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 beproduced 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 nanoas 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.