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It is once said that 'He who wishes to be obeyed must know how to command.' Inspired by this saying, the dynamics of the partially known flexible motion system are considered in the making process of the desired trajectory signals it has to follow by exploiting systems and signals relations. Accordingly, the trajectory generator system activates the motion of the driven system whose tracking performance inhibits the generator and forces it to modify its trajectories while ensuring the desired motion requirements are met. Using singular perturbation theory, a near optimal trajectory generator system is designed, and with the aid of a suitable state observer a cascaded head-to-tail activator-inhibitor system configuration is realized. Essentially, the closed-loop error is fed-back to the trajectory generation process rather than using a limited feedforward controller alone based on the partially known dynamics. The superiority of the proposed technique is compared to the Sine-Squared motion trajectory, and its performance is evaluated through simulation.

The tracking accuracy in motion control systems like the moving stages in lithography machines, e.g., wafer scanners or metrology inspection tools, is partly determined by how the frequency content of its reference trajectories is transferred to the closed-loop tracking error. In this regard, fourth-order reference trajectories for point-to-point motion will be studied from a frequency-domain perspective. By appropriately pairing the maximum snap and maximum jerk values, weakly-damped modes in the closed-loop response can be robustly dealt with without introducing a penalty on throughput.

This paper investigates output feedback tracking control of Unmanned Aerial Vehicles using only the measured inertial coordinate. The output feedback control is based on two cascade high-gain observers combined with a full-state feedback control that is based on the backstepping approach. In this work, the backstepping controller is designed to solve the tracking control problem of the underactuated system. Then, an observer comprised of two cascaded high-gain observers with different speeds is considered; the faster observer provides estimates of the output position and velocity of the system in three dimensions and feeds a virtual nonlinear output to estimate the Euler angles (pitch, roll, and yaw) and angular velocity. We show that the equilibrium point of the full-state feedback control system under full knowledge of the system information is exponentially stable. The simulation results show that the output feedback control achieves the tracking control objective and recovers the performance of the state feedback control. Also, the simulation results show convergence and the boundedness of the estimation errors.

In semiconductor manufacturing, lithography machines are becoming more and more sophisticated system of systems. As an example, a TWINSCAN wafer scanner machine is composed of a wafer, and reticle handlers, reticle, optics, and two wafer chains or systems. In previous studies, we covered the interactions between the reticle, optics, and wafer chains during the step-and-scan cycle. In this study, we focus on the interaction between the additional wafer chain responsible for aligning the wafer substrate and taking its height map during the measurement cycle, and the other chains that are active during the step-and-scan cycle. Working in parallel to increase machine throughput, the inertial forces associated motion of the two cycles induce vibration that may propagate throughout the chains in the machine if no appropriate measures are taken. In this investigation, we look at the reference trajectories responsible for steering the chains throughout the two cycles, and propose two reference trajectory orchestrations that factor in the machine design, geometry, mass distribution, and functions. Theoretically, these orchestrations lead to suppressing the induced vibration without sacrificing the machine throughput while keeping the involved control loops intact.

Stretching the definition of the standard Sine profile allows building a generalized symmetric frequency-aware basis function that can be used to generate reference motion trajectories. Other profiles such as polynomials, sigmoid, and harmonic-based models can be equally used under the proposed technique. Despite being suitable at the level of any higher-order time derivative, in this study, the generic basis function is realized at the jerk level such that the generated signals adhere to the limitations of the driven motion system. Introducing suitable time shifts, replicas of basis functions can be obtained giving rise to B-spline like frequency-aware profiles that can be used to realize the actual motion under any desired kinematical constraints, which are neatly written to reduces the computation burden at the motion controller side. Utilizing mainly the frequency-aware B-spline profiles, frequency-dependent random walk motion is presented and used to collect information about the driven motion system to help in characterizing any position-dependent errors through the statistical means, i.e. Analysis of Variance, and Design of Experiments. This allows dividing the working space in which motion takes place into several spatial regions with preferred frequency contents. The effectiveness of these proposed profiles is shown through hardware experiments using a precision motion system.

The operation time of an ideal reliable wafer scanner model is defined at the die level where the actual exposure process takes place as the time unit per die, or at the wafer substrate level as the time unit per wafer substrate. Therefore, the machine throughput is given as the reciprocal of the operation time. The involved motion profiles of a machine, namely the step-and-scan trajectories, function as the heartbeats that drive its multidisciplinary elements, which suggests that a multidisciplinary design optimization should be involved when such profiles are selected or designed. This is also true when considering the traverse motion profiles among rows and columns within the wafer substrate. The step-and-scan trajectories affect the machine throughput, performance, and die yield. The effects of tracking such profiles appear as structural vibration, tracking errors, and thermal loading at various machine elements such as the actuators, the reticle, the wafer, and the projection elements specifically when the exposure high-energy duration and frequency are not taken into consideration while designing the reference motion. From the dynamics perspective, having a reference motion with nonzero and bounded higher-order derivatives is recommended since it enhances the tracking performance of the machine, however, its ability to increase the operation time is usually overlooked. In an attempt to understand such effects, we present a case study that outlines the aforementioned aspects using three step-and-scan profiles of mainly $3^{rd}$ -order. Taking the dynamics of the driven stage into consideration through input shaping, both the step-and-scan and traverse motion profiles are analyzed. We provide analytical expressions that can be used to generate both types of motion profiles on the fly without additional optimization. A simulation example of a simplified wafer scanner machine shows the usefulness of the proposed framework. Note to Practitioners - Choosing the m