parallel-operating units are subject to overcurrent stresses, which are caused by unequal load current sharing or currents that flow between the units. Commonly, the term ’circulatingcurrent’ is used to describe both the unequal load current sharing and the currents flowing between the units. Circulating currents, again, are caused by component tolerances and asynchronous operation of the parallel units. Parallel-operating units are also subject to stresses caused by unequal thermal stress distribution. Both of these problemscan, nevertheless, be handled with a proper circulating current control. To design an effective circulating current control system, we need information about circulating current dynamics. The dynamics of the circulating currents can be investigated by developing appropriate mathematical models. In this dissertation, circulating current models aredeveloped for two different types of parallel two-level three-phase inverter configurations. Themodels, which are developed for an arbitrary number of parallel units, provide a framework for analyzing circulating current generation mechanisms and developing circulating current control systems. In addition to developing circulating current models, modulation of parallel inverters is considered. It is illustrated that depending on the parallel inverter configuration and the modulation method applied, common-mode circulating currents may be excited as a consequence of the differential-mode circulating current control. To prevent the common-mode circulating currents that are caused by the modulation, a dual modulator method is introduced. The dual modulator basically consists of two independently operating modulators, the outputs of which eventually constitute the switching commands of the inverter. The two independently operating modulators are referred to as primary and secondary modulators. In its intended usage, the same voltage vector is fed to the primary modulators of each parallel unit, and the inputs of the secondary modulators are obtained from the circulating current controllers. To ensure that voltage commands obtained from the circulating current controllers are realizable, it must be guaranteed that the inverter is not driven into saturation by the primary modulator. The inverter saturation can be prevented by limiting the inputs of the primary and secondary modulators. Because of this, also a limitation algorithm is proposed. The operation of both the proposed dual modulator and the limitation algorithm is verified experimentally.

Induction Motor Drive Energy Efficiency - Simulation and Analysis

A coupled system simulator, based on analytical circuit equations and a finite element method (FEM) model of the motor has been developed and it is used to analyse a frequency-converterfed industrial squirrel-cage induction motor. Two control systems that emulate the behaviour of commercial direct-torque-controlled (DTC) and vector-controlled industrial frequency converters have been studied, implemented in the simulation software and verified by extensive laboratory tests. Numerous factors that affect the operation of a variable speed drive (VSD) and its energy efficiency have been investigated, and their significance in the simulation of the VSD results has been studied. The dependency of the frequency converter, induction motor and system losses on the switching frequency is investigated by simulations and measurements at different speeds for both the vector control and the DTC. Intensive laboratory measurements have been carried out to verify the simulation results.

Non-Markovianity and Quantum Correlations in Qubit-Systems

In this Thesis I discuss the exact dynamics of simple non-Markovian systems. I focus on fundamental questions at the core of non-Markovian theory and investigate the dynamics of quantum correlations under non-Markovian decoherence. In the first context I present the connection between two different non-Markovian approaches, and compare two distinct definitions of non-Markovianity. The general aim is to characterize in exemplary cases which part of the environment is responsible for the feedback of information typical of non- Markovian dynamics. I also show how such a feedback of information is not always described by certain types of master equations commonly used to tackle non-Markovian dynamics. In the second context I characterize the dynamics of two qubits in a common non-Markovian reservoir, and introduce a new dynamical effect in a wellknown model, i.e., two qubits under depolarizing channels. In the first model the exact solution of the dynamics is found, and the entanglement behavior is extensively studied. The non-Markovianity of the reservoir and reservoirmediated-interaction between the qubits cause non-trivial dynamical features. The dynamical interplay between different types of correlations is also investigated. In the second model the study of quantum and classical correlations demonstrates the existence of a new effect: the sudden transition between classical and quantum decoherence. This phenomenon involves the complete preservation of the initial quantum correlations for long intervals of time of the order of the relaxation time of the system.

Studies on the Multifaceted Interaction of Atoms and an Electromagnetic Field

In this Thesis the interaction of an electromagnetic field and matter is studied from various aspects in the general framework of cold atoms. Our subjects cover a wide spectrum of phenomena ranging from semiclassical few-level models to fully quantum mechanical interaction with structured reservoirs leading to non-Markovian open quantum system dynamics. Within closed quantum systems, we propose a selective method to manipulate the motional state of atoms in a time-dependent double-well potential and interpret the method in terms of adiabatic processes. Also, we derive a simple wave-packet model, based on distributions of generalized eigenstates, explaining the finite visibility of interference in overlapping continuous-wave atom lasers. In the context of open quantum systems, we develop an unraveling of non-Markovian dynamics in terms of piecewise deterministic quantum jump processes confined in the Hilbert space of the reduced system - the non-Markovian quantum jump method. As examples, we apply it for simple 2- and 3-level systems interacting with a structured reservoir. Also, in the context of ion-cavity QED we study the entanglement generation based on collective Dicke modes in experimentally realistic conditions including photonic losses and an atomic spontaneous decay.

Regulation of B Cell Gene Expression and Function by Ikaros, Helios and Bcl6

B lymphocytes constitute a key branch of adaptive immunity by providing specificity to recognize a vast variety of antigens by B cell antigen receptors (BCR) and secreted antibodies. Antigen recognition activates the cells and can produce antibody secreting plasma cells via germinal center reaction that leads to the maturation of antigen recognition affinity and switching of antibody effector class. The specificity of antigen recognition is achieved through a multistep developmental pathway that is organized by interplay of transcription factors and signals through BCR. Lymphoid malignancies arise from different stages of development in abnormal function of transcriptional regulation. To understand the B cell development and the function of B cells, a thorough understanding of the regulation of gene expression is important. The transcription factors of the Ikaros family and Bcl6 are frequently associated with lymphoma generation. The aim of this study was to reveal the targets of Ikaros, Helios and Bcl6 mediated gene regulation and to find out the function of Ikaros and Helios in B cells. This study uses gene targeted DT40 B cell lines and establishes a role for Ikaros family factors Ikaros and Helios in the regulation of BCR signaling that is important at developmental checkpoints, for cell survival and in activation. Ikaros and Helios had opposing roles in the regulation of BCR signals. Ikaros was found to directly repress the SHIP gene that encodes a signaling lipid-metabolizing enzyme, whereas Helios had activating effect on SHIP expression. The findings demonstrate a balancing function for these two Ikaros family transcription factors in the regulation of BCR signaling as well as in the regulation of gene expression. Bcl6 was found to repress plasma cell gene expression program while maintaining gene expression profile of B cells. Analysis of direct Bcl6 target genes suggested novel mechanisms for Bcl6-mediated suppression of plasma cell differentiation and promoting germinal center phenotype.

Ja vet int va de heter på svenska : interaktion mellan tvåspråkiga elever och deras lärare i en enspråkig klassrumsdiskurs

This is a study about language and learning aspects in the interaction between pupils and teachers in classrooms, where the majority of the pupils are bilingual. The aim of the dissertation is to develop the understanding of interactional learning possibilities and constraints in relation to a bilingual context. Language related learning is used as an overall conception which covers learning related to classroom discourse, language and subject. The empirical study has been made in a Swedish speaking school in a strongly Finnish dominated environment in the south of Finland. In the material, mainly consisting of video recorded lessons in forms one to three, the interaction between the pupils and the teachers is analysed. Building on a social constructionist perspective, where learning is regarded as a social phenomenon, situated and visible in changing participation, sequences where pupils or teachers make the language relevant are emphasised. The sequences are analysed in line with the conversation analytic (CA) approach. A fundamental result is an understanding of a monolingual classroom discourse, jointly constructed by teachers and pupils and visible in the pupils' interactionally problematized code-switching. This means that the pupils are not victims of a top-driven language policy; they are active co-constructors of the monolingual discourse. Through different repair initiations the pupils are doing interactional work in positioning themselves correctly in the monolingual discourse, which they simultaneously maintain. This work has a price in relation to time, knowledge and exactness. The pupils' problematized code-switching is often directly and shortly repaired by the teachers. This kind of repair promotes the pupils' participation and is not, as opposed to the results of research in everyday talk, dispreferred in pupil-teacher talk. When the pupils use the possibility to, in a comparatively easy way, participate and thus express their knowledge through codeswitching, and simultaneously talk a monolingual discourse into being, the teacher can, through direct repair, show an understanding in regard to the content, facilitate language learning and simultaneously confirm the pupils as competent speakers and bilingual individuals. Furthermore, significant results show that the monolingual norm has a function of a contrasting background which gives the pupils and the teachers a possibility to use language alternation as a functional and meaningful activity. The pupils use codeswitching as a way of protesting or expressing non-participation in the classroom talk. By making the pupils' bilingualism relevant, the teachers express understanding and empathy and encourage the pupils' participation in the classroom talk. Bilingualism is a nonpreferred, but functioning, resource in the interaction between pupils and teachers.

Vaihtosuuntaajan reaaliaikainen lämpömalli

Vaihtosuuntaajan IGBT-moduulin liitosten lämpötiloja ei voida suoraan mitata, joten niiden arviointiin tarvitaan reaaliaikainen lämpömalli. Tässä työssä on tavoitteena kehittää tähän tarkoitukseen C-kielellä implementoitu ratkaisu, joka on riittävän tarkka ja samalla mahdollisimman laskennallisesti tehokas. Ohjelmallisen toteutuksen täytyy myös sopia erilaisille moduulityypeille ja sen on tarvittaessa otettava huomioon saman moduulin muiden sirujen lämmittävä vaikutus toisiinsa. Kirjallisuuskatsauksen perusteella valitaan olemassa olevista lämpömalleista käytännön toteutuksen pohjaksi lämpöimpedanssimatriisiin perustuva malli. Lämpöimpedanssimatriisista tehdään Simulink-ohjelmalla s-tason simulointimalli, jota käytetään referenssinä muun muassa implementoinnin tarkkuuden verifiointiin. Lämpömalli tarvitsee tiedon vaihtosuuntaajan häviöistä, joten työssä on selvitetty eri vaihtoehtoja häviölaskentaan. Lämpömallin kehittäminen s-tason mallista valmiiksi C-kieliseksi koodiksi on kuvattu tarkasti. Ensin s-tason malli diskretoidaan z-tasoon. Z-tason siirtofunktiot muutetaan puolestaan ensimmäisen kertaluvun differenssiyhtälöiksi. Työssä kehitetty monen aikatason lämpömalli saadaan jakamalla ensimmäisen kertaluvun differenssiyhtälöt eri aikatasoille suoritettavaksi sen mukaan, mikä niiden kuvaileman termin vaatima päivitysnopeus on. Tällainen toteutus voi parhaimmillaan kuluttaa alle viidesosan kellojaksoja verrattuna suoraviivaiseen yhden aikatason toteutukseen. Implementoinnin tarkkuus on hyvä. Implementoinnin vaatimia suoritusaikoja testattiin Texas Instrumentsin TMS320C6727- prosessorilla (300 MHz). Esimerkkimallin laskemisen määritettiin kuluttavan vaihtosuuntaajan toimiessa 5 kHz kytkentätaajuudella vain 0,4 % prosessorin kellojaksoista. Toteutuksen tarkkuus ja laskentakapasiteetin vähäinen vaatimus mahdollistavat lämpömallin käyttämisen lämpösuojaukseen ja lisäämisen osaksi muuta jo prosessorilla olemassa olevaa systeemiä.

Vuotasapainon hallinta kokosiltasyötetyssä muuntajassa

Keskitaajuudella toimivia muuntajia käytetään laajalti tehoelektroniikkasovelluksissa kuten DC/DC-konverttereissa ja muissa hakkuriteholähteissä. Muuntaja on induktiivinen komponentti, jonka magneettisen tasapainon säilyttäminen hakkuriteholähteissä on laitteen virheettömän toiminnan kannalta tärkeää. Muuntajaa syöttävän virtapiirin on muodostettava symmetrinen syöttöjännite, jotta muuntajan vuo ei ajaudu positiiviseen tai negatiiviseen kyllästykseen. Tässä diplomityössä esitetään muuntajan sähkömagneettinen toimintaperiaate, kyllästymisen syyt hakkuriteholähteissä sekä kehitetään aktiivinen ohjaus vuotasapainon säilyttämiseksi. Hakkuriteholähteissä käytettävissä muuntajissa on monesti useampi kuin kaksi käämiä. Tässä työssä tutkittavassa muuntajassa on useita ensiöitä ja useita toisioita ja muuntajaa syötetään keskitaajuudella. Tämä tuo uusia ongelmia verrattuna perinteiseen yksivaiheiseen DC/DC-konvertteriin. Näihin ongelmiin esitetään ratkaisut diplomityön tutkimuksessa.

Esiopetuskirjojen harjoitukset kielellisen tietoisuuden kehittäjinä

Tutkimus oli kasvatustieteellinen varhaiskasvatuksen alan tutkimus, jossa hyödynnettiin kielitieteellistä käsitteistöä. Tutkimuksen kohteena olivat esiopetuskirjojen kielellisen tietoisuuden harjoitukset. Aineistona oli 12 esiopetuksen harjoituskirjaa ja opettajan opasta. Kirjoissa oli yhteensä yli 2000 sivua ja yli 1300 harjoitusta. Tarkemmassa analyysissä olleiden harjoitusten määrä oli noin 460. Analyysimenetelmänä käytettiin sisällönanalyysiä, jonka avulla tutkittiin, millaisia kielellisen tietoisuuden harjoituksia esiopetuskirjoissa oli ja miten harjoitukset etenivät. Kielellisen tietoisuuden harjoitukset luokiteltiin fonologisen, morfologisen ja syntaktisen tietoisuuden harjoituksiin. Fonologinen tietoisuus käsitettiin lapsen kyvyksi havaita ja käsitellä kielen äännerakennetta. Morfologisella tietoisuudella tarkoitettiin kykyä havaita ja käsitellä kielen morfeemeja eli pienimpiä merkityksellisiä osia. Syntaktisella tietoisuudella tarkoitettiin lapsen tietoisuutta siitä, miten lauseet rakentuvat. Olennaisiksi piirteiksi fonologisen tietoisuuden harjoituksissa identifioituivat harjoitusten edellyttämä tai harjoittama tietoisuuden taso, harjoitusten kohteena olevien lingvististen yksiköiden taso ja harjoitustyyppi sekä morfologisen ja syntaktisen tietoisuuden harjoituksissa tietoisuuden taso ja harjoitustyyppi. Tutkimuksessa luotiin aikaisempien tutkimusten pohjalta mallit siitä, miten eri harjoitukset etenisivät optimaalisesti lapsen kielellisen tietoisuuden kehittymisen kannalta. Eri harjoituskirjojen harjoitusten etenemistä verrattiin näihin malleihin. Fonologisen tietoisuuden harjoituksista voitiin tunnistaa viisi päätyyppiä, joista useat jakautuivat vielä alatyypeiksi. Harjoitusten alatyypit ilmaisivat yleensä harjoituksissa käytettävän kognitiivisen operaation – käytettiinkö harjoituksessa tunnistamista, yhdistämistä vai osiin jakamista. Tämä samoin kuin harjoituksessa käytetty lingvistinen yksikkö (sana, loppusointu, tavu tai äänne) ja tietoisuuden taso olivat yhteydessä harjoituksen vaikeuteen. Tutkimuksissa ja interventioissa esiopetusikäisilläkin käytettyjä muunteluharjoituksia, joissa sanasta tai tavusta poistetaan osa, siihen lisätään osa tai osaa siirretään, harjoituskirjoissa ei ollut. Morfologisen tietoisuuden harjoitukset kohdistuivat yhdyssanoihin, taivutuspäätteisiin tai johdoksiin. Syntaktisen tietoisuuden harjoituksista identifioitui yhdentoista harjoituslajin alatyypin kautta kuusi päätyyppiä. Tutkimusta voidaan hyödyntää esiopetuskirjojen arvioinnissa ja laatimisessa sekä varhaiskasvatus- ja esiopetuspedagogiikassa.

Algorithmic Solutions for Combinatorial Problems in Resource Management of Manufacturing Environments

This thesis studies the use of heuristic algorithms in a number of combinatorial problems that occur in various resource constrained environments. Such problems occur, for example, in manufacturing, where a restricted number of resources (tools, machines, feeder slots) are needed to perform some operations. Many of these problems turn out to be computationally intractable, and heuristic algorithms are used to provide efficient, yet sub-optimal solutions. The main goal of the present study is to build upon existing methods to create new heuristics that provide improved solutions for some of these problems. All of these problems occur in practice, and one of the motivations of our study was the request for improvements from industrial sources. We approach three different resource constrained problems. The first is the tool switching and loading problem, and occurs especially in the assembly of printed circuit boards. This problem has to be solved when an efficient, yet small primary storage is used to access resources (tools) from a less efficient (but unlimited) secondary storage area. We study various forms of the problem and provide improved heuristics for its solution. Second, the nozzle assignment problem is concerned with selecting a suitable set of vacuum nozzles for the arms of a robotic assembly machine. It turns out that this is a specialized formulation of the MINMAX resource allocation formulation of the apportionment problem and it can be solved efficiently and optimally. We construct an exact algorithm specialized for the nozzle selection and provide a proof of its optimality. Third, the problem of feeder assignment and component tape construction occurs when electronic components are inserted and certain component types cause tape movement delays that can significantly impact the efficiency of printed circuit board assembly. Here, careful selection of component slots in the feeder improves the tape movement speed. We provide a formal proof that this problem is of the same complexity as the turnpike problem (a well studied geometric optimization problem), and provide a heuristic algorithm for this problem.