Abstract
Variability reduction strategy for processes with PID controllers and oscillatory disturbances
Author(s): Alex Borrero, Luis D�az-Charris, Alberto Manotas, Elena Romero, Jos� Ruiz-Ariza, Javier Jim�nez-Cabas
The quality and cost of several industrial product's plants are affected by variability and disturbances that appear in processes. Oscillatory disturbances are harmful both because they affect mechanical components and because their propagation leads to an increase in the variance of the plant. Poor performance of the control system plus oscillatory disturbances leads to a higher cost of production. This research develops a technique for reducing variability in control loops for processes with PID controllers against oscillatory disturbances by re-tuning the controller, obtaining better results than traditional tunings while decreasing cost production by reduction of process variance. A factorial experiment was designed to obtain tuning equations of the controller to attenuate the effect of an oscillatory disturbance to the control loop. Two experiments were performed: the proportional controller (P) and the other for the Proportional-Integral controller (PI). The response variable is lambda 
, which is the parameter that is varied in the range 
for each experimental condition. The design concept of this control strategy is that when an oscillatory disturbance occurs, instead of designing the controller to reach the setpoint, it is re-tuned to act as the best possible filter. Due to this, a performance criterion was defined that sought to minimize the effect of an oscillatory disturbance. The equations developed in this research are limited to self-regulated processes, where proportional (P) or proportional-integral (PI) controllers are implemented. The ranges of the process parameters are those specified in this research. This technique is not limited or restricted to processes with a single control loop because the modification is done on each individual controller. This strategy can be extended to more controllers without additional mathematical developments since this self-tuning technique when operating on each controller individually, seeks to cancel a disturbance that affects each controller independent of the control action of other adjacent controllers. Each controller perceives a behavior and applies the technique to know if the source of the disturbance comes from itself or a disturbance, if the oscillation is not the cause of itself (the controller) then it is due to a disturbance. An index that seeks to minimize the amplitude of this oscillation is proposed. If the oscillation cannot fade, at least its impact can be decreased by reducing its amplitude. By reducing the amplitude, the output can be kept as close as possible to its average value, which is the setpoint from a control engineering perspective. The standard deviation is an ideal statistic for this function since it quantifies the amount of variation in a data set. A lower value of the standard deviation would indicate that the data tend to be closer to the mean (the setpoint). In contrast, a high value of the standard deviation would show that the data are spread over a wider area farther away from the setpoint.