van Cmm Nelis Lierop

Control-Oriented Hysteresis Models for Magnetic Electron Lenses

This paper deals with finding appropriate hysteresis models that predict the behavior of electro-magnetic lenses used with electron microscopy. The iterative selection procedure consists of experiment design and mathematical analysis of hysteresis models. We will show two examples of pitfalls when the suitability of models is assessed by means of curve-fitting to observations. The first example illustrates the inability of models with local memory to describe the magnetic hysteresis in our application. The second deals with accommodation. With both, the experiments carried out on an off-line setup of a magnetic lens are compared to hysteresis models.

Modal observer design for a flexible motion system with state dependent sensor positions

This paper focuses on observer design for a flexible motion system with a state dependent output map. After rewriting the modal system to parameter varying form sufficient conditions are derived to obtain a parameter varying modal observer with bounded ℒ2 gain. These conditions translate to linear matrix inequalities (LMIs) when the time derivative of the Lyapunov function is multiconvex. The derived theory is applied to a model of the Herringbone Pattern Planar Actuator (HPPA) where noise and input disturbance affect the system. Using the theory it is possible to estimate independent rigid body motion in six degrees of freedom (DoF) and two flexible modes.

Smooth Parametric Hysteresis Operator for Control

Abstract Hysteresis is a non-linear phenomenon present in many physical systems that is usually undesirable and degrades their performance. Models which accurately reproduce hysteresis are often very complex and hard to implement. For that reason, the hysteresis is generally, when the performance specifications are not too strict, treated as a bounded disturbance or is approximated with piecewise affine structures. Control design requires models which extract the most fundamental behavior of phenomena and, in this article, such a model was constructed for the hysteresis phenomenon. It is shown that the obtained model can be easily shaped, mathematically manipulated and used for general control design of hysteretic systems, e.g. feed-forward compensation.

On hysteresis in magnetic lenses of electron microscopes

This paper deals with an experimental procedure to illustrate the problems introduced by ferromagnetic hysteresis present in magnetic lenses of electron microscopes. The magnetic flux density is not available as a measurable quantity. Hysteresis expresses itself in the relation between the input current applied to the lens-coil and the level of sharpness (defocus) of the resulting images. The familiar hysteresis loops are not available, instead we measure hysteresis in the so-called butterfly representation. The input-profiles are non-periodic and illustrate the difficulties with reproducibility in microscopy applications. Image based feedback control is impossible since 99% of the input range yield unusable images. Analysis of the experiments is carried out using a qualitative model consisting of an interconnection of hysteresis representing the magnetic lens and a nonlinear function representing electron optics. Because this model introduces the intermediate magnetic field variable, it is possible to reconstruct and explain the results observed in the experiments.

Feed forward initialization of hysteretic systems

The paper analyzes a strategy to force step-convergent dynamical hysteretic systems to a well-defined output value using only feed forward. Due to the multi-valued input-output relation of hysteresis, the relation between a constant input and the corresponding steady-state output is not unique. By using a well-designed input trajectory, based on qualitative system behavior only, such a system can still be forced to a predefined output value. Moreover, for reasons of performance the initialization time has to be as short as possible. The rate-independent Duhem and the multi-play hysteresis models are used to illustrate, analyze and synthesize an appropriate initializing input to obtain the required output without any sensor information. Dynamics are included using the nonlinear feedback model with dead-zone.

Electron microscopy experiments concerning hysteresis in the magnetic lens system

Ferromagnetic hysteresis and coupled dynamics in the magnetic lens system of electron microscopes degrade the machines performance in terms of steady-state error and transition time. To get a clear understanding of the exact problem and the way it is expressed in the application a commercial scanning electron microscope is extended with a data-acquisition and rapid proto-typing system. By means of conditioned experiments the significance of the hysteresis effects for microscopy applications is quantified. The response is evaluated by an analysis of synchronized lens currents and estimated sharpness of the resulting images. The sensitivity of image sharpness versus input variation is obtained in a local operating point. The hysteresis effect and its coupling with dynamics, as a response to changes over the complete working range, result in a significant deviation in image sharpness. Since the magnetic field is not available for measurement, the error is expressed in the quasi-static input variation required to correct for it. In order to get a good understanding of the observed effects and the magnetic lens as a system, an interconnected dynamics-hysteresis-electron optics model is used to analyze and to reproduce the experimental results.

Implementation of a linear quadratic bumpless transfer method to a magnetically levitated planar actuator with moving magnets

A linear quadratic bumpless transfer technique for a six-degree-of-freedom planar actuator with integrated active magnetic bearing is proposed to solve the lift-off and landing problem by switching between different controller sets. The need for multiple controller operation states results from the difference between robustness and wind-up concerns during lift-off and landing and the high performance tracking requirements for accurate operation. A procedure for tuning the plant input and error matrices used in the Linear Quadratic Bumpless Transfer method based on new observations is presented. The procedure has been applied to synthesize a bidirectional bumpless switching mechanism that was successfully applied and tested on a 6 DOF laboratory setup.

On hysteresis and air gap disturbance in current and voltage mode feed-forward control of variable reluctance actuators

Current and voltage mode control approaches in feed-forward force control of variable reluctance actuators are analyzed and compared. Two major error generators, the unknown air gap variation and hysteresis, are investigated together with the quantification of their influence on the final force tracking error, and it is shown that voltage control has fundamental advantages over current control. Furthermore, linearization laws with hysteresis compensation based on the parametric hysteresis operator are proposed and compared on a high-fidelity actuator model which is derived from the behavior of magnetic materials, the actuator structure, and first principle physical models.

Control of a hysteretic electromagnetic electron lens system

The design of electron lenses for high-precision applications is complicated by ferromagnetic properties such as limited transition time and hysteresis. To be able to achieve high focusing precision and fast transition times, these properties should be taken into account when designing suitable controllers. In this project, feedback control, feed-forward control and feedback/feed-forward control topologies have been evaluated and trajectory planning has been implemented to reduce overshooting. Feed-forward control in particular proved to be a low-cost solution while the achievable transition time reduction is significant using the proposed automated tuning procedure.