The real-time and accurate measurement of tip-sample interaction forces in Tapping Mode Atomic Force Microscopy (TM-AFM) is a remaining challenge. This obstruction fundamentally stems from the causality of the physical systems. Since i) the input of the dynamic systems propagates to the output with some delay, and ii) , multiple different inputs can generate the same output, there exist no measurement or estimation technique that can estimate the force input of the systems in real-time without phase and amplitude distortion. However, an approximate and delayed estimation can still be possible. This article presents a general-purpose algorithm which aims to estimate an approximation of the force input of TM-AFM with minimum delay and error. For this reason, first, the input estimation problem is converted to an ill-posed state observation problem. Then, a Tikhonov-like regularization technique is applied to eliminate the ill-conditioning and estimate the force input using a linear Kalman filter. The proposed input observer is remarkably robust, real-time in the order of the sampling frequency, and applicable for any Linear Time Invariant (LTI) system with a (semi-) periodic process. Simulation and experimental results show that using the proposed algorithm with a wide-band AFM probe; one can determine the tip-sample forces with only a few percent error and a delay in the order of sampling time. Unlike the existing force estimation techniques for AFM, this algorithm does not require any prior knowledge of the force-distance relationship which can be very beneficial for the closed-loop control of AFM.@en

In pursuit of better accuracy, higher speed and larger scale, manufacturers of high-performance devices increasingly rely on components which have been designed with a multidisciplinary approach from the outset. In the context of motion systems, this means that for instance structural mechanics, control engineering and thermal analysis are considered early in the design. In addition, the prospect of producing freeform device components using additive manufacturing at full scale allows designers to even further refine components to a specific purpose, or even integrate multiple functions into a single component. The design freedom offered by additive manufacturing is far greater than that offered by traditional techniques. To exploit this freedom a topology optimization framework is proposed that allows to determine the optimal material quantity and distribution within a design volume. In particular, this article focuses on the closed-loop control performance of a motion system component, while simultaneously ensuring that mechanical requirements are met. Based on an example, it is demonstrated that this leads to nontrivial and non-intuitive designs which provide improved performance at lower structural mass compared to eigenfrequency designs. The framework allows rapid development of prototype designs, which may eliminate some of the costly design iterations which are currently made in industrial practice.

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The design of high performance instruments often involves the attenuation of poorly damped resonant modes. Current design practices typically rely on informed trial and error based modifications to improve dynamic performance. In this article, a multi-material topology optimization approach is presented as a systematic methodology to develop structures with optimal damping characteristics. The proposed method applies a multi-material, parametric, level set-based topology optimization to simultaneously distribute structural and viscoelastic material to optimize damping characteristics. The viscoelastic behavior is represented by a complex-valued material modulus resulting in a complex-valued eigenvalue problem. The structural loss factor is used as objective function during the optimization and is calculated using the complex-valued eigenmodes. An adjoint sensitivity analysis is presented that provides an analytical expression for the corresponding sensitivities. Multiple numerical examples are treated to illustrate the effectiveness of the approach and the influence of different viscoelastic material models on the optimized designs is studied. The optimization routine is able to generate designs for a number of eigenmodes and to attenuate a resonant mode of an existing structure.@en

Topology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution. This paper discusses the relation between the number of design variables per element and the order of the elements used for analysis. We derive that beyond a maximum number of design variables, certain sets of material distributions cannot be discriminated based on the corresponding analysis results. This makes the design description inefficient and the solution of the optimization problem non-unique. To prevent this, we establish bounds for the maximum number of design variables that can be used to describe the material distribution for any given finite element scheme without introducing non-uniqueness.@en

The design of high performance instruments often involves the attenuation of poorly damped resonant modes. Current design methods typically rely on informed trial and error based modifications to improve dynamic performance. In this contribution, we present a multi-material topology optimization as an alternative, systematic methodology to design structures with optimized damping characteristics. A parametric, level set-based topology optimization is employed to simultaneously distribute structural and viscoelastic material to optimize the structure’s damping characteristics. To model the viscoelastic behavior a complex-valued material modulus is applied. The structural loss factor is determined from the complex-valued eigensolutions and its value is maximized during the optimization. We demonstrate the performance of the optimization by maximizing the damping of a cantilever beam.@en

This chapter considers subspace predictive control of systems whose dynamics can be described locally by LTI models. The control algorithm is based on the predictor-based subspace identification framework. In a linear least-squares problem, the observer Markov parameters of the system are recursively estimated. Those parameters are used to construct an output predictor which is in turn used to solve a predictive control problem subject to constraints.@en

The design case of a simplified motion system serves to demonstrate the potential of topology optimisation (TO) techniques for improving the performance of such systems. The presented methodology allows the extensive design freedom offered by topology design to be explored and results in a conceptual design. The intrinsic capability of TO of coming up with complex geometries suggests a very natural and powerful link with Additive Manufacturing techniques that can realise such geometries with few restrictions.@en