For purposes of analysis of the impact on industrial process control, the sources of a PID input error (deviation between the true process variable and the measurement signal) and a PID output error (deviation between valve-VFD signal and actual stroke-speed) are (Measurement-Valve-Errors.pdf):
(7) Backlash (deadband)
Offset, drift, and nonlinearity affect measurement accuracy, the difference in the peak of a distribution of measurements from the true value. The remaining terms (4) => (10) affect the precision of the measurement, which can be viewed as multiple of the standard deviation.
Offset is a fixed bias from setpoint often the result of the tolerance of sensor, transmitter, or calibration method. The biggest tolerance error is typically associated with the sensor. For example, when a thermocouple or pH electrode is replaced, there may be an offset of 2 degrees Centigrade and 0.2 pH, respectively. Factory calibrations can quantify the offset, and the grade, design, and quality control during manufacturing can minimize the offset. More insidious are tolerance errors introduced by calibration standards that have deteriorated (e.g. poorly regulated temperature baths and contaminated buffer solutions).
Drift can be viewed as a shifting offset over a relatively long period of time (months or years). Thus a thermocouple and pH electrode may drift 5 degrees and 0.5 pH units per year. For pH electrodes, an offset of 100 or millivolts at 7 pH (millivolts at 7 pH should be zero) is a sign the electrode should be replaced.
Nonlinearity shows up as an error that is a consistent function of size of the process variable or manipulated variable. Adjustment of equation coefficients for the sensor in use (sensor matching) in smart temperature transmitters can compensate for the nonlinearity of the sensor and eliminate the tolerance error. If you also consider a differential head flow meter has the square root extracted in a DP transmitter and a nonlinear function of radiation received versus level for a point source nuclear level device is compensated by signal characterization, the measurement error seen today from nonlinearities is rather minimal and limited to special cases. For control valves, the nonlinearity between the stroke and signal is negligible unless deliberately imposed by signal characterization to compensate for the valve characteristic and system curve. Similarly, the nonlinearity between the pH signal and the actual pH is not significant unless signal characterization is used to compensate for the titration curve.
Interference can be classified as any change in process and installation conditions that cause an offset. Interference is typically a shifting offset over a relatively short period of time (hours or days). The Nov 25 blog titled “Secret Installation Effects” describes some of the more common interferences. Smart transmitters and smart positioners (digital valve controllers) have done a remarkable job at addressing these errors in recent years.
Very short term process interferences can show us as noise. If the noise is much less than the loop deadtime, it can be adequately attenuated by a transmitter damping adjustment or signal filter. Another common source of noise is electromagnetic interference and fluctuating ground potentials (significant problems for thermocouples and pH electrodes).
Hysteresis is the maximum bow between the complete traverses of the signal or stroke in both directions. Hysteresis is normally seen in diaphragm actuators and valves or any device that stores and release energy or mass, depending on the direction of the change.
Backlash is the deadband in signal or stroke whenever there is a change in direction. Backlash is large in mechanical devices particularly in rotary valves. The source are links, levers, and play in connections that is greatest when there is a translation of motion from linear to rotary and when there shaft windup. Dampers and on-off valves posing as control valves may have a backlash (deadband) of 5% or more even with a smart positioner if the position feedback is actuator shaft rather than internal control element.
Resolution is the smallest change in signal that can be reported or the smallest change that can be enacted. The response is either direction is a staircase where the step size is the resolution limit. The largest sources of resolution limits is the number of bits used for quantization of a signal, friction (stick-slip) in control valves, and the gear teeth spacing in a motorized or rack and pinion piston actuator. Note that one of the bits for A/D I/O cards is a sign bit so that the 12 bits of the 1980s DCS A/D caused a resolution error that was the measurement span divided by 2 to the eleventh power. The use of wide range thermocouple cards with these vintage DCS often caused a resolution error of 0.2 degrees centigrade. For analyzers, the resolution limit is often set by the smallest reagent dose.
Sensitivity is the smallest change that can trigger an updated signal or stroke. The update in the signal or stroke is not quantized like a resolution limit but will take on a value that exactly matches the actual value. Thus, there is no uniform staircase seen with a resolution limit. Once triggered, the updated value matches the actual value. The default trigger level setting in a wireless transmitter is a sensitivity limit. The biggest inherent sources of sensitivity limits are the type of sensor in measurement and the friction in the packing and sealing surfaces in a control valve.
Repeatability is the biggest separation successive traverses in the same direction of the entire signal range. Often repeatability is taken to be differences between the signal value and true value for repeated measurements and between the enacted value and actual value for a stroke. In reality these differences could be caused by interference, noise, resolution limits, and sensitivity limits and is not really a repeatability error per the ISA definition.
So what is the impact? For control valves and lower (secondary) loops, such as flow, all of these errors except for resolution and sensitivity can be corrected by a self-regulating upper (primary) process loop such as temperature or pH. For integrating upper loops, such as level and batch temperature, backlash and repeatability besides resolution and sensitivity create limit cycles. All of the errors are important for the upper loop although some are more easily corrected than others. Noise, can be filtered and drift and be corrected by periodic calibration. An offset in the uppermost loop is often compensated for by a bias of the setpoint either usually by experience (e.g. column or reactor product quality is better at a slightly different temperature setpoint) or by runs of a process simulation. Replacing the upper loop sensor with a tolerance error not corrected by calibration can suddenly cause perplexing poor performance because operations did not realize the real source of the setpoint bias.