van de Mjg René Molengraft

Frequency domain identification of dynamic friction model parameters

This paper presents a frequency domain identification of dynamic model parameters for frictional presliding behavior. The identification procedure for the dynamic model parameters, i.e., (1) the stiffness and (2) the damping of the presliding phenomenon, is reduced from performing several dedicated experiments to one experiment where the system is excited with random noise and the frequency response function (FRF) of the phenomenon is measured. Time domain validation experiments on a servomechanism show accurate estimates of the dynamic model parameters for the linearized presliding behavior.

Brief Friction induced hunting limit cycles: A comparison between the LuGre and switch friction model

In this paper, friction induced limit cycles are predicted for a simple motion system consisting of a motor-driven inertia subjected to friction and a PID-controlled regulator task. The two friction models used, i.e., (i) the dynamic LuGre friction model and (ii) the static switch friction model, are compared with respect to the so-called hunting phenomenon. Analysis tools originating from the field of nonlinear dynamics will be used to investigate the friction induced limit cycles. For a varying controller gain, stable and unstable periodic solutions are computed numerically which, together with the stability analysis of the closed-loop equilibrium points, result in a bifurcation diagram. Bifurcation analysis for both friction models indicates the disappearance of the hunting behavior for controller gains larger than the gain corresponding to the cyclic fold bifurcation point.

Experimental modelling and LPV control of a motion system

The objective of this paper is to show how experimentally based modelling can be used for designing Linear Parametrically Varying (LPV) controllers. As a test system we use an industrial pick and place unit with one linear X-drive and two independent linear Ydrives. The dynamics of the Y-axes depend on the Xposition. An LPV model is derived by using measured Frequency Response Functions at different positions, fitting a parametric model on each measurement and combining these models by linking parameters via a fit as a function of operating point. Rewriting the LPV model into a LFT structure and applying model reduction in the space of the scheduling variable finalizes the modelling phase. With this model an LPV controller is calculated and shows robust performance for the whole operating range, in contrast to local H∞ controllers.

Assessing geometrical errors of multi-axis machines by three-dimensional length measurements

In this paper a method is presented for assessing geometrical errors of multi-axis machines based on volumetric three-dimensional length measurements. A universal machine error model is proposed since a large variety of machine configurations exists. Such models can be used for software error compensation techniques in order to improve the machine’s positioning behaviour as well as for diagnostic purposes. Length measurements are chosen for the measurement of the positioning errors of a multi-axis machine because these measurements can be executed in a short period of time in a relatively simple way combined with a high accuracy. In order to get comparable results for the geometrical errors as measured with conventional techniques, i.e., laser interferometry, the design of the measurement setup as well as the formulation of the machine error model (including parameter correlation effects) appeared to be of major importance and are subject of this paper.

Using a Walking Piezo Actuator to Drive and Control a High-Precision Stage

Piezoelectric actuators are commonly used for micropositioning systems at nanometer resolution. Increasing demands regarding the speed and accuracy are inducing the need for new actuators and new drive principles. A nonresonant piezoelectric actuator is used to drive a stage with 1-DOF through four piezoelectric drive legs. In order to improve the positioning accuracy of the stage, a new drive principle and control strategy for the walking piezomotor are proposed in this paper. The proposed drive principle results in overlapping tip trajectories of the drive legs, resulting in a continuous and smooth drive movement. Gain scheduling feedback in combination with feedforward control further improves the performance of the stage. With the developed drive principle and control strategy, the piezomotor is able to drive the stage at constant velocities between 100 nm/s and 1 mum/s with a tracking error below the encoder resolution of 5 nm. Constant velocities up to 2 mm/s are performed with tracking errors below 400 nm. Point-to-point movements between 5 nm and the complete stroke of the stage are performed with a final static error below the encoder resolution.

Modeling and Waveform Optimization of a Nano-motion Piezo Stage

Piezo actuators are used in high-precision systems that require nanometer accuracy. In this paper, we consider a nano-motion stage driven by a walking piezo actuator, which contains four bimorph piezo legs. We propose a (model-based) optimization method to derive waveforms that result in optimal driving properties of the walking piezo motor. A model of the stage and motor is developed incorporating the switching behavior of the drive legs, the contact deformation, and stick-slip effects between the legs and the stage. The friction-based driving principle of the motor is modeled using a set-valued friction model, resulting in a model in terms of differential-algebraic inclusions. For this model, we developed a dedicated numerical time-stepping solver. Experiments show a good model accuracy in both the drive direction and the perpendicular direction. The validated model is used in an optimization, resulting in waveforms with optimal driving properties of the stage at constant velocity. Besides the model-based optimization, also a direct experimental data-based waveform optimization is performed. Experiments with the optimized waveforms show that compared to existing sinusoidal and asymmetric waveforms in literature the driving properties can be significantly improved by the model-based waveforms and even further by the data-based waveforms.

Explicit MPC design and performance evaluation of an ACC Stop-&-Go

This paper presents the synthesis, the implementation and the performance evaluation of an Adaptive Cruise Control (ACC) Stop-&-Go (S&G) design. A Model Predictive Control (MPC) framework is adopted, enabling hybrid control synthesis. Performance of the controller is evaluated, distinguishing between comfort of the resulting longitudinal vehicle behavior and the behavior due to traffic requirements. Comfort is related to vestibularly detectable variables, whereas required behaviour is related to visually and auditorily detectable variables. Metrics are determined to enable objective performance evaluation of an ACC (S&G) system in a qualitative manner.

Integrating experimentation into control courses

The Department of Mechanical Engineering at the Technische Universiteit Eindhoven, the Netherlands, aims to provide a stimulating educational environment that emphasizes the role of hands-on experiments. To achieve this goal, the Department integrated an experimentation program with courses in the mechanical engineering bachelors curriculum, starting in the first year and gradually building in complexity through the third year. To make it possible for students to perform experiments, a new approach, which include a personal notebook, a set of 30 portable data acquisition devices, a varied set of small-scale systems, and MATLAB-based software, was introduced. This approach allow the students to plan, prepare and analyze the experiments on their own notebook computers whenever they wish. While this approach has broken through the practical barriers to large-scale experimenting, the success of further integration of student experimentation into mechanical engineering curriculum ultimately depends on the efforts and creativity of staff members.

Data-based optimal control

This paper deals with data-based optimal control. The control algorithm consists of two complementary subsystems, namely a data-based observer and an optimal feedback controller based on the systems Markov parameters. These parameters can be identified on-line using only input/output data. The effectiveness of the resulting controller is evaluated with a regulation and a tracking control experiment, performed on a direct-drive robot of spatial kinematics.

H 2 performance analysis of reset control systems

To overcome fundamental limitations of linear controllers, reset controllers were proposed in literature. Since the closed loop system including such a reset controller is of a hybrid nature, it is difficult to determine its performance. The focus in this paper is to determine the performance of a SISO reset control system in H2 sense. The method is generally applicable in the sense that it is valid for any proper LTI plant and linear-based reset controller. We derive convex optimization problems in terms of LMIs to compute an upperbound on the H2 norm, using dissipativity theory with piecewise quadratic Lyapunov functions. Finally, by means of a simple multiobjective tracking example, we show that reset control can outperform a linear controller obtained via a standard multiobjective control design method.