The mechanical properties of a material are determined by using a testing machine to push, pull or twist a sample of the material. Many materials are strain rate sensitive which means their properties vary with test speed. A valid comparison of mechanical properties between suppliers can only be achieved if the same test speed is used by all.
The American Society of Testing and Materials (ASTM) and the International Standard Organization (ISO) are two organizations that govern mechanical test specifications. Each specification requires that the force be applied at a specific strain, crosshead position or stress rate. One function of the testing machine controller is to ensure that the specified test rate is accurately maintained throughout the test. ADMET testing systems equipped with controllers such as the MTESTQuattro controller (shown above) are part of the motor control system responsible for regulating the speed of the motor.
The test rate is proportional to the motor speed. Control of motor speed is accomplished by increasing the voltage to the power amplifier if the test speed is too low or decreasing it if the test speed is too high. A simple rule for regulating motor speed is to make a change in the power amplifier voltage proportional to the test speed error (difference between the actual and desired test speed).
Test Speed Error = Desired Test Speed – Actual Test Speed (Eq. 1)
Amplifier Voltage = Kp x Test Speed Error (Eq. 2)
Equation 2 is a proportional control algorithm. Kp is the proportional gain and is adjusted to minimize the test speed error. From the point of view of the motor control system, how well the test speed is controlled will depend on how much demand is placed on the MTESTQuattro controller. If the analog to digital (A/D) and digital to analog (D/A) converters as part of the controller require little intervention; if the MTESTQuattro control algorithm used for computing the power amplifier voltage as a function of measured test speed can be updated quickly; then it is reasonable to expect minimal error between the actual and desired test speeds. Since the calculation of the power amplifier output voltage does not depend on time (see Eq. 2), the strategy for the MTESTQuattro controller is to update the power amplifier voltage as frequently as possible. We define the servo update rate as the time interval between each amplifier voltage computation. The servo update rates for our examples are fixed at 1 millisecond or 1,000 times per second (1,000 Hz). To relate the servo update rate to actual testing applications, see examples below.
- Example 1: ASTM D638 Standard Test Method for Tensile Properties of Plastics specifies a constant
crosshead testing speed of 2 in/min or 0.033 in/sec. With a servo update rate of 1,000 times per
second, the desired crosshead movement per servo update = 0.033/1000 = 0.000033 inches/servo
- Example 2: Apply a 10 lbf peak to peak sinewave force amplitude at 5 Hz (cycles per second) to a test
sample. Based on the 5 Hz specification, each cycle is to be completed every 0.2 seconds (1/5 Hz). The
number of servo updates per cycle = 1000 x 0.2 = 200 servo updates per cycle. During each cycle the
actuator will apply 10 lbf then remove 10 lbf from the sample for a total force traversal of 20 lbf. The
average change in force per servo update is 20 lbf / 200 = 0.1 lbf/servo update.
- Example 3: Apply a 10 lbf peak to peak sinewave force amplitude at 50 Hz to a test sample. Based on the
50 Hz specification, each cycle is to be completed every 0.02 seconds (1/50 Hz). The number of servo
updates per cycle = 1000 x 0.02 = 20 servo updates per cycle. The average change in force per servo
update is 20 lbf / 20 = 1 lbf/servo update.
In Example 1, the test is performed at a constant displacement rate of 0.000033 inches/servo update. Because the desired rate does not vary during the entire test and the control algorithm updates the amplifier voltage 1,000 times per second, the motor control system is capable of precisely following the desired test speed.
On average there is a 0.1 lbf and 1 lbf change in force per servo update in Examples 2 and 3, respectively. However, the motor during the sinewave profile is continuously accelerating and decelerating producing a varying test speed error. As we increase the cycling frequency, accelerations get larger and there are fewer servo updates each cycle. Therefore, the servo update errors will grow with increasing frequency which will demand more from the controller to achieve accurate control.
Figure above is a block diagram of the testing application on Example 1 where the test rate is based on the crosshead position (specified as 0.033 in/sec or 0.000033 in/servo update). With closed loop control, at each servo update, the MTESTQuattro controller subtracts the actual crosshead position from the desired crosshead position to obtain the crosshead position error.
- If the error for that servo update is zero, the power amplifier voltage will be zero.
- If there is an error, corrective action will occur. The motor will be told to speed up if the actual position lags the desired position (positive error) or told to slow down if the error is negative. As the test is progressing, the force is increasing but then the material begins to yield (a process disturbance). Suddenly there is less resistance to stretching the test specimen and the actual position gets ahead of the desired position. The controller will decrease the power amplifier voltage so that the motor slows down. After a while, the material may begin to strain harden creating more resistance to movement. The actual position falls behind and the controller then increases the power amplifier voltage to speed the motor up.
Without a feedback loop, the testing machine would have no knowledge of it’s actual crosshead position. Once a disturbance is encountered such as increasing load, yield, or rupture, the error between the actual and desired crosshead position would vary along with the test speed.
Click below for a comparison of open-loop and closed-loop controls in materials testing.
ADMET MTESTQuattro controller employs a Proportional, Integral, Derivative (PID) control algorithm.
The PID controller works the following way. Each servo update, the actual crosshead position is subtracted from the desired crosshead position to obtain a position error. The error is passed into one, two or all three of the P, I and D modes depending on which modes are turned on. Then the outputs from each mode are added together. The resulting sum is the controller output or power amplifier voltage which sets the speed of the motor for that servo update. One, two or all three of the modes can be turned on. The possible combinations are listed below with the most common being PI control.
- Proportional Control Only, P
- Proportional plus Integral Control, PI
- Proportional plus Integral plus Derivative, PID
- Proportional plus Derivative, PD
Integral control action continuously adds the errors at subsequent servo updates together producing a ramp like change in the power amplifier voltage. This action will drive the servo update error to zero over time and also overcome the changing motor resistance caused by varying loads during a test.
In general, one set of crosshead position PID control gains on a static testing machine will produce acceptable crosshead position control over almost the entire speed range of the machine. For very slow speeds, a second set of crosshead position PID control gains with larger proportional gain (Kp) and integral control gain (Ki) values may be required. For fatigue testing applications, a different set of PID control gains may be required for cyclic waveforms differing in amplitude and frequency. Thus, requiring more frequent gain tuning.
Click below for an overview of MTESTQuattro gain tuning procedure.
There are several key points to keep in mind when tuning force control loops. The stiffness of the test specimen or how much it stretches under load relative to the stiffness of the testing machine load frame and motor control system matters.
- If the test specimen is very compliant (stretches much more) relative to the testing machine, good control over the entire force range is achievable.
- If the stiffness of the test specimen is equal or greater than the stiffness of the testing machine, then instability at higher forces may be experienced.
To eliminate the instabilities at higher loads make the control loop more sluggish by reducing the proportional and integral gains. The end result of reducing the gains is larger control errors at lower loads but a stable control loop at higher loads.