CALVIN ENGR 315 - Overview and Control of DC and AC Motors

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I. NomenclatureII. IntroductionIII. Motor OverviewIV. Transfer FunctionsV. ControlVI. Time ConstantsVII. AcknowledgmentsVIII. ReferencesIX. BiographyAbstract— an overview of the differences in form andfunction between DC and AC motors. An in-depth analysis ofthe general differential equations and transfer functions of DCand AC motors. Strategies for controlling DC and AC motorsusing gain and PID control are discussed and analyzed in depth.Methods for determining the time constants of DC and ACmotors are discussed and analyzed.Index Terms – AC motors, Control systems, DC motors, Motor drives.I. NOMENCLATUREPID Proportional Integral DerivativeII. INTRODUCTIONMotors are an integral part of engineering in today’ssociety. They are used in a wide variety of applications, fromrunning fans to driving belts to turning wheels. Yet, despitetheir prevalence in the designs of undergraduate engineeringstudents, most such students have very little idea of howmotors actually work, or of how to control them safely anddependably. This paper describes both DC and AC motors,analyzes them from a control standpoint, and determinesadequate strategies for controlling them in a manner which isboth safe and reliable. Stepper and servo motors will not bediscussed here, as their form, function, and application areconsiderably different from that of DC and AC motors, andthe analysis of those four motor types would be too muchinformation to cover in this setting.III. MOTOR OVERVIEW To the uninformed observer, DC and AC motors appear tobe basically identical. Even though they seem to operate inessentially the same way, their physical structures, and thustheir range of applications, vary significantly. The brush DC motor is arguably the simplest variable-speed DC motor design, in addition to being the mostcommon. For these reasons, the brush design is the one beingdescribed and analyzed here. The brush DC motor (or all DCmotors, for that matter) is made up of a stator and a rotor(refer to Fig. 1 for all descriptions relating to the brush DCmotor). As the names suggest, the rotor (the circular portionof Fig. 1 made up of eight “T”-shaped parts) is the part of themotor that rotates during operation, while the stator (the darkblue block and light blue “fingers” around the rotor in Fig. 1)remains stationary during operation, relative to the motor’scasing and mounting [3]. The stator is made up of either awinding or a magnet, which creates magnetic flux in theThis work was done for Engineering 315 at Calvin College in GrandRapids, Michigan, in the fall of 2004. All software used in this paper wassupplied by Calvin College. This project was supported financially by CalvinCollege and Smiths Aerospace LLC.Brian Bouma works for Smiths Aerospace LLC and attends Calvin Collegein Grand Rapids, MI 49546 USA (e-mail: [email protected]).magnetic field formed between the stator and the rotor [3].For the simple analytical purposes herein, it makes nodifference whether a winding or a magnet is used in thestator, so the use of a magnet will be assumed. The rotor hasa winding on its surface, termed the armature, in whichelectromotive forces are induced by the magnetic field formedbetween the stator and the rotor [3]. The armature winding issupplied current through the collector (the yellow cylinderattached to the rotor in Fig. 1), on which the brushes (the twobrown tabs touching the collector) apply pressure [3]. Thecollector is mounted on the same shaft as the armature, andthe fixed brushes are connected to the armature terminals [3].Thus, the power to the motor runs through the brushes, intothe collector, and through the armature winding to producethe electromotive forces between the stator and the rotor (thepower cables are the red lines attached to the brushes in Fig.1). The brush-collector assembly provides current to thearmature windings in such a way that the current flows in onedirection when the windings are under a magnetic North pole(from the stator magnet), and in the other direction when thewindings are under a magnetic South pole [3]. The rotorwindings are made up of coils, called sections, all sectionsbeing of an equal number of turns (in Fig. 1, the eight coloredsets of line segments, two segments per set, on the “front” ofthe T-shaped parts of the rotor are the ends of the coils; thecoils run through the length of the rotor and wrap around theopposite end of the T-shaped parts of the rotor) [3]. Eachsection has two sides, which are inserted into two slots spacedapart a distance equal to the distance between the two fieldpoles [3]. This way, when the conductors of one side of asection are under the North pole, the conductors of the otherside of the same section are under the South pole [3]. Thesections of armature winding are all connected together, inseries, with the end of the last section being connected to thebeginning of the first section, so that the winding as a wholeis continuous, having no particular start or finish [3]. Forthis to work, each slot must contain two sides of sections (halfeach of two different sections) [3]. As the rotor rotates, whena section changes from being under the North pole to beingunder the South pole (and hence the current in that sectionreverses direction), that section commutates. Commutationof a section of the winding is the changing of the section frombeing under one pole to being under the other pole [3]. Twosections (two sections that are opposite each other on therotor) commutate at a time, one switching from North toSouth pole, the other switching from South to North pole.Because the two poles “swap” sections simultaneously, half ofthe windings are under each pole at all times. The North andSouth poles are an effect of the flux in the armature createdby the current flowing through the two sets of windings (eachpole containing one set). When a section commutates, thebrushes, applying pressure on the collector, short-circuit thetwo ends of that section together, to release the energy storedin the coils of the section before the direction of


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CALVIN ENGR 315 - Overview and Control of DC and AC Motors

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