The PID enhancement for wireless (PIDPlus) offers an improvement wherever there is an update time in the loop. In the broadest sense, an update time can range from seconds (e.g. wireless updates and valve or measurement sensitivity limits) to hours (e.g. failures in communication, valve, or measurement). Some of the sources of update time are:
(1) Wireless measurement default update rate for periodic reporting (refresh time)
(2) Wireless measurement trigger level for exception reporting (sensitivity limit)
(3) Wireless communication failure
(4) Broken pH electrode glass or lead wires (failure point is about 7 pH)
(5) Large valve operating on upper part of installed characteristic (low sensitivity)
(6) Valve with backlash (deadband) and stick-slip (resolution and sensitivity limit)
(7) Valve with solids, high temperature, or sticky fluid that causes plugging or seizing
(8) Plugged impulse lines
(9) Analyzer sample processing delay and analysis or multiplex cycle time
(10) Analyzer resolution and sensitivity limit
The PIDPlus waits for an update in the measurement whereas a traditional PID continually ramps the output acting on old information. When there is an update, the PIDPlus considers the changes to have occurred over the elapsed time from the last update whereas the traditional PID thinks the entire change occurred in the PID module execution time. The result is a spike from derivative action by a traditional PID that is particularly large when a measurement recovers or a valve trim or solids break free.
The improvement in control by the PIDPlus is most noticeable as the update time becomes much larger than the 63% process response time (defined in the white paper as the sum of the process deadtime and time constant). When the update time becomes 4 times larger than the 63% process response time that roughly corresponds to the 98% response time frequently cited in the literature, the controller gain can be set equal to the inverse of the process gain. This controller gain can provide an exact correction for changes in the measurement and setpoint.
The PIDPlus execution is kept fast so that the PID immediately responds to changes in setpoint, feedforward, mode, tuning, detail display parameters, and remote output. We have the interesting result that when the update is much larger than the 63% process response time so we can set the controller gain equal to the inverse of the process gain, the controller output goes immediately to the value needed to achieve the setpoint. An increase in update time to prolong battery life can actually translate to a faster setpoint response. However, if the process gain changes with time or operating point, the PID will require several updates to home in on the proper correction. An increase in update time will increase the settling time for unrecognized changes in the process gain. The use of an adaptive tuner such as DeltaV Insight that automatically identifies the process gain and schedules the tuning setting accordingly can sustain a fast setpoint response despite nonlinearities and a large update time.
The Emerson White Paper DeltaV-v11-PID-Enhancements-for-Wireless.pdf discusses these opportunities in more detail. Later this month, an entry on this site will show and discuss the trend plots that compare the enhanced PIDPlus with the traditional PID for the applications tested including valves with stick-slip and backlash.
It is important to distinguish between an update time and process deadtime. The update time is the time interval between successive updates by the final control element (initiated changes to the process input) and successive updates by the measurement (reported changes in the process output). The process deadtime is a continuous train of values delayed by the deadtime. The most common source of a pure process deadtime is a transportation delay of temperature and composition changes in a conveyor, extruder, dip tube, heat exchanger, pipeline, sheet line, or any volume where there is plug flow (no back mixing). Small time constants such as thermal lags, sensor lags, signal filter times, transmitter damping settings, effectively become additional deadtime in terms of a first order plus deadtime approximation (single time constant plus deadtime). The PIDPlus algorithm does not correct for process deadtime. As the process deadtime increases and approaches the update time, the opportunity to increase the PIDPlus gain decreases. For compensation of deadtime, a standard deadtime block can be inserted between the BKCAL_OUT of the AO block and the BKCAL_IN of the PID block if the DCS uses the positive feedback method for the integral mode (external reset) as reported in Advanced Application Note 3 “Compensation of Deadtime in PID Controllers“.
In a future Deminar we will look in greater detail at the effect of updates time of discontinuous measurements and process deadtimes on the ultimate period and ultimate gain and if there is an improvement in loop performance offered by a combination of PIDPlus and deadtime compensation.