The Optimal Locus Approach With Machining Applications

An optimal locus concept is introduced as the basis for an optimization methodology for real-time control subject to time-varying constraints. The optimal locus in the control plane contains all possible optimum points, and the actual point is found at the intersection of the optimal locus with the most limiting constraint. The mathematical basis of the approach is a given set of equations which is less than the number of unknowns, and the addition of real-time measurements to compensate for the missing information. The control system generates the optimal parameters in real time, and uses them as references to the control loops. The optimization methodology and control architecture are structures in a generalized way for application to processes having multiple variables and subject to several constraints. The proposed controller architecture can effectively control many machining processes. The optimal locus approach was applied to a grinding system and the experimental results verify the proposed theory.