Optimization of Active Vibration Control of a Laser Pattern Generator in Micro Lithography

The extreme precision requirements in semiconductor manufacturing drive the need for an active vibration isolation system in a laser pattern generator. Optimizing the controller would not only improve isolation performance, but could also reduce the cost of ownership by extending lifetime of consumables and stretch service intervals. The optimization has been performed and evaluated in a model using a high level programming tool [1]. The areas of optimization were 1) Decoupling strategies for decentralized control and 2) Improved feed forward control. The results of this study are general and could be used for various control applications. Only a limited description of the model itself is given here. A more thorough description is presented in [2] and [3]. 1 Decoupling strategies A system with multiple inputs and multiple outputs (MIMO), as the Active vibration control, can be controlled with a set of single input and single output (SISO) regulators, so called decentralized control. This can be done by combining sensors to a set of regulator inputs and applying the output signal from each regulator on a combination of actuators, using matrices MS and MM as preand post compensators respectively. The choice of strategy for creating these matrices will strongly affect the performance of the control system. Good performance is achieved when the regulators are well decoupled, i.e. minimizing the cross coupling between regulators. 1.1 Geometric decoupling The original decoupling strategy is using the geometrical center of the sensors and actuators as reference point and applies a coordinate system with three translation and three rotation axes, parallel to the geometrical axes. This simple strategy does not attempt to compensate for cross coupling between translation and rotation axes. Proceedings of the euspen International Conference – Delft June 2010 1.2 Center of gravity decoupling In an attempt to improve decoupling, the true motion of the center of gravity (COG) of the vibration isolated unit is controlled in three translation and three rotation axes. The inherent cross coupling between rotation and translation axes, due to sensor and actuator offset from COG, is compensated for. To preserve the intuitive understanding of the system the axes are still parallel to the geometrical axes. Figure 1: Sensors, actuators and control axes for geometricand COG-decoupling 1.3 Modal decoupling Because the rigid body vibration modes of the isolated unit do not correspond to the geometrical axes of the system, cross coupling between the regulators will occur as long as the geometrical axes are used as base for the decoupling. If instead a modal decoupling strategy is used, i.e. using the eigenvectors of the system and transform the geometrical coordinates into modal coordinates, each resonance mode is controlled independently and thus the decoupling is theoretically complete. The equations of motion in the state-space form is given by ) ( ) ( ) ( ) ( ) ( t Cx t y t Bu t Ax t x = + = & A matrix E containing the eigenvectors of A can be used to transform the physical coordinates into modal coordinates. According to [4] the preand post compensation matrices for the modal decoupling are given by