Charlie Cutler's Latest Ideas for Multivariable Controllers

Process Variable Models and Adaptive Transforms

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Using PVs as the independent variables contributes to better control by keeping the predictions correct for sticking valves. A sticking valve corrupts the controller's predictions when setpoints are used as independent variables, since it is assumed the valve moves with a setpoint change. The predictions are updated for the setpoint change. When the valve moves free again, the PV changes, but the prediction does not get updated. In effect, the prediction is corrupted two times: when a valve first sticks, and when it becomes free again. Using the PV as the independent variable in the controller model maintains the integrity of the prediction, since the PV is correct even when the valve sticks.

When PVs are independent manipulated variables in the controller, the changes in the PVs are transformed into valve position changes for execution. With the valve transforms outside the controller, they can be adapted for changes in both the upstream and downstream pressures. Obviously the PID controller's performance is affected by the changes in the valve for a constant flow.

The PID controller may become unstable if the position on the plot of flow versus valve position changes significantly. The behavior of the PID controller can adversely affect the controller model, since its behavior is implicit in the step response models of the controller. This is a further advantage of switching to a PV model, which is not effected by the behavior of the PID controllers that are put in manual.

The use of adaptive transforms and PV modeling are synergistic and have the potential to significantly improve the performance of present day multivariable controllers. Universal Process IDentification (UPID) is a commercially available product that permits the rearrangement of the independent and dependent variables in a finite impulse response model. The critical information for the PID control system is input to UPID. The tuning constants, configuration (auto, manual, cascade), the PID equation type, the brand of DCS, the valve action, the control interval, etc. are used. The first step in changing the configuration with UPID is to remove the PID controller dynamics from the model for the PID loop that is to be changed. In effect the PID controller is put into the manual mode. When the PID dynamics are removed from the model, every step response curve in the model can potentially change. This is illustrated with the following example.

Consider the interactions between the three PID controllers on a partial burn fluid catalytic cracking unit. The PID controller for the reactor temperature manipulates the regenerated catalyst slide valve. The regenerator temperature is controlled by a PID controller that moves the air flow to the regenerator. The overhead pressure on the main fractionator is controlled by the speed of the wet gas compressor. There are eight permutations for the configuration of these three controllers, i.e. they can all be on automatic or all on manual or any combination in between.

The general equation for the number of permutations of interactions is 2 raised to the power of the number of controllers, i.e. 2 cubed is 8 for the permutations in Table 1. The number of interactions can be quite large for a complex system. The following table

Shows the eight permutations that exist for three PID controllers and the interactions between these controllers.

When a process is moved from one region of operation to another, it is not uncommon to retune some of the PID Controllers due to the nonlinearity of the control valves. During the course of a run from start-up to shutdown, the configuration of some of the PID control system is changed by switching one or more PID controllers to manual. There are a number of reasons for PID controllers to be switched to manual. Valves begin to stick or develop hysteresis, which causes the PID controllers to cycle. Many times the solution to the cycling is to put one or more of the PID controllers on manual or change the tuning of the PID controllers. The sticking valve may not be fixed until the next turnaround due to block valves not holding on the up- or downstream side of the valve, or the bypass valve around the control valve may be undersized or plugged, which may require a significant drop in feed rate while the control valve is out of service. Tightening the packing on control valves to reduce emissions has made sticking valves a common place occurrence.

The most significant problem with the current generation of multivariable controllers is the deterioration of the controllers' models with time. The ability of UPID to change the state of the independent variables in a controller's model provides insight that explains why many models deteriorate with time. The illustrations which follow clearly indicate that one major factor in the loss of the model quality and accuracy is changing the PID configuration by putting a controller on manual or retuning PID controllers. Changing the state of one key PID controller will change the step response models for all the dependent variables in the multivariable controller.

Figure 1 is plot of the step response curves for a change in the reactor temperature for a step change in the feed to the unit for the eight permutations in Table 1. For four of the permutations the reactor temperature is on control, so the temperature returns to its setpoint for a net change of zero. However, the times to reach the setpoint are spread between 25 minutes and 175 minutes, while the deviations of the temperature from setpoint, range between -2 ºF to -8 ºF degrees F. The steady-state gain for the four permutations when the reactor temperature was not on control ranged between -2 ºF and -6.8 ºF. The scale on the reactor temperature is plus or minus 9 ºF.

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