Hans Butler

Position Control in Lithographic Equipment [Applications of Control]

This article describes the basic optical principles in the lithographic tool, with the resulting positioning accuracy requirements. For three generations of lithographic tools, the mechatronic architecture and control implications are discussed. Then, six degrees of freedom (DOF) stage control is described with the main focus on actuator force decoupling, allowing the use of classical single-input, single-output (SISO) controllers.

Adaptive Feedforward for a Wafer Stage in a Lithographic Tool

The wafer stage and reticle stage in a lithographic tool, used to manufacture integrated circuits (ICs), operate at nanometer accuracy during a scanning motion. The position accuracy and settling time after accelerating to the scanning velocity are largely determined by the feedforward controller. The feedforward controller calculates the required force for the stage to move according to its position profile by multiplying the reference acceleration with the known stage mass. Two effects limit the accuracy directly after the acceleration phase. First, the actual stage acceleration in response to the controller-calculated force depends on the position of the stage in its working range. A variation of 0.1% is observed. Second, dynamic resonances in the stage response require a higher-order feedforward model. Combined, these effects result in a 20-30 nm peak position error. This brief investigates online adaptation of the feedforward mass parameter, with the aim of reducing the position-dependent stage behavior. Adaptation of only the feedforward mass is shown not to be able to compensate for stage dynamics, additionally requiring a higher-order feedforward element. From the control force and the measured motion response, the feedforward mass parameter is estimated on line. Least-squares estimation is fast enough to update the mass parameter during the acceleration phase, which takes less than 100 ms. This brief addresses a number of practical aspects and shows that adaptive feedforward estimation in combination with higher-order feedforward reduces the peak position error consistently by creating position-independent behavior.

Performance trade-offs in disturbance feedforward compensation of active hard-mounted vibration isolators

With disturbance feedforward compensation (DFC), input disturbances are measured and compensated to cancel the effect of the disturbance. Perfect cancellation is not possible in practice due to the causal nature of DFC, in which the compensation generally comes too late. Therefore, non-perfect plant inversion, controller discretization and sensor dynamics lead to a non-zero residual error. The properties of this residual error are described in the frequency domain using a theoretical framework that is closely related to the design constraints known from filtering theory. It is shown that, like in feedback control systems, performance limitations of DFC systems are described by a waterbed effect. An experimental validation is included to demonstrate the properties of the residual error on an active hard-mounted vibration isolation setup.

Exact plant inversion of flexible motion systems with a time-varying state-to-output map

Many high-accuracy positioning systems have a target performance location that varies with time and position. A typical example is given by wafer stage positioning systems in the lithographic industry. The design of feedforward compensators for such a class of systems, i.e. flexible motion systems having Linear Time Invariant (LTI) state dynamics with Linear Time-Varying (LTV) state-to-output map, can be considerably enhanced if such time or position-varying characteristics of the systems are taken into account. In this work, a strategy to construct a feedforward controller that exactly matches the time-dependent inverse of such a system is investigated. Analysis and simulation on a simplified model show the potential performance improvement obtained with such a strategy.

Cable connection to decrease the passing on of vibrations from a first object to a second object

A cable connection between a first object and a second object includes a cable bundle of one or more cables having a certain length. One end of the cable bundle is fixed to the first object and another end of the bundle is fixed to the second object. A cable bundle holder configured to hold the cable bundle at a certain location along the length of the cable bundle, and a control system configured to control the position of the cable bundle holder with respect to the second object are presented. A control system for cable connection, and a method of reducing the transfer of vibrations from a first object to a second object via a cable connection are also presented.

High-Precision Force Control of Short-Stroke Reluctance Actuators with an Air Gap Observer

A short-stroke reluctance actuator linearization scheme that simultaneously achieves high linearity, high bandwidth, and low stiffness is demonstrated. These properties are required in high speed and high precision motion systems. They are achieved by combining various control schemes, namely flux feedforward and analog sensing coil feedback for high bandwidth, Hall probe feedback to stabilize the drift, and an air gap observer together with gain scheduling to reduce the remaining stiffness. Using the presented scheme, the attractive force of the actuator can be controlled with high precision without the need for a position or force sensor. Experiments indicate that a linearization error of 50 mN for second-order 200 N force reference profiles is obtained. This translates into force predictability of 99.98%. Furthermore, absolute actuator stiffness below 500 N/m at force levels of 100 N is achieved, which is comparable to more linear Lorentz actuators.

Cancellation of normal parasitic forces in coreless linear motors

An ideal coreless linear motor produces no forces in non-driving directions. However, in practice, the translator can be misaligned with the center of the stator due to manufacturing tolerances, which causes undesired normal parasitic forces. This misalignment on the other hand provides the ability to generate force in the normal direction. This paper proposes a novel commutation method which utilizes this ability to compensate for normal parasitic forces caused by the misalignment of the translator as well as other manufacturing tolerances. The proposed commutation algorithm is fully analytical and hence requires low computational power. Simulation results are presented to demonstrate the effectiveness of the proposed commutation algorithm.

Self-tuning disturbance feedforward control with drift prevention for air mount systems

A MIMO disturbance feedforward control strategy is presented to isolate an industrial active vibration isolation system with air mounts from broadband floor vibrations. The feedforward controller compensates for the static damping and stiffness of the air mount suspension, leading to significant improvement of the vibration isolation performance. At low frequencies the controller gain is limited using higher-order weak integrators to prevent drift and actuator saturation. To minimize performance limitations due to model uncertainties, the MIMO feedforward controller is implemented as an IIR filter with fixed poles and self-tuning zeros, having the ability to fine-tune the parameters online using a combination of filtered-ϵ least mean squares (FϵLMS) optimization and residual noise shaping. An experimental validation on a full-scale vibration isolation system with air mounts shows performance improvements up to 30 dB for frequencies between 30 and 80 Hz.

An analytical commutation law for parasitic forces and torques compensation in coreless linear motors

For ideal coreless linear motors, simple classical commutation using three-phase sinusoidal currents is sufficient to achieve low propulsion force ripple and zero parasitic force and torque in non-driving directions. However, in nonideal coreless linear motors, there are various parasitic forces and torques for which the classical commutation cannot compensate. This paper proposes an analytical commutation law which can eliminate the parasitic forces and torques. Simulation results with a finite element method model are presented to demonstrate the effectiveness of the proposed commutation law.

A Hessian-free algorithm for solving quadratic optimization problems with nonlinear equality constraints

The classical method to solve a quadratic optimization problem with nonlinear equality constraints is to solve the Karush-Kuhn-Tucker (KKT) optimality conditions using Newtons method. This approach however is usually computationally demanding, especially for large-scale problems. This paper presents a new algorithm which is more computationally efficient, since it does not require either additional optimization variables or computation of the Hessian matrix. It is proven that the proposed algorithm converges locally to a solution of the KKT optimality conditions. An application example is presented to demonstrate the effectiveness of the proposed algorithm.