ME 515 Mechatronics. Overview of Computer based Control System

Transcription

1 ME 515 Mechatronics Introduction to Sensors I Asanga Ratnaweera Department of Faculty of Engineering University of Peradeniya Tel: (3627) asangar@pdn.ac.lk Overview of Computer based Control System 2 1

2 Sensors and Transducers A sensor is an element in a mechatronic or measurement system that acquires a physical parameter and changes it into a signal that can be processed by the system Active element of a sensor is referred to as a transducer 3 Sensors: Classification Signal Characteristics Analogue or Digital Power supply Active or passive Method of operation Resistive, Capacitive or Inductive, piezoelectric Subject of Measurement Acoustic, Biological, Chemical, Electrical, Mechanical, Optical, Thermal, Other 4 2

3 Sensors : Types Temperature sensors Pressure sensors Strain sensors (Strain gauges) Piezoelectric sensors Position sensors Proximity sensors Velocity sensors Light sensors 5 Physical Sensors Physical Quantity Fluid Force-Torque Geometry Kinematic Sensor Pressure transducer Flow meter Load cell Strain Gauge LVDT Potentiometer Encoder Velocimeter Accelerometer Variable Pressure Flow rate Force/Torque Strain Displacement Displacement Displacement Velocity Acceleration Thermal Thermocouple Thermistors Temperature Temperature 6 3

4 Sensor Performance Characteristics Transfer Function: The functional relationship between physical input signal and electrical output signal. For sensors which are individually calibrated, this might take the form of the certified calibration curve. Output (usually an electrical signal) Input 7 Sensor Performance Characteristics Span or Dynamic Range: The range of input physical signals which may be converted to electrical signals by the sensor. Signals outside of this range are expected to cause unacceptably large inaccuracy. Span is the difference between the max. and the min. values of the input. EX: sensor measures force might have a range of 0-50 kn and a span of 50 kn 8 4

5 Sensor Performance Characteristics Error The discrepancy between the instrument reading and the true value is called error. Absolute error = measured value - actual value Relative error = absolute error / true value Hysteresis Error Transducers can give different outputs from the same value of quantity being measured according to whether that value has been reached by a continuously increasing change or a continuously decreasing change. 9 Sensor Performance Characteristics Non-Linearity Error For many transducers a linear relation-ship between the input and output is assumed over the working range. Few transducers, however, have a truly non-linear relationship and thus errors occur as a result of the assumption of linearity. Various methods are used for the numerical expression of the non-linearity error End-range values Best straight line for all values Best straight line through zero point 10 5

6 Sensor Performance Characteristics Non-Linearity Error Best straight line for all values End-range values Best straight line through zero point 11 Sensor Performance Characteristics Non-linearity O IDEAL (I) Maximum nonlinearity O(I) 12 6

7 Sensor Performance Characteristics Sensitivity The sensitivity K is defined as the rate of change of the output (O) with respect to the input (I). For a linear sensor: For a non-linear sensor Ex: Thermometer would have "high sensitivity" if a small temperature change resulted in a large voltage change. 13 Sensor Performance Characteristics Environmental effects Environmental effects can lead to variations in the degree of non-linearity, the sensitivity and the offsets 14 7

8 Sensor Performance Characteristics Resolution Resolution is defined as the largest change in I that can occur without a corresponding change in O: R = In most applications, we want the best possible resolution (ie. the finest) without paying too much for it. 15 Sensor Performance Characteristics Stability The stability of a transducer is its ability to give the same output when used to measure a constant input over a period of time. The term drift is often used to describe the change in output that occurs over time. The drift may be expressed as a percentage of the full range output. 16 8

9 Sensor Performance Characteristics Error bands It is often impractical to separate and determine nonlinearity, resolution and other such effects in these cases, nonideal performance is classified by one broad term: the error band Accuracy: Generally defined as the largest expected error between actual and ideal output signals. 17 Sensor Performance Characteristics Dead-band The dead-band or dead space of a transducer is the range of input values for which there is no output. The dead time is the length of time from the application of an input until the output begins to respond and change. Noise All sensors produce some output noise in addition to the output signal. The noise of the sensor limits the performance of the system based on the sensor. 18 9

10 Resistive sensors There are number of ways in which resistance can be changed by a physical phenomenon. At a constant temperature, the resistance of a conductor can be expressed as; R = ρl A ρ Resistivity, Ωm R Resistance, Ω l Length, m A Cross section area, m 2 19 Resistive sensors Output voltage is proportional to the change in resistance of the sensor. Obey the Ohms law: V =IR Ex: Potentiometers Strain gauge 20 10

11 Inductive sensors The basic principle of operation of inductive sensors is based on Faraday s law of induction in a coil. di Output voltge V = L dt Inductance (L) of a circuit is defined as the total flux linkage per unit current Nφ L = i Ni φ = R N Ni N L = = i R R 2 R Reluctance of the flux path N Number of turns of the coil Φ magnetic flux 21 Inductive sensors Reluctance is expressed as l R = µ A Where, µ Effective permeability of the medium in and around the coil l Length of the coil, m A Cross sectional area of the coil, m 2 Therefore inductance can be expressed as: A L = N 2 µ l 22 11

12 Inductive sensors The inductance change can be caused by any of the following : Variation in Area or/and length of the coil Change in the effective permeability of the medium in and around the coil Change in reluctance of the magnetic path or variation in air gap Change in mutual inductance (by changing the coupling between coils 1 and 2 with siding or opposing field. Ex: 23 Capacitive Sensors In capacitive sensors, the measurement of physical phenomena is made based on the variation in capacitance between two separate members or electrodes. dv q= CV I = C dt The capacitance C: C ε 0 εa d ε o - Permittivity of free space (=8.85pF/m); = ε - Relative Permittivity A - overlapping area of plates (m2) d - Plate separation (m) 24 12

13 Capacitive Sensors A change in capacitance can be brought about by varying any one of the three parameters listed below. Changing distance between two parallel electrodes ε A C 0 ε = d Capacitance, C d Distance, d 25 Capacitive Sensors Changing the dielectric constant, permittivity of dielectric medium ε Ex: C ε 0 εa = A linear relationship d 26 13

14 Capacitive Sensors Changing the area of the electrodes A Ex: A linear relationship 27 Piezoelectric sensors A piezoelectric material produces voltage by redistributing charge when mechanical strain/stress is applied. Strain causes a redistribution of charges and results in a net electric dipole (a dipole is kind of a battery!) 28 14

15 Piezoelectric sensors Some piezoelectric materials are; Quartz Crystal (SiO2) - Most commonly used material Rochelle salt PZT (lead zirconium titanate) PVDF (polyvinylidene fluoride) BaTiO3 (barium titanate) LS (lithium sulfate) Ex: Quartz Crystal - O 2 F F F F - + Si 29 The Piezoelectric Effect Crystal material at rest: No forces applied, so net current flow is 0 Crystal Current Meter = 0 Charges cancel each other, so no current flow

16 The Piezoelectric Effect Crystal material with forces applied in direction of arrows Crystal Force Due to properties of symmetry, charges are net + on one side & net - on the opposite side: crystal gets thinner and longer Current Meter deflects in + direction 31 The Piezoelectric Effect Changing the direction of the applied force.. Crystal Force. Changes the direction of current flow, and the crystal gets shorter and fatter Current Meter deflects in - direction 32 16

17 Piezoelectric sensors The Charge Generation Longitudinal effect Transverse effect F F Conductive surface a Voltage F Q = df Piezoelectric material d piezoelectric coefficient b F Voltage Q = df a b 33 Piezoelectric sensors The piezoelectric coefficient, d, also known as charge sensitivity factor is a constant for a given piezoelectric martial. If the ratio a/b is greater than 1, the transverse effect produces more charge than the longitudinal effect. If the thickness of the crystal is t and change in thickness due to the force F is t, the stress strain relationship (Young s Modulus) is: E = Stress Strain F = A = t t Ft A t A - area of the crystal 34 17

18 Piezoelectric sensors Therefore, the force F, However, F = AE t t For Longitudinal effect Q = df Therefore, AE Q = d t t The capacitance of the piezoelectric material C V = = ε 0 ε r Q C = A t ε o - Permittivity of free space (=8.85pF/m); ε r - Relative Permittivity of the piezo. material However, Charge Q Q = CV Therefore, the voltage V dt ε r ε o A F 35 Piezoelectric sensors Therefore the voltage V, Where, r t V = g F = gtp A d g = ε ε is crystal voltage sensitivity factor o P Pressure or the stress 36 18

19 Piezoelectric sensors Basic characteristics of Piezoelectric material Material Density (ρ) 10 3 kg/m 3 Permittivity (ε r ) Young s Modulus (E), N/m 2 Piezoelectric charge sensitivity (d) pf/n Quartz (SiO 2 ) Barium Titanate (BaTiO3) PZT PVDF The crystal voltage sensitivity factor can be calculated using d g = ε ε r o 37 Sensors: position and speed measurement Translational and Rotational Potentiometers Translational or angular displacement is proportional to resistance

20 Position sensor: Potentiometer Translational Potentiometers R = R 1 + R 2 R = Rx 1 R2 = R(1 x) V 2 V = V 2 = ir2 1 ir 1 = V 1 V V + V = ir = 1 2 V V out = R R 1 V out = Vx 39 Position sensor: Potentiometer Rotational Potentiometers v = o v i φ i 40 20

21 Position sensor: Potentiometer Effect of loading V OUT = R R L Vx x( 1 x) + 1 This is a non-linear function of x with the degree of non-linearity dependent on the ratio R. R L 41 Position sensor: Potentiometer Thus, we desire R L >>R in order to achieve a linear response from the potentiometer we should therefore measure the output voltage V out using apparatus of high input impedance. Devices with this characteristic often use buffers, one form of which can be made using operational amplifiers (op-amps). Some of the disadvantages of potentiometer sensors are its slow dynamic performance, low resolution and susceptibility to vibration and noise

22 Position sensor: Linear Variable Differential Transformer (LVDT) An Inductive Sensor A L = N 2 µ l µ Effective permeability of the medium in and around the coil 43 Position sensor: Linear Variable Differential Transformer (LVDT) Primary Secondary Displacement Sensor An inductor is basically a coil of wire over a core (usually ferrous) It responds to electric or magnetic fields A transformer is made of at least two coils wound over the core: one is primary and another is secondary Inductors and transformers work only for ac signals 44 22

23 Position sensor: Linear Variable Differential Transformer (LVDT) Basic features High resolution High accuracy Good stability Therefore, ideal for applications involving short displacement measurements. 45 Position/Velocity sensor: Digital Sensors Optical encoders are widely used in applications involving measurement of linear or angular position, velocity and direction of movement. Ex: rotary optical encoders

24 Position/Velocity sensor : Optical Encoders Optical encoders are usually used to measure rotational movement precisely. The major advantages of these sensors are simplicity, high accuracy, suitability for sensitive applications. There are two types of optical encoders: absolute and incremental. 47 Position/Velocity sensor : Optical Encoders Relative position light sensor mask/diffuser grating light emitter decode circuitry 12 December 2006 Asanga Ideal Ratnaweera, Department Real of 48 24

25 Position/Velocity sensor : Incremental Encoders Incremental encoders provide a simple pulse each time the object to be measured has moved a given distance. These encoders are usually used for counting applications There are two types of incremental encoders: tachometer type quadrature type. 49 Position/Velocity sensor : Incremental Encoders Tachometer type Incremental encoders The tachometer type encoders used for relative position velocity measurement, and have one output channel. The velocity measurement is done by looking at the pulses during a certain time interval. Direction of rotation cannot be measured Resolution = 360/ no. of slots 12 December 2006 output Asanga Ratnaweera, Department of 50 25

26 Position/Velocity sensor : Incremental Encoders Quadrature type. Have dual channels A and B The output waveform is arranged in such a way that channel A is 90 degrees out of phase with channel B. By utilizing quadrature detection and decoding output signals, one can obtain precise direction, distance and velocity information. 51 Position/Velocity sensor : Absolute Encoder An absolute encoder provides a unique binary word coded to represent a given position of an object. Wheel with 4 tracks 12 December 2006 Asanga Ratnaweera, Department Resolution of = 360/2 4 =

27 Position/Velocity sensor : Optical Encoders disc Incremental encoder disc Absolute encoder disc Wheel with 8 tracks Resolution = 360/2 8 =