ET 438a Automatic Control Systems Technology 1lesson4et438a.pptx

Learning Objectives lesson4et438a.pptx2 After this presentation you will be able to:  Develop mathematical relationships for a sensor that has a linear output.  Convert linear mathematical equations into block diagrams that represent sensor scaling circuits.  Adjust the output range of a sensor using operational amplifier circuits.

Scaling Sensor Outputs lesson4et438a.pptx3 x= transducer input (measured value) V T = transducer output voltage K T = transducer gain (slope) K s = scalar gain V s = scalar output x1x1 x2x2 V T2 V T1 KTKT x VTVT Span = max. value - min. value

Sensor Scaling Case 1: No Offset in Scalar or Sensor lesson4et438a.pptx4 Transducer gain formula: V T = K T x Required scalar gain: Scalar output formula x VTVT KsKs KTKT Sensor K T Block Diagram Scalar K s VTVT VsVs Input Output V T = K T x V s = K s V T x

Example 4-1: Case 1 Sensor lesson4et438a.pptx5 A pressure transducer has a usable range P (x) range of 0-50 psig (lb/in 2 gauge). It has a voltage output range of Vdc over the pressure range. Scale the output to a range of 0-10 Vdc Find K T Find scalar gain K T =0.025 V/psig K s =8 V/V VTVT VsVs P

Sensor Scaling Case 2: Offset in Sensor No Offset in Output lesson4et438a.pptx6 KTKT KsKs Sensor gain formula: V T = K T x + b Whereb = transducer offset Scalar gain formula must subtract offset Correct form of scalar output Scalar equation x VTVT b Block diagram Sensor K T ∙x+b Scalar K s ∙V T - K s ∙ b VTVT VsVs x V T =K T ∙x+b V s =K s ∙V T - K s ∙ b

Example 4-2: Offset Sensor Output Range lesson4et438a.pptx7 A temperature transducer has a range of C (input x) It has a voltage output range of 1-5 Vdc (V T ) over this temperature range. Scale the output to a range of 0-10 Vdc. Find the transducer gain, K T, and the offset,b. Find the scalar relationship required to get the desired output range. Draw a block diagram of this sensor/scalar system that includes the mathematical relationship derived above. Find K T Find b from point slope form of line b=1.0

Example 4-2: Solution (2) lesson4et438a.pptx8 Find scalar gain Scalar formula Transducer 0.04x+1 V T = 0.04x+1 x VTVT VsVs Input Output Scalar 2.5V T -2.5 V s = 2.5V T -2.5 Block Diagram

Sensor Scaling Case 3: Transducer with no offset, Output offset lesson4et438a.pptx9 KTKT KsKs VTVT x c = scalar offset can be +- value Transducer gain formula: V T = K T x Scalar formula must add a constant To find c, use point slope form using scalar points c

Example 4-3: Case 3 Sensor Scaling lesson4et438a.pptx10 A pressure transducer has an input range of psig (x) and an output range of V (V T ) Find the scaling equation to convert this range into the desired range of -5 V to +5 Vdc) Find transducer gain and scalar gain formulas. Draw the block diagram of the complete system Find K T Find K s

Example 4-3: Solution (2) lesson4et438a.pptx11 Use point-slope form of line to find the value of c Can use either point in pair defining range Scalar gain formula c=-5 Transducer 0.04x V T = 0.04x x VTVT VsVs Input Output Scalar 10V T -5 V s = 10V T -5 Block Diagram

Example 4-4 Scalar Equations lesson4et438a.pptx12 Range of linear temperature transducer is F with a transducer gain of 10 mV/F. The desired output of the transducer for the range of temperature is Vdc. Find the gain formula. Find span of transducer Move origin to (32, 0.32)

Example 4-4 Solution (2) lesson4et438a.pptx13 Compute sensor equation Shift origin to (32 F, 0.32 V) So b=0.32 Check equation at data points

Example 4-4 Solution (3) lesson4et438a.pptx14 lesson4et438a.pptx Transducer 0.01x V T = 0.01T T VTVT VsVs Input Temp Output Scalar 5.56V T V s = 5.56V T Block Diagram

Example 4-5 lesson4et438a.pptx15 A linear temperature transducer has an input range of -20 C to 50 C and a gain of K T = 20 mV/C. The desired output range is Vdc. The transducer output voltage is bipolar (+-). Find the scaling equation. Compute the transducer and scalar span Scalar formula Find b graphically. Must shift origin to (-20 C, -0.4 V)

Example 4-5 Solution (2) lesson4et438a.pptx16 Find scalar gain Check scalar equation at data points Transducer 0.02x V T = 0.02T T VTVT VsVs Input Temp Output Scalar 3.571V T V s = 3.571V T Block Diagram

Practical Realization of Scalar Equations Using OP AMPs lesson4et438a.pptx17 Scaling without offset: use inverting or non-inverting amps to implement K s For inverting amps V0V0 RfRf R in V cc Sensor For non-inverting amps

Practical Realization of Scalar Equations Using OP AMPs lesson4et438a.pptx18 For transducers with offset use inverting and summation amps Stage 2 OP AMP changes sign if R f1 = R in A V = -1 Stage 1 Overall gain

Practical Realization of Scalar Equations Using OP AMPs lesson4et438a.pptx19 Equate the sensor with offset formula to the OP AMP gain derived on the last slide so

Example 4-6: Implementing Scalar Equation with OP AMPs lesson4et438a.pptx20 Design an OP AMP circuit that will implement the scalar equation from Example 4-5 Assume R f1 = R in = 100 k  R f = 470 k  Scalar relationship for Example 4-5 From scalar equation K s = 3.571

Example 4-6: Solution (2) lesson4et438a.pptx21 Value of R T is not a standard value. Use a standard value near the computed value in series with a potentiometer and calibrate circuit. Use -0.4 and 1.0 V and adjust the potentiometer 127 k10 k

Example 4-6: Solution (3) lesson4et438a.pptx22 Compute the value of R b Simpler design method: Let R b =R f So…. Set V b to the numerical value of K s b

Example 4-6: Solution (4) lesson4et438a.pptx23 Completed design

ET 438a Automatic Control Systems Technology lesson4et438a.pptx24