Actuators...physical devices that transform electrical, chemical, or thermalenergy into mechanical energy...• hydraulic• pneumatic• electric– stepper motors– permanent magnetDC motors• artificial muscles– shape memory alloys– polymers– protein-based actua-tors– bucky tubes1 Copyrightc2013 Roderic GrupenActuators: Hydraulicservoservo• energy is stored in the high pressure fluid reservoir (1000-3000psi)• open - l oop control - fork lifts, back hoes• good bandwidth (5 KHz - fluid reverses direction 5 msec)PROS1. good power/weight2. safe in explosive environ-mentsCONS1. expensive servos2. messy3. high maintenance2 Copyrightc2013 Roderic GrupenActuators: Pneumatic• compressible fluid (air)• jet-pipe servo controlNSgraphitepistonglasscylinderreservoir80 psicontrol+VPROS1. light and cheap2. passively back-drivableCONS1. stiction2. delicate3 Copyrightc2013 Roderic GrupenActuators: Stepper Motors• precise (low torque), open-loop position control• resonance - typically between 50 and 150 steps/sec• coggingNSNSNS(A)NSoffoffN Soffoff(B)SNNNSSSNSNS(C)SNoff offNNSoffoffSNNNSS(D)4 Copyrightc2013 Roderic GrupenPermanent Magnet DC Motors• run continuousl y in both directions• closed-loop servo control w/position feedback• relaible, good power/weight, high torques possibleLorentz ForceNSBqvF = qV × B5 Copyrightc2013 Roderic GrupenPermanent Magnet DC MotorIron Core:• high inertia, cogging• very reliabl e• che apBNSMoving Coil:• rare earth magnets - coil is roto r• low rotor inertia - minimal cogging• large torque• can be thin (0.0 2′′), large diameter(12′′)• printed-circuit motors• very expensive6 Copyrightc2013 Roderic GrupenDC Motors - Electrodynamicsforce: Newton N = kg · m/sec2torque: the product of a force and a moment armN · m =kg · m2sec2power: energy per unit time (Watts)P = V I(electrical)= τω(mechanical)W att =volt · coulombsec=Nmsec7 Copyrightc2013 Roderic GrupenDC Motors - ElectrodynamicsBSNF+VsupplyFqvqvThe Lorentz Force+VBFgeneratorFgenerated currentmechanical inputqvqvBack ward ElectromotiveForce (Back EMF)• Ktproportional to the number of loops• commutation - the rotor runs out of torque when the c u rrentloop is perpendicular to B, revers in g the current can continueto provide torque in the same direction.• for a commutated motor, the rotor current alternates with fre-quency proportional to ωback emf = LdIdt= Kbω8 Copyrightc2013 Roderic GrupenDC Motors - ElectrodynamicsτRLVτ = KtI motor torqueVb= LdIdt= Kb˙θ back emfV = IR + Kb˙θmechanical electricalpowero ut = powerin − lossesτ˙θ = V I − I2R(KtI)˙θ = (IR + Kb˙θ)I − I2R= KbI˙θKt= Kb9 Copyrightc2013 Roderic GrupenDC Motors - Electrodynamics (cont.)τRLVforwardcurrentXτ = J¨θ = KI = K"VR−K˙θR#backcurrent¨θ +K2JR˙θ +KVJR= 010 Copyrightc2013 Roderic GrupenDC Motors/Gearhe ad CombinationsJLBLJMBMτ = η τLM*Lττ= KIif the transmission is perfectly efficient:τoutωout= τinωinτout(ηωin) = τinωinτout= (1/η)τinif η = 0.01, the outpu t shaft carries on e hundred times the torqueat one hundredth the velocity of the input shaft11 Copyrightc2013 Roderic GrupenDC Motors/Gearhea dCombinations — Compound Loadsdynamic equation of motion - equate the torque derivedfrom Lorentz forces with the torques required to accelera te theload and to overcome viscous friction.τ =hJM¨θM+ BM˙θMi+ ηhJL¨θL+ BL˙θLibut:θL= ηθM,˙θL= η˙θM, and¨θL= η¨θMso:τ =JM+ η2JL ¨θM+BM+ η2BL ˙θMand:Jeff= JM+ η2JLBeff= BM+ η2BL12 Copyrightc2013 Roderic GrupenMore on Interf a cing DC MotorsH-BridgeVs2s3s4s1Vs2s3s4s1• cont inuous forward/backward speedcontrol• (s1, s2, s3, s4) open - freewheel• (s1, s2, s3, s4) closed - (regenerative)braking• RMS voltage s - pulse width modu-lation (PWM)13 Copyrightc2013 Roderic GrupenPulse Width Modulation−V+VRMS Vtontofft+100−100−V+Vtontoff+100−100−V+VRMS Vtontofft+100−100RMS V14 Copyrightc2013 Roderic GrupenArtificial MusclesMcKibben Air Muscles - non-linear pn eu ma ti c actuators, at-tract interest because th ey are among the strongest and fastestof the “artificial” muscles.Smart A ctua to rs - hi gh performance DC motors with localcomputation an d load sensing, simulate reference dynamics,coupled-oscillators, Matsuoka oscillators.Muscle Wire - Nitinol (mickel-titaniu m all oy) relatively slow?commercially available, forces o n the order of a few grams (si m-ilar to all options below this on in the lis t), low band wi d th( 1Hz)Polymers - electrostatic, chemical, and thermal15 Copyrightc2013 Roderic