Equations 1b, 2b, and 3b show that the ultimate gain increases as the ultimate period and process gain decreases and as the largest process time constant increases. For properly designed reactors, the ultimate gain for the primary loop is normally greater than five unless an extremely narrow temperature measurement span is used, which increases the process gain seen by the controller. Primary temperature controller gains less than one are the sign of poor tuning, a slow secondary loop, or an unusual reactor design. The ultimate gain in benefits from a cascade control system depends upon the user recognizing the ultimate gain of the controller and tuning the controller to have a closed loop time constant less than the open loop time constant by initially overdriving the setpoint of the secondary controller beyond its resting value. However, for split-ranged valves, this requires that tuning be switched to match the valve and heat transfer media. If the overdrive causes an unnecessary transition from heating to cooling or vice versa, the dead zone and discontinuity from overdrive may cause hesitation or oscillation. In this case it may be necessary to limit the overdrive to be just short of the transition point.
Traditional manual open-loop tuning methods, where step changes are made and held in the manual output of the primary controller, are not practical for these reactors because the steady state is too long and reactor temperature may ramp or accelerate into an undesirable operating region that ends up testing interlock, relief, and flare systems and evacuation procedures. An adaptive controller that is set up for tight feedback and feedforward control of an integrating process that looks at the normal set point changes in the batch with the cascade control system in its normal mode provides the fastest tuning.
Survival of the Fittest
The process time constants and process gain are highly nonlinear in batch operation because the reaction rate is a moving target. If you throw a transition between heating and cooling into the mix, you are headed for less than the best quality and efficiency. The preemptive adaptation of the controller to changing batch conditions is as important as the preemptive adaptation of a company to changing business conditions. The primary controller tuning settings should be scheduled based on totalized feeds and the secondary controller tuning settings scheduled based on the position of the split ranged valves4. The adaptive controller should trim the settings as the reactor moves into the scheduled regions and provide a closed loop response faster than the open loop response.
Technical Terms Used Interchangeably in Process Control
Time Delay – Dead Time
Derivative Action – Rate Action
Derivative Time – Rate Time
Digital Valve Controller – Digital Valve Positioner
Integral Action – Reset Action
Integral Time – Reset Time
Time Lag – Time Constant*
Open Loop Gain – Process Gain
Proportional Action – Gain Action
* A closed loop time constant defines the exponential response for a step change in the controller set point with the controller in automatic. An open loop time constant defines the exponential response for a step change in the controller output with the controller in manual. An open loop time constant for a self-regulating process is a negative feedback time constant. The positive feedback time constant for a runaway process is not common but is useful for describing the acceleration. There is no steady state for a runaway except as forced by the gain action of a controller in automatic.
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