Sensors & Actuators Actuators 014-015 Sensors & Actuators - H.Sarmento
Outline Mechanical actuators Electromechanical actuators Electric motors Piezo actuators 014-015 Sensors & Actuators - H.Sarmento 1
Actuators An electrical signal generates an action: Heat actuators (resistive heaters). Light actuators: Incandescent light bulbs or fluorescent lamps, LEDs, LCDs. Sound actuators: Speakers Mechanical actuators: relays, solenoids and motors. Mechanical actuators: generation of motion: Non electric. Electric. 014-015 Sensors & Actuators - H.Sarmento
Non electric mechanical actuators An action generated by non electrical form of energy: rotary motion converted to linear motion or to rotary motion with a different angular velocity; air pressure used to create motion (pneumatic actuator); liquid pressure used to create motion (hydraulic actuator). 014-015 Sensors & Actuators - H.Sarmento 3
Electric mechanical actuators Electrical energy transformed into mechanical energy, producing motion: Electromagnetic actuators: relay; solenoid; motor. Piezoelectric actuators. 014-015 Sensors & Actuators - H.Sarmento 4
Relay (1) A relay is an electromechanical device actuated by energizing a wire coil which magnetically attracts an armature to physically open and close a circuit. When the circuit is open, no power is conducted across the contacts. When the circuit is closed, power is conducted to the load with virtually no voltage drop. 014-015 Sensors & Actuators - H.Sarmento 5
Relay () Relays have two circuits: A control circuit (in green) with a coil. A load circuit (in red) with a switch. The coil controls the operation of the switch. [Source: K. Sullivan] 014-015 Sensors & Actuators - H.Sarmento 6
Relay operation Current flowing though the control circuit (pin 1 and 3) creates a magnetic field which causes the switch (pin 1 and ) to close. relay on relay off [Source: K. Sullivan] When current stops flowing, no magnetic field exists and the switch opens. 014-015 Sensors & Actuators - H.Sarmento 7
Relay design Normally open: the switch remains open until the relay is energized (on). De-energized (off) Energized (on) De-energized (off) Energized (on) Normally closed: the switch remains closed until the relay is energized (on). 014-015 Sensors & Actuators - H.Sarmento 8
Relay contact variations Single pole, single throw Single pole, double throw SPST SPDT Double pole, single throw Double pole, double throw DPST SPDT 014-015 Sensors & Actuators - H.Sarmento 9
Example of application PLC operating a relay within the output module connecting the control voltage to the output port and hence to the solenoid. Internal relay contact Common port PLC Output port Control Voltage (+) Load (solenoid) 014-015 Sensors & Actuators - H.Sarmento 10
Commercial relays 014-015 Sensors & Actuators - H.Sarmento 11
Solenoid Solenoid is an actuator for linear motion. A coil wound around a cylindrical tube with a plunger (piston like cylinder) that is free to move or slide IN and OUT of the coils body. [Source: societyofrobots] Current flow through the solenoid coil winding creates a magnetic field that applies a force to the shaft attracting or repelling it. 014-015 Sensors & Actuators - H.Sarmento 1
Magnetic field in a solenoid If the coil is long when compared with its diameter, magnetic field: B ni L B - approximate field in the center. I electric current n number of turns L length of the wire permeability of the material 014-015 Sensors & Actuators - H.Sarmento 13
Working principle [Source: societyofrobots] In this example, the plunger is normally outside the solenoid forced by the spring. When energized, the plunger moves inside the core of the coil assembly. When the magnetic field is turned off, the spring returns the plunger to its original 014-015 Sensors & Actuators - H.Sarmento 14
Solenoid types In pull type solenoids, the plunger is normally outside the solenoid forced by the spring. When energized, the force pulls the plunger into the solenoid. In push type solenoids, the spring forces the plunger into the solenoid, but when energized the plunger is pushed out. 014-015 Sensors & Actuators - H.Sarmento 15
Applications Electronically activated door locks Pneumatic or hydraulic control valves Robotics Automotive engine management Irrigation valves to water. 014-015 Sensors & Actuators - H.Sarmento 16
Solenoid valve A solenoid valve is a combination of two basic functional units: a solenoid and a valve body containing one or more orifices. Flow through an orifice is shut off or allowed by the movement of the core when the solenoid is energized or deenergized. [Source: reackoneup] 014-015 Sensors & Actuators - H.Sarmento 17
Rotary solenoids Most solenoids are linear devices. However, rotational solenoids are also available which produce an angular or rotary motion. 014-015 Sensors & Actuators - H.Sarmento 18
Electric motor Electrical energy is converted to mechanical energy by the interaction between two magnetic attractive/repulsive forces. Magnetic fields can be created: by electric currents flowing through windings, usually wrapped around a laminated soft iron core; by permanent magnets. Motion in a motor is the result of the continuous alignment of south poles of the rotor with north poles of the stator. 014-015 Sensors & Actuators - H.Sarmento 19
Brushed/brushless motors (1) Brushes: mechanical commutator contacts to deliver current to the windings. Example: brushed DC motor. brush commutator Brushes [Source: Wikipedia ] [Source: electronicdesign.com ] brush 014-015 Sensors & Actuators - H.Sarmento 0
Brushed/brushless motors () In brushless motors, the commutator is replaced by an electronic digital switching circuit. Example: Stepper motor. Vcc b0 b1 T1 b T b4 T3 b3 b5 T4 T5 T6 IB IA IC I ph 014-015 Sensors & Actuators - H.Sarmento 1
AC and DC motors DC motors (for position-control applications) Brushed DC motor. Brushless DC (BLDC) motor. Stepper motor (digital actuator). AC motors (primarily for high-power applications) Induction or asynchronous motor. Synchronous motor. 014-015 Sensors & Actuators - H.Sarmento
Electric motor types Electric motors AC DC Asynchronous Synchronous Variance reluctance Induction Sinusoidal Brushless Reluctance SR Stepper Permanent magnet Surface PM SR Switched Reluctance Wound Field Interior PM [source: Freescale ] 014-015 Sensors & Actuators - H.Sarmento 3
AC induction motor (1) AC voltage applied to the stator creates a rotating magnetic field. The rotating magnetic field induces an alternating e.m.f. into the rotor conductors, generating a current. This induced current in the rotor interacts with the magnetic field of the stator producing a force that results in a torque to turn the rotor. The rotor speed is less than the rotating speed of the magnetic field (synchronous speed): asynchronous motor. 014-015 Sensors & Actuators - H.Sarmento 4
AC induction motor () When the rotor is at rest and power is applied to the stator, the stator magnetic field rotates at the synchronous speed Ns. The stator magnetic field is cutting the rotor at the synchronous speed. The interaction between the rotate magnetic field in the stator and the magnetic field in the rotor due to the induced current put the rotor to rotate. As the rotor is rotating, the rate at which stator flux cuts the rotor is the difference between synchronous speed and actual rotor speed. The ratio of actual flux cutting the rotor to synchronous speed is defined as slip. 014-015 Sensors & Actuators - H.Sarmento 5
AC induction motor: stator Stator: the stationary part of the electromagnetic circuit. [Source: electrical-knowhow] Made of thin metal sheets, called laminations (to reduce energy losses) punched and clamped together to form a hollow cylinder with slots. Coils of insulated wires are inserted into these slots. 014-015 Sensors & Actuators - H.Sarmento 6
Squirrel cage rotor Winding made of metal bars connected together (short circuit) at each end by a metal ring. No insulation required between the core and the bars. [Source: mpoweruk] 014-015 Sensors & Actuators - H.Sarmento 7
Wound rotor A set of windings not short-circuited, that are terminated to a set of slip rings, permitting to add resistors and contactors. Rotor windings Slip rings [Source: openticle] 014-015 Sensors & Actuators - H.Sarmento 8
Single and three phase induction motors Single phase used in home appliances (smaller loads). Three-phase used in industrial motion control systems. [source: Freescale] Example: three-phase stator (outermost) with the winding displaced by 10. 014-015 Sensors & Actuators - H.Sarmento 9
Three-phase induction motor Two poles stator: One set of windings, two coils per phase. The three phase power curve is made up of three single phase sine waves separated by 10º or 1/3 of a cycle. [Source: P. Girão, 006] 014-015 Sensors & Actuators - H.Sarmento 30
Working principle Three phase AC induction motor with poles: Phase shift: 10º. Rotating field cycle: 1 rotation per period. 1 N s rot/s T N s 60 f s rpm 60 s N s [Source: P. Girão, 006] 014-015 Sensors & Actuators - H.Sarmento 31
Synchronous speed (1) Four poles stator: Two set of windings. Four coils per phase. 1 period rotation of magnetic field 360º 180º [Source: allaboutcircuits] N s 60 f rpm N s 30 f rpm [Source: quora.com] 014-015 Sensors & Actuators - H.Sarmento 3
Synchronous speed () Three phase AC induction motor N s 10 p f s (rpm) f s - frequency of the AC voltage (Hz) p - number of poles on the stator Rotating field cycle: 60 s N s 014-015 Sensors & Actuators - H.Sarmento 33
Slip The magnetic field rotates at angular speed s. The rotor runs slower than the speed of the stator field, at angular speed. The rate at which stator flux cuts the rotor is r = s -. The ratio of actual flux cutting the rotor to synchronous speed is defined as slip: s r s 1 s s 0, motor is rotating s = 1, motor stopped. s s 014-015 Sensors & Actuators - H.Sarmento 34
Analysis of induction motor Analysis of the induction motor can be done using an electric model based on the transformer model. E1 k E I I k stator rotor Induced voltage and current in the rotor windings (E, I ) depends on the magnitude of the magnetic field in the stator (E 1, I 1 ) and the frequency of flux variation ( r = s -I). 014-015 Sensors & Actuators - H.Sarmento 35
Transformer equivalent model (1) Under stationary conditions the equivalent circuit for the induction motor is identical to that of a transformer with the secondary short circuited. The difference between transformers and induction motors is the relative movement between rotor and stator. 014-015 Sensors & Actuators - H.Sarmento 36
Transformer equivalent model () Equivalent model of stator winding per phase: R 1 X 1 stator winding resistance stator winding reactance R 0 core loss resistance X M magnetizing reactance Equivalent model of the rotor: R X rotor resistance rotor reactance 014-015 Sensors & Actuators - H.Sarmento 37
Transformer equivalent model (3) In a transformer primary and secondary voltages and currents have the same frequency in : I E k E 1 k I s r In the model of an induction motor: s r = s s 014-015 Sensors & Actuators - H.Sarmento 38
Transformer equivalent model (4) Model with s in primary and r in secondary: E k E I 1 k I Model with in both sides of the transformer with s : X sx E se Faraday s Law emf t B 014-015 Sensors & Actuators - H.Sarmento 39
Transformer equivalent model (5) E k E se I 1 k I jsx R I E R jx I s 014-015 Sensors & Actuators - H.Sarmento 40
014-015 Sensors & Actuators - H.Sarmento 41 1 X j R I E Analysis referred to the primary Transformer equivalent model (6) k E E 1 k I I 1 jx s R k I E k k I ke I E s R k R X X k
Power (1) Power loss (dissipated in the windings) per phase: P loss R I 1 1 R0I 0 RI 014-015 Sensors & Actuators - H.Sarmento 4
Power () Power delivered to the motor per phase: k X R k s P in V s I R 1 R1I 1 R0I 0 k I s 014-015 Sensors & Actuators - H.Sarmento 43
014-015 Sensors & Actuators - H.Sarmento 44 Power delivered to the load per phase: For the three phases Power (3) loss in out P P P I R I k s R P out 0 0 1 1 I R I R R I P loss 0 0 1 1 I s R k I R R I P in s s I R P out 1 s s I R P out 1 3 I R I s R P out k I I
014-015 Sensors & Actuators - H.Sarmento 45 Torque (T) Torque out out P T T P s s s s 1 1 s s s I R P T s out 1 1 3 s I R P T s out 3
Commercial AC induction motors. Primarily for high power applications [Source: Dytrade] [Source: kailidamotors] [Source: ehow] 014-015 Sensors & Actuators - H.Sarmento 46
Synchronous AC motor Synchronous motors are constant-speed motors. Speed of the motor in synchronism with line frequency (synchronous speed). Like the asynchronous motor, the synchronous motor consists of a stator and a rotor separated by an air gap. However, unlike asynchronous motor, the magnetic flux in the rotor is created by permanent magnets or by the currents from an outside source of direct current (electromagnets). 014-015 Sensors & Actuators - H.Sarmento 47
Stator of synchronous AC motor Similar to the AC induction rotor. A housing, a magnetic circuit, generally comprising silicon steel laminations, and windings that produce a rotating magnetic field. [Source:. electrical-knowhow.] 014-015 Sensors & Actuators - H.Sarmento 48
Rotor of synchronous AC motor Permanent magnets Windings powered by external DC source (brushed or brushless). [source: leeson.com] [source: processmodeling.org] Usually a second winding, the damper winding, to produce torque for motor starting. 014-015 Sensors & Actuators - H.Sarmento 49
Commercial synchronous AC motor [Source:.Hansen smart] [Source: indiamart] [Source: Texas Instrument] More expensive than induction motors but offering higher efficiency. Used for large motor drives. 014-015 Sensors & Actuators - H.Sarmento 50
Rotor structure (1) Salient pole (for low speed) [source: electrical-knowhow.com] [source: Chee Mun ONG] 014-015 Sensors & Actuators - H.Sarmento 51
Rotor structure () Round or cylindrical (high speed) [source: electrical-knowhow.com] [source: Chee Mun ONG] 014-015 Sensors & Actuators - H.Sarmento 5
Working principle (1) Rotor stopped: Currents in the stator windings create a rotating field. The DC current in the rotor produces a static field (brushed or brushless). Magnetic fields interact. 014-015 Sensors & Actuators - H.Sarmento 53
Working principle () Rotor stopped: The force of attraction between stator poles and rotor poles produces a torque in clockwise direction. [source: K. Vasudevan] The rotor cannot move due to its mechanical inertia: not self starting. 014-015 Sensors & Actuators - H.Sarmento 54
Working principle (3) [source: K. Vasudevan] North and south poles in the stator at any location change with time: a south pole becomes a north pole after half a cycle (1/f). Poles experience a force of attraction and a force of repulsion. Rotor does not start, there is a vibration. 014-015 Sensors & Actuators - H.Sarmento 55
Working principle (4) Synchronous motor can be started as an induction motor: A damper winding (starting winding) is mounted on the rotor. The rotor winding is left unexcited. The motor starts as an induction motor. The motor speeds up and approaches synchronous speed. The rotor poles are then excited from a DC source. The rotor runs at synchronous speed. 014-015 Sensors & Actuators - H.Sarmento 56
Working principle (5) Rotor into rotation: Poles in rotor and stator get attracted and try to maintain this alignment. A situation of balance is attained when the rotor speed is equal to the speed of the rotating field. 014-015 Sensors & Actuators - H.Sarmento 57
Working principle (6) Rotor into rotation in the direction of the rotating field: The field of the rotor is delayed relative to rotating field by an angle. The value of the angle depends on the mechanical load in the rotor, increasing with it. While this angle does not reach half angle between poles synchronism can exist. 014-015 Sensors & Actuators - H.Sarmento 58
Equivalent model (1) Rotor Stator (per phase) Resistance and inductance of rotor windings (X 1 and R 1 ). Resistance and inductance of stator windings per phase (X A and R A ). No voltage is induced in the rotor by the stator field (rotation at the same speed). A voltage (E A ) is induced in the stator winding by the rotor static field: depends upon rotor speed and current in the rotor (I 1 ). 014-015 Sensors & Actuators - H.Sarmento 59
Equivalent circuit (3) E A V R Phasor diagram of tree-phase synchronous motor per phase. jx A I A A I A 0 E A V jx A I A R A I A jx A I A R A I A EA V I A 014-015 Sensors & Actuators - H.Sarmento 60
Equivalent circuit (3) E A V jx A I A R A I A In a synchronous motor, the value of X A is 10 to 100 times greater than R A. R A can be neglected unless we are interested in efficiency or heating effects. Neglecting R A : V E A V jx A I A E A jx A I A I A 90º 014-015 Sensors & Actuators - H.Sarmento 61
Power (1) Input power (cos : motor power factor) Pin V I A cos E A V jx A I A I A Neglecting losses, the electromagnetic power (amount of power being converted from the electrical into the mechanical power): Pem P in 90º 014-015 Sensors & Actuators - H.Sarmento 6
Power () Pin V I A cos V jx A I A I A E A 90º 90º P in V I A cos V EA Pem V sin X A E X A A sin X A I A E I cos A A sin X I cos A A EA cos sin X A E sin A 014-015 Sensors & Actuators - H.Sarmento 63
DC motors The stator: permanent magnet (PM DC motor ). or electromagnets (wound-field DC motor). Rotor (armature): electric windings, generating a magnetic field when energized by the external DC current. 014-015 Sensors & Actuators - H.Sarmento 64
Commercial DC motors [source: Galco] [source: nmbtc] [source: music.columbia.edu] 014-015 Sensors & Actuators - H.Sarmento 65
Types of DC motors DC motors Brushed DC motor. Brushless DC (BLDC) motor. 014-015 Sensors & Actuators - H.Sarmento 66
Working principle of a DC motor The stator magnetic poles attract the opposite poles of the rotor. The rotor will rotate until poles are aligned with the stator poles. When the rotor reaches alignment, the brushes move across the commutator contacts and energize the next winding. Brushless DC motor substitute mechanical contacts (brushes and commutator) by control electronics. 014-015 Sensors & Actuators - H.Sarmento 67
Stepper motor (1) DC motors (for position-control applications) Brushed DC motor. Brushless DC (BLDC) motor. Stepper motor. AC motors (primarily for high-power applications) Induction or asynchronous motor. Synchronous motor. 014-015 Sensors & Actuators - H.Sarmento 68
Commercial stepper motors. [Source: Jameco] [Source: Haydonkerk ] [source: Wikipedia] 014-015 Sensors & Actuators - H.Sarmento 69
Stepper motor () This type of motor moves in a discreet way, a step at a time. It can be considered as a digital version of an electric motor. It is easily controlled with microprocessors. Used in position applications (ex: floppy disk). Can be used in open loop positioning control, without feedback loop. 014-015 Sensors & Actuators - H.Sarmento 70
Stepper motor components Stator with multiple windings or phases energized with a DC current. Rotor that can either be magnetized or non-magnetized depending on the type of motor. 014-015 Sensors & Actuators - H.Sarmento 71
Working principle of stepper motor Rotor rotates in order to minimize its magnetic reluctance. rotor stator 014-015 Sensors & Actuators - H.Sarmento 7
Types of Stepper Motors Permanent Magnet (PM). Variable Reluctance (VR). Hybrid: combining characteristics from PM and VR 014-015 Sensors & Actuators - H.Sarmento 73
VR stepper motor (1) Rotor made of soft iron with teeth and slots, not magnetized. [source: wisc-online] Rotor teeth are attracted to the energized stator poles to reduce reluctance of the magnetic flux between stator poles, rotating the rotor. 014-015 Sensors & Actuators - H.Sarmento 74
VR stepper motor () [source: wisc-online] The stator poles in each pair, located in front of each other, are energized at the same time (coils in series). The way coils are wound the poles have opposite polarity. 014-015 Sensors & Actuators - H.Sarmento 75
VR stepper motor (3) [source: wisc-online] Rotor teeth become aligned with stator poles: the rotor turns so that the magnetic flux lines pass through the iron teeth rather than through the air slots between them. 014-015 Sensors & Actuators - H.Sarmento 76
VR stepper motor (4) [source: wisc-online] To step the motor (CCW) A and A are de-energized and B and B energized. The rotor teeth closest to the B coils will align themselves with the B poles. The next step is to de-energize coils B B and to energize C C. 014-015 Sensors & Actuators - H.Sarmento 77
PM stepper motor (1) Rotor with permanent magnets. Stator with electromagnets (windings). 014-015 Sensors & Actuators - H.Sarmento 78
Outer rotor Pancake stepper motor 014-015 Sensors & Actuators - H.Sarmento 79
Inner rotor Inner rotor [Source: Solarbotics] 014-015 Sensors & Actuators - H.Sarmento 80
Permanent Magnet Stepper Motor (1) This motor has a magnetized rotor. To rotate the motor, current is flowing in each phase of the stator sequentially. Current flow generates magnetic polarity on each stator inner rotor. A A B B B B A [source: Freescale ] A 014-015 Sensors & Actuators - H.Sarmento 81
Permanent Magnet Stepper Motor () This motor has a magnetized rotor. To rotate the motor, current is flowing in each phase of the stator sequentially Current flow generates magnetic polarity on each stator D A B D A B C C C C B A D B D A 014-015 Sensors & Actuators - H.Sarmento 8
Full Step Stepper Motor A B B A The two phases alternate on and off and also reverse polarity: commutation sequence has 4 steps (90º). When the rotor aligns with one of the stator poles, the second phase is energized. 014-015 Sensors & Actuators - H.Sarmento 83
Half Step Stepper Motor The main difference is that the second phase is turned on before the first phase is turned off: commutation sequence has 8 steps (45 º). [Source: Freescale ] 014-015 Sensors & Actuators - H.Sarmento 84
Phases, poles and step angle (1) Full step S N N S [Source: M. lawford] 360º Step angle poles in rotor. N N ph r 1 phase in the stator. When the current in the phase (A1 A) changes the direction the rotor moves 180º. 014-015 Sensors & Actuators - H.Sarmento 85
Phases, poles and step angle () Full step S S N [Source: M. lawford] N poles in rotor. phase in the stator. 360º Step angle N N ph r When the phase changes (A1 A B1 B) the rotor moves 90º. 014-015 Sensors & Actuators - H.Sarmento 86
Phases, poles and step angle (3) Full step S S S N N N poles in rotor. 360º Step angle 3 phase in the stator. N N ph r When the phase changes (A1 A B1 B) the direction the rotor moves 60º. 014-015 Sensors & Actuators - H.Sarmento 87
Phases, poles and step angle (4) Improving the resolution: [Source: M. lawford] 014-015 Sensors & Actuators - H.Sarmento 88
Phases, poles and step angle (5) step 1 step Step angle 360º N N ph r step 3 4 step [Source: M. lawford] 014-015 Sensors & Actuators - H.Sarmento 89
Phases, poles and step angle (4) Nr poles in rotor and m phases in the stator: Step angle 360º N ph N r Lab assignment: 360 35 1º 360 31 5º 014-015 Sensors & Actuators - H.Sarmento 90
Piezo actuators A piezoelectric actuator converts an electrical signal into a controlled linear displacement. If displacement is prevented, a useable force will develop. Piezoelectric actuators are used to finely adjust machining tools, lenses, mirrors, or other equipment. 014-015 Sensors & Actuators - H.Sarmento 91
Advantages of piezo actuators No rotating parts. Unaffected by magnetic fields. Fast response without delay. Compact design. High mechanical power density. Consumes power only when motion is generated,. Very high acceleration rates. Very high power generation. 014-015 Sensors & Actuators - H.Sarmento 9
Types of piezo actuators Stack actuators Discrete ceramic disks, rings or plates with thin metal leaf electrodes interlaced between the ceramics. [Source: APC Internations] Stripe actuators (also called bending actuators) Two thin layers of piezoelectric ceramic bonded together 014-015 Sensors & Actuators - H.Sarmento 93
Bibliography (1) K.R. Sullivan, Understanding relays. Available at: http://www.autoshop101.com/forms/hweb.pdf Linear Solenoid. http://www.electronics-tutorials.ws/io/io_6.html Solenoid Design and operation, Bicron Electronics company. Available at:http://www.sal.wisc.edu/pfis/docs/rss-vis/archive/public/product%0manuals/bicron/soldesop.pdf Motor Types and Their Control, Summary of key motor types and control, Freescale. Available at: http://cache.freescale.com/files/3bit/doc/brochure/bbmtrcntrlart.pdf Induction Asynchronous machines. Available at: http://www.ece.msstate.edu/~donohoe/ece3183asynchronous_synchronous_machines.pdf Rakesh Parekh, AC Induction Motor Fundamentals, Application Note AN887, Microchip Technology, 003. Application basics of operation of three-phase induction motors, Technical manual, Rockwell Automation,1996. T. Flack, Electric Power Lectures 11 and 1, Cambridge Unversity. Motor specifications, Wermac. Available at: http://www.wermac.com/acm_.pdf M.V.Bakshi U.A.Bakshi, Electrical Machines III, Technical Publications Pune, 009 P. Girão, Sensores e Actuadores, Slides LEEC/MEEC, IST. 003/004. 014-015 Sensors & Actuators - H.Sarmento 94
Bibliography () S. Shahl, Synchronous Motors, Available at: http://www.uotechnology.edu.iq/depeee/lectures/3rd/electrical/machines%0/iii_sm.pdf Classification of Electric Motors - Part Four. Available at: http://www.electricalknowhow.com/01/05/classification-of-electric-motors-part_.html Terry Bartelt, The Variable Reluctance Stepper Motor, Wisc-online. Available at: http://www.wisc-online.com/objects/viewobject.aspx?id=iau1408 Stepper Motor Basics, Industrial Circuits Application Note.,Solarbotics. Available at: http://www.solarbotics.net/library/pdflib/pdf/motorbas.pdf university-logo Marc McComb, Introduction to Stepper Motors, Microchip Web Seminars. Available at: www.microchip.com/stellent/groups/sitecomm_sg/documents/devicedoc/en543047.pdf Mark Lawford, Actuators: Stepper Motors. Available at: http://www.cas.mcmaster.ca/~lawford/3tb4/slides/stepper.pdf Piezo actuators: types and applications, APC International. Available at: https://www.americanpiezo.com/piezo-theory/actuators.html. 014-015 Sensors & Actuators - H.Sarmento 95