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Deadtime Dominance - Sources, Consequences and Solutions

Thu, 01 Dec 2016 20:30:00 -0500

If the total loop deadtime becomes larger than the open loop time constant, you have a deadtime dominant loop. There is a lot of misunderstanding posed by this difficult challenge including a lot of prevalent myths.  Here we look at how we get into this situation, what to expect and what to do. Deadtime is the ultimate limit to loop performance. A controller cannot correct for a disturbance until it starts to see a change in the process variable and can start to change the manipulated variable (e.g., flow). If the deadtime was zero, the controller gain could be set as large as you want and the peak and integrated errors made as small as you want provided there is no noise. The PID gain could theoretically approach infinity and lambda approach zero. Without deadtime, I would be out of job. Sources Fortunately, deadtime dominant loops where the deadtime is much larger than the open loop time constant, is usually relegated to a few loops for processes involving liquids and gases.  Deadtime dominance typically occurs due to transportation delays (deadtime = volume/flow), cycle times of at-line analyzers (deadtime = 1.5 x cycle time, or improper setting of PID execution rates or wireless update rates (dead time = 0.5 execution or update rate time interval). Deadtime dominance due to transportation delay is more common in the mining industry and other processes that are primarily dealing with solids. Large transportation delays result from conveyors or feeders or extruders where the feed of solids are manipulated at the inlet and the quality or quantity is measured at the outlet (discharge) assuming the sensor lag is much less than the transportation delay (i.e., total loop deadtime). The use of a gravimetric feeder can eliminate the delay for feed flow control making a much more precise and responsive loop.  A kiln has a temperature sensor lag that creates an open loop time constant that is usually larger than the transportation delay. However, the use of an optical sensor (e.g., pyrometer) for temperature control eliminates this lag possibly making the loop deadtime dominant. In vessels and pipes where there is no axial mixing, also known as back mixing due to an agitation or recirculation or sparging, there is no mixing up and down in the vessels and mixing forward and backwards in the pipe. We call this plug flow. There may be radial mixing, to make the concentration or temperature in a cross section of the vessel or pipe more uniform or to keep solids dispersed. Radial mixing does not reduce transportation delays whereas axial mixing eliminates plug flow decreasing transportation delays. Any remaining delay from axial mixing depends upon the degree of mixing. For vessels with good geometry and axial agitators, the delay is approximately the turnover time that is the volume divided by the summation of the agitator pumping rate, recirculation rate and feed rate.       Deadtime dominance usually doesn’t occur in temperature loops except for inline systems, such as plug flow liquid or polymer reactors where there is negligible heat transfer lag in the equipment or sensor.   Consequences For a deadtime dominant system, the peak error for a step load disturbance approaches the open loop error (error if loop is in manual). Better tuning and feedback control algorithms cannot do much to improve the peak error. There can be a significant improvement in the integrated error by better tuning and feedback algorithms for a load disturbance but the ultimate limit to the integrated error is the peak error multiplied by the deadtime. Solutions The best solution is to eliminate the deadtime that is the source of deadtime dominance by better process, equipment or automation system design. The next best solution is feedforward control given a reliable timely measurement of the disturbance. The feedforward measurement does not need to be extremely accurate. An error of 20% will still result in an 80% improvement in integrated error if the feedforward timing is right. The correct timing cannot be achieved when the correctio[...]

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