(Dr. Tom Kurfess, advisor)

"Adaptive Statistically based Controller for Through-feed Centerless Grinding"

Abstract

The purpose of this research is to develop a statistically based controller that is "self-tuning."  High speed manufacturing processes such as through-feed centerless grinding are best controlled with a statistical approach, but traditional statistical methods generally rely on fixed parameters that must be determined.  These values must be precisely known and the true physical characteristics they model must remain constant throughout grinding, or the statistical control method may break down.

Our self-tuning controller constantly monitors and estimates the mean and standard deviation of the process and makes control decisions based on the real-time values of these quantities.  If the standard deviation increases an allowance is made for this decrease in machine precision.  If the standard deviation decreases the algorithm will take advantage of this.

We are using a Cincinnati Milacron Viking through feed centerless grinder with a CBN wheel.  The only commands that the machine accepts are "compensate in", "compensate out", or "do not move."  This enables the grinder to control the diameters which it produces.  An LVDT is used to measure the part diameters in real time as they flow out of the machine.  These data are used to estimate the mean and standard deviation of the parts.  With each iteration we calculate the t-statistic associated with a hypothesis test for the mean.  This test is a comparison between the process mean and two values: the target +/- one half of a compensation step.  This reference t-value is chosen to correspond to a process mean and standard deviation that is a desired distance from the target.  This is what we choose as the process drift from the target.  This distance is chosen to be small to keep the parts lose to the target, but far enough to ensure that when a compensation is made, there is only a small chance that an immediate move in the other direction is made.  This "double-compensating" can lead to machine instability and is undesirable.  In fact this is just what happens to traditional methods that rely on constant decision parameters-if something changes and the standard deviation increases, the control algorithm requests repeated compensation commands.

The advantage of this method is that if the machine parameters change, the algorithm adjusts to the changes.  If the machine is left running for hours with a traditional approach and the process cariance changes, the operator can be left with an entire run of scrap parts.  The self-tuning method can adjust for such aberrations and keep the run on target.