Multiscale Control for Nanoprecision Positioning Systems With Large Throughput

A problem of continuing interest in feedback control is handling conflicting time-domain performance specifications. Semiconductor manufacturing is one of the applications of particular interest in this context with the demanding feature sizes (on the order of a few tens of nanometers) to be produced on a wafer while still requiring high throughput (greater than 100 wafers per hour). In this brief, we propose a multiscale control design method based on a reduced-order model-following scheme for the dynamic systems with such conflicting time-domain performance requirements. This method uses a dynamic reference model to make the plant output track the model output as closely as possible without increasing the overall order of the control system. Optimal proportional-integral (PI) control is used, which is essentially a modification of the conventional optimal control. A detailed analytical proof is given to show that this control scheme effectively overcomes the limitations of the conventional optimal control techniques and provides consistent performances at nano- as well as macroscale positioning with fast rise and settling times. Benefits and limitations of the proposed control scheme are described and stability and performance analyses are discussed. A six-degree-of-freedom (6-DOF) extended-range magnetically levitated (maglev) nanopositioning stage, which is open-loop unstable, is used as a test bed to demonstrate the developed control strategy. Step responses under a variety of conditions are obtained to verify the effectiveness of the proposed method. This method exhibits significantly better and robust performances in terms of transient as well as steady-state behavior compared with conventional optimal-control schemes. Furthermore, it can be applied to a general class of higher-order linear time-invariant (LTI) systems with or without open-loop instability.