1. MECH 373 Instrumentation and Measurement
Lecture 2
(Course Website: Access from your “My Concordia” portal)
Contents of today’s lecture:
• Dealing with error
– Error reduction techniques
– Standards
– Calibration
• Dynamic measurements
– Zero order, first order, second order systems
– Time constant, response time, rise time, settling time
– Frequency response 1

2. Essential Elements Measurement System Input Output Sensing Element
True value of variables
Measurement
System
Output
Measured value of variables
Sensing Element
Conditioning Element
Processing Element
Displaying Element 2

3. Resolution 3

4. Types of Measurement Errors
Sources of errors
Improper sensing position
Improper element calibration
Improper data acquisition method
Improper sampling rate
Elements non-linearity
Environment effects
Characteristic of errors
Systematic errors
Random errors
Parameter tracking errors 4

5. Summary How to reduce the measurement errors? Topic in today’s lecture5

6. Error Reduction Techniques (1)
The most effective method of reducing measurement error (systematic) is to:
Set the sensing element at the right position.
Area with low stress gradient and low temperature. 6

7. Error Reduction Techniques (2)
An effective and useful method of reducing measurement error (systematic) is to:
Calibrate each element to eliminate or reduce bias. DC shift.
Offset 7

8. Error Reduction Techniques (3)
Another effective method of reducing measurement error (systematic) is to:
Setup a proper sampling rate for data acquisition.
At least 2 times of the highest frequency of interest. D 8

9. Error Reduction Techniques (4)
Another effective method of reducing measurement error (systematic and random) is to:
compensate the environmental effects
Environmental effects isolation:
Environmental input cancellation: 9

10. Random error reduction (5)
Random errors – Originate from measuring systems and experimental systems.
In measuring systems – Temperature effects on amplifier performance.
Environmental causes – Electrical noise from electric and magnetic field around the equipments.
Solution – Proper shielding or grounding the measuring systems – Minimise electrical noise.
Statistical analysis – Large number of samples. 10

11. Unknown system 11

12. Standards
The first step before performing a measurement is instrument calibration
When a measurement system is calibrated it is compared with some standard whose value is presumably known
The standard may be a piece of equipment, an object having a well-defined physical attribute to be used as a comparison, or a well accepted technique known to produce a reliable value
The accuracy of a standard needs to be higher than the one of the instrument being calibrated.
A rule often followed is that the calibrated standard has an accuracy four times better than the instrument being calibrated 12

13. Basic Dimensions: Standards, Units
The basic dimensions are:
Mass - Kg
Time - Second
Length - meter
Temperature – Celsius, Kelvin (0 K = C) and Fahrenheit
Electric Current (Amp)
..... 13

14. Calibration
Relationship between measurement and true value is the first task performed in a measurement: calibration
Calibration - Applying known input value (standard) to unknown measurement system for the purpose of observing the output and establishing an input-output relationship.
Applying a range of known values for the input and observing the output – Develop a direct calibration curve.
Use the calibration curve in later measurements to ascertain the unknown input value (actual value) based on the output value. 14

15. Calibration Calibration:
A test in which known values of the input are applied to a measurement system (or sensor) for the purpose of observing the system (or sensor) output.
Static calibration:
A calibration procedure in which the values of the variable involved remain constant (do not change with time or change slowly) – static weights.
• Dynamic calibration:
When the variables of interest are time dependent and time-based information is need. The dynamic calibration determines the relationship between an input of known dynamic behavior and the measurement system output – Accelerometers. 15

16. Static Calibration
In performing a static calibration, the following steps are necessary:
Examine the construction of the instrument and identify and list all the possible inputs.
Decide, as best as you can, which of the inputs will be significant in the application for which the instrument is to be calibrated – Establish range.
Find an apparatus that will allow you to vary all the significant inputs over the ranges considered necessary. Find standards to measure inputs.
By holding some inputs constant and varying others, record the output and develop the desired static input-output relation as a best-fit curve. 16

17. Best-fit Curve
If the output data of a measurement system is to give a meaningful description of the measurement process, the data must form what is called a random sequence.
In a calibration we specify that certain inputs must be held constant within certain limits. Those are the inputs that hopefully will have the most influence in the measurement.
However, there are many extraneous input variables that are uncontrolled – environment effects.
A reasonable assumption is that the aggregate of their effect on the instrument output will be of a random nature.
We can then apply the least-squares method to find the best-fit curve – ‘Eye-ball’ approach. 17

18. Best-fit Line
R = 1.290W – 0.374 18

19. Static calibration - Deviation
Max. repeatability error – UP cycles 19

20. Static calibration - Average deviation
Max. systematic error

21. Static calibration – Error summary
Several cycles before data recording. Typical 5 cycles recommended for static calibration. ANSI/ISA(1979).
Establish best fit curve (eye-ball).
Output span:
W = 0 lb., R = lb. and W = 5 lb., R = lb.
O/S = – (-0.374) = 6.45 lb.
Accuracy limits – Max and min deviations from best fit line.
+0.45 lb. at 0 lb. (down cycle), 7% of output span;
-0.40 lb. at 2 lb (up cycle) % of O/S.

22. Static calibration – Error summary
Non-linearity – Average of all data taken for each weight value in both up and down cycles – Solid dots in Fig. E2.3(d).
Max. = 0.41 lb. (6.4% of O/S) at 0 lb.
Repeatability error – Max variability of successive measurements of same input value approached same loading direction – Fig. E2.3(c)
At 1 lb. up cycle - Range to – 0.17 lb.
2.6% of O/S, +/-1.3% of output span.

23. Static calibration – Error summary
Max hysteresis error – Max difference between the Up and the correspond Down reading for any calibration cycle – Table E2.3(b).
– Cycle 3 at 2.5 lb., lb. in up cycle, lb., in down cycle.
Total = 0.52 lb., 8.1% of O/S, +/-4.05% of O/S.

24. Static calibration – Error summary
Max. systematic error – Max deviation of the averaged calibrated values (average of up and down readings) for all cycles – Fig. E3.2(d).
At 0 lb., +0.41lb, +6.4% of O/S.
At 2.5 lb., -0.35lb, -5.4% of O/S.
Max. random error – repeatability error – same input and same loading direction.
At 1 lb. in up cycles,
Cycle 3 = lb., Cycle 5 = lb.
Range = 0.17 lb, 2.6% of O/S, +/- 1.3% of O/S.