L17 6.111 Fall 2003 – Introductory Digital Systems Laboratory Motors and Position DeterminationMotors and Position DeterminationL17 6.111 Fall 2003 – Introductory Digital Systems Laboratory Controlling PositionControlling Position! Feedback is used to control position." Measure the position, subtract a function of it from the desired position and then use this resulting signal to drive the system towards the desired position. This is negative feedback." The natural frequencies of the feedback system are the “zeros” of 1 + G(s)H(s).# The total system is unstable if these “zeros” are in the right half plane (RHP). With 180 degrees phase shift, “negative” feedback becomes “positive” feedback.# So we want these “zeros” to be in the left half plane (LHP).# Putting an integrator into H(s) drives steady state error to zero.# But high order systems are more likely to have RHP zeros.# Time delay and high gain lead to RHP zeros.1 + G(s) H(s)H(s)G(s)++−xyY(s)X(s)=H(s)L17 6.111 Fall 2003 – Introductory Digital Systems Laboratory ServosServos! We can control parts of the servo, but the system dynamics is often a part we can’t control." The system dynamics results from masses. springs, losses, etc.! Likely, we will implement servos as digital systems." Digital systems are more flexible to design.# They are more repeatable; they are not subject to gain drift.# We can use as many bits as we like so we can keep the computation noise small." Digital systems can have significant delays.# These delays are sometimes fixed, but are sometimes stochastic.digital systemPosition++−xyOutputPositionG(s)C(s) A(s)MeasurementSystem DynamicsControlsLikely boundary ofDesiredL17 6.111 Fall 2003 – Introductory Digital Systems Laboratory Analog Position MeasurementsAnalog Position MeasurementsxVVxLPosition Sensing: AnalogLinear PotentiometerVLθSinusoidal PotentiometerVV12Voltage is proportional to position.A linear or rotary potentiometer canbe used.Accuracy is limited to that of thepotentiometer and the noise of thepower supply voltage.Two sinusoidal potentiometersare used.V1 = V0 cos (theta)V2 = V0 sin (theta)This can also be done magnetically.This is called a resolver andrequires a complex analog signaldetection. The computation can bedone with either analog or digitalcircuitry.L17 6.111 Fall 2003 – Introductory Digital Systems Laboratory Digital Position MeasurementDigital Position Measurement! Sense light transmission to determine position." Typically through a transparent sector" Gives a reading over a range of positions.# Depends on extent of transparent sector." We may need a lot of sensors to determine multiple positions.PhotosensorSensing RingOpaque TransparentLight SourceL17 6.111 Fall 2003 – Introductory Digital Systems Laboratory Digital Absolute PositionDigital Absolute Position! Typically, this is used for relatively low resolutions.Use a Gray code to0 0 0 00 0 0 10 0 1 10 0 1 00 1 1 00 1 1 10 1 0 10 1 0 01 1 0 01 1 0 11 1 1 11 1 1 01 0 1 01 0 1 1 1 0 0 1 1 0 0 0Here is a 4−bit (22.5 degree)resolution wheel.One source per sensorbit.Resolution is360o2Neliminate chatter.Can make these wider.L17 6.111 Fall 2003 – Introductory Digital Systems Laboratory TwoTwo--Phase EncoderPhase Encoder! Two Source – Sensor Sets" Their position is offset by half the sector width." This example has 30 degree sectors" and 15 degree resolution.o15L17 6.111 Fall 2003 – Introductory Digital Systems Laboratory Use of TwoUse of Two--Phase EncoderPhase Encoder! This circuit generates:" An Up/Down signal depending on whether the motion is clockwise (CW) or counterclockwise (CCW)." A clk signal which rising edge is to operate the counter.L17 6.111 Fall 2003 – Introductory Digital Systems Laboratory WaveformsWaveforms! A and B are signals derived from sensors.! Rotating one way, the rising edge of clk is when U/D is high.! Rotating the other way, the rising edge of clk is when U/D is low.ClockwiseSRU/DABθCLK = A*BU/DCounterClockwiseL17 6.111 Fall 2003 – Introductory Digital Systems Laboratory Another Way of Making an EncoderAnother Way of Making an Encoder! Use two sensors like the two-phase encoder but use only one ring and displace the sensors by ½ band.! Add another ring and a sensor to sense the “home” position. LocationsRelativeHomeSensorL17 6.111 Fall 2003 – Introductory Digital Systems Laboratory MotorsMotors! Simple servomechanisms are made with DC motors." DC motor model is very simple:# It consists of a resistor in series with a voltage source.# The voltage source is proportional to the rotational speed." The mechanical system (controlled system) determines the speed as influenced by the torque.Torque T = G I VI+−V = G Ω + R IL17 6.111 Fall 2003 – Introductory Digital Systems Laboratory Permanent Magnet DC MotorsPermanent Magnet DC Motors! They are very commonly used." The ‘Back Voltage’ is proportional to speed." The torque is proportional to the current.! Servo Strategy:" Command torque by setting current." Measure the speed.! Running open loop:" There is a ‘zero torque’ speed." Torque is proportional to the difference from that speed.T Ω T=0VT=ConstantΩΩ0=VGL17 6.111 Fall 2003 – Introductory Digital Systems Laboratory Stepper MotorsStepper Motors! Digital Motors" Two ‘stacks’ (phases)" Usually biased by permanent magnets" Move a discrete distance per ‘step’." This is an axial view cut through both of two sections.SSSNNNNSL17 6.111 Fall 2003 – Introductory Digital Systems Laboratory Stepper Motor WindingsStepper Motor Windings! Two distinct ‘phases’" May be driven as distinct windings." Or may be driven as ‘bifilar’ windings." Bifilar is easier but less efficient.NA−A+B−B+A−A+B−B+Bipolar WindingUnipolar(BifilarWinding)L17 6.111 Fall 2003 – Introductory Digital Systems Laboratory Bipolar WindingBipolar Winding! Driven by ‘H-bridges’ of transistors" Can put current through windings in either direction." But note that the upper transistor drive is tricky." Uses all of the winding.Bipolar MotorIBIAA− A+ B− B++VL17 6.111 Fall 2003 – Introductory Digital Systems Laboratory Bifilar WindingBifilar Winding! Driven by four transistors to ground." Note that the center of the windings is held high." Transistors are between winding and ground." NPN bipolar transistors work well." Transistor drives are easily handled.Unipolar MotorN+VA− A+ B−
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