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

2. Experimental Design
Experimental design is the first step in any measurement experiment. It involves developing a measurement test plan following three steps:
Parameter Design Plan – test objective and identification of process variables and parameters and a means for their control. You should ask:
What question am I trying to answer ?
What variables to be measured ?
What variables will affect my results ?
System and Tolerance Design Plan – selection of measurement technique, equipment and test procedure based on some preconceived tolerance limits for error. You should ask:
How will I do the measurement and how good do the results have to be ?

3. Experimental Design (cont’d)
3. Data Reduction Design Plan – Plan ahead on how to analyze, present, and use the anticipated data. You should ask:
How will I interpret the resulting data ?
How will I use the data to answer my question ?
Step 1 needs the following important concepts:
Variables
Parameters
Noise and Interference
Random Tests
Replication and Repetition
Concomitant Methods

4. Variables
One variable in the measurement system is obviously the targeted measured variable, but there might be other variables that affect the outcome
All known process variables should be listed and evaluated for any possible cause and effect relationships
A variable that can be changed independently of other variables is known as an independent variable
A variable that is affected by changes in one or more other variables is known as a dependent variable
Variables that cannot be controlled during measurements but that affect the value of the measured variables are called extraneous variables.
If the values of a variable can be enumerated it is called discrete. Otherwise it is called continuous

5. Variables
Example: For the following calibration system. Identify the independent, dependent, and possible extraneous variables.
Answer:
Independent variables: piston displacement x, temperature T
Dependent variables: gas pressure p
Extraneous variables: noise effects due to room temperature; line voltage variations, connecting wires

6. Parameters A parameter is a function relationship between variables
A parameter that has an effect on the behavior of the measured variable is called a control parameter
A control parameter is completely controlled if it can be set and held at a constant value during a set of measurements
Example (Pendulum):
period
Ratio of l and g is a completely controlled parameter
because l is fixed and g is known

7. Noise and Interference
The way of extraneous variables affects measured data can be classified into noise and interference
Noise is a random variation of the value of the measured signal as a consequence of the variation of the extraneous variables
Interference produces undesirable deterministic trends on the measured value because of extraneous variables
Example:

8. Random Tests
It is important to minimize the effects of extraneous variables in a measurement using random tests
A random test is defined by a measurement matrix that sets a random order in the value of the independent variable applied to measure the dependent variable
Example:
Extraneous
Variable
Pressure
Transducer
+ Voltmeter
Independent
Varables
Dependent
Variable
Apply Random Sequence
(holding temperature constant)

9. Random Tests (cont’d)
Assuming that we can hold the temperature fixed, applying a random sequence of volume values rather than a sequential sequence will allow us to average out the effects of extraneous variables
We will see later that when the measurement system is subject to hysteresis, applying an increasing sequence of values for the independent variable produces a different result as compared to the case of applying the same set of values in a decreasing order
A random sequence enables us to deal with this effect by providing a unique value of the independent variable for each value of the dependent variable in the random sequence
After applying several random sequencies the results are averaged out to find a best-fit curve

10. Random Tests (cont’d)
We have seen that random tests are effective for the local control of extraneous variables that change in a continuous manner
Discrete extraneous variables can also be dealt with by performing a random test
The use of different instruments and different test operators are examples of discrete extraneous variables that can affect the outcome of a measurement
These effects are usually reduced by randomizing a test matrix by using random blocks
A block consists of a data set of the measured variable in which the control variable is varied but the extraneous variable is fixed
The extraneous variable is then varied between blocks

11. Example: Randomized Matrix
The manufacture of a particular composite material requires mixing a percentage by weight of binder with resin to produce a gel. The gel is used in a lay-up procedure to impregnate the fiber. The strength will depend on both the percent binder in the gel and the test operator performing the lay-up.
Formulate a test matrix to find the percent binder influence on strength
Solution: Pick three different bider-gel ratios A, B, C and three typical operators to produce N separate composite test samples for each of the 3 ratios
Create the following test pattern:

12. Replication and Repetition
In general the estimated value of a variable improves with the number of measurements. The mean over measurements is taken as the estimated value
Repeated measurements made during any single test run or on a single batch are called repetitions. It allows for quantifying the variation in a measured variable as it occurs during any one test or batch while the operating conditions are held under nominal control
An independent duplication of a set of measurements using similar operating conditions is referred to as a replication. It allows for quantifying the variation in a measured variable as it occurs between different tests, each having the same nominal values of operating conditions

13. Concomitant Methods
A good strategy is to incorporate the use of concomitant methods in a measurement plan. The goal is to obtain two or more estimates for the result, each based on a different method, which can be compared as a check for agreement
Example: Establish the volume of a cylindrical rod of known material.
Method 1: Measure the diameter and length
Method 2: Measure the weight and compute volume based on specific weight of material