Arvid Amthor

High Precision Position Control Using an Adaptive Friction Compensation Approach

The presented work concerns the development of a trajectory tracking controller which is able to improve clearly the dynamical performance of a high precision positioning stage. Experiments in the pre-rolling and rolling friction regimes are conducted and a hybrid parameter estimation algorithm is used to fit the parameters of a simple dynamic friction model based on experimental data. Further experiments show that the identified model does not represent the system behavior over the whole operating range of 200 mm. To solve this problem the linear model parameters are adjusted online to ensure precise dynamic friction compensation. Finally, the extended friction model is utilized in a feed-forward controller in combination with a standard feedback controller to compensate for the effects of the friction force and other disturbances while moving.

Asymmetric motion profile planning for nanopositioning and nanomeasuring machines

Abstract This work presents an analytic fourth-order trajectory planning algorithm, which is able to plan asymmetric motions with arbitrary initial and final velocities. Furthermore, the proposed algorithm is based on a set of quadratic derivates of jerk (djerk) functions and generates continuously differentiable trajectories in jerk, acceleration, velocity, and position under consideration of kinematic constraints in all these kinematical values. The trajectories planned by the algorithm also have time-optimal characteristics, and a synchronization between the three motion axes of the Cartesian coordinate system is ensured by the proposed method. These characteristics make it ideally suited for use as a trajectory planning algorithm in high-precision applications such as nanopositioning and nanomeasuring machines.

Position control on nanometer scale based on an adaptive friction compensation scheme

This work concerns a non-model-based friction compensation scheme for dynamic position control on nanometer scale. The main goal of this work is to build up and implement a simple dynamic friction observer which allows an estimation of the friction force in combination with the system inertia against displacement. Experiments in the pre-sliding and sliding friction regimes are conducted on an experimental setup. After a short review of friction compensation, the experimental setup is explained in detail. Next, the observer is modeled mathematically and the used control scheme is presented. Finally, the friction observer is utilized as a non-model-based friction estimator combined with a classical feedback controller to compensate the nonlinear friction force and reduce tracking errors significantly. It is shown that the proposed controlling approach is able to realize a fast and ultra precise positioning over long distances.

Decentralized high precision motion control for nanopositioning and nanomeasuring machines

The presented work concerns a model-based friction compensation scheme which is able to improve the dynamical behavior of a two dimensional high precision positioning stage. The proposed structure consists of a state space controller and a disturbance observer. The system model for the state space controller represents the inertia as well as the friction force, it utilizes the elasto-plastic friction model. A Kalman filter serves as disturbance observer. The developed model-based control scheme is used for one axis of the positioning stage. For control of both axes of the fine positioning stage a decentralized approach is presented. In an extensive experimental study the proposed scheme is compared to a well tuned PID controller without friction cancellation as well as the state space controller without observer. Experiments show that the dynamical behavior of the system can be improved significantly. In all test scenarios the presented structure produces the smallest tracking error. The decentralized control approach shows, that the axes of the experimental set-up are coupled and a model-based decoupling can possibly lead to a further reduction of the tracking error.

Communication of the multi laser tracker system used as position feedback sensor

This paper presents a communication as well as localization algorithm of a multi laser tracker system (MLTS). The proposed localization algorithm enables the possibility to find a retro-reflector, which is mounted on the Tool Center Point (TCP) of a positioning stage. The MLTS consists of four laser trackers and is used as a high precision feedback sensor in order to provide a contactless measurement of the position. A single laser tracker is build up out of a homodyne laser interferometer as well as a galvanometer scanner and tracks the retro-reflector by utilization of a model-based PID controller. Using the Archimedean spiral a mathematical localization algorithm of the retro-reflector is designed. This approach was chosen due to the fact, that it allows the laser beam to search the retro-reflector in the complete working range of the tracker. The algorithm is derived in polar coordinates and is afterwards transformed into angle coordinates of the galvanometer scanner. In the second part of the presented study, a communication channel between the laser trackers is designed. This enables the possibility to speed up the localization of the retro-reflector significantly, because the position of the TCP is determined using the triangulation. Hence only two laser trackers are required in the first localization step. In the case, that the TCP was found, the information is utilized to support the residual laser trackers of the MLTS to localize the retro-reflector. At the end it is shown by experimental results, that the communication between the laser trackers is effective in order to localize the retro-reflector as fast as possible.

High precision laser tracker system for contactless position measurement

This paper presents the development of a multi laser tracker system (MLTS) used as position feedback sensor, which can track a retro-reflector mounted on the moving kinematic. Four laser trackers build up the MLTS. In the first part of the study, we present the required algorithms that enable the MLTS to measure the position of the retro-reflector. The algorithms include the localization of the retro-reflector, the communication between the laser trackers as well as the tracking control of the laser beam. The localization algorithm is designed to find the retro-reflector within an initialization phase, which is based on an Archimedean spiral derived in polar coordinates. Furthermore, the proposed algorithm allows the single laser tracker to search the retro-reflector in the complete working range. To accelerate the initialization phase a communication channel between the laser trackers of the MTLS is designed. In the case that two laser trackers at least hit the target, the position information is utilized to support the residual laser trackers of the MLTS to localize the retro-reflector. In the second part of this study we present the tracking control to follow the retro-reflector. After the initialization phase is finished the tracking control algorithm is activated to follow the retro-reflector. The model-based control consists of a PID controller in combination with disturbance compensation.

Nonlinear modeling and identification of a dc-motor with friction and cogging

In the presented work a nonlinear, analytic model of a permanent magnet direct current motors with brushes is proposed. Besides the theoretical modeling an automated identification algorithm for this detailed model is deduced. The resulting model includes the electromechanic and electromagnetic effects of the direct current machine, like voltage induction or motor torque, and additional nonlinear phenomena. These nonlinearities include cogging torque, eddy current, hysteresis losses and tribological aspects. The cogging torque is caused by a variation of the magnetic flux density, which manifests itself as a periodic oscillation in the torque curve. In addition, eddy current and hysteresis losses arise by the commutation of the magnetic field in the armature, are also captured by the motor model. The tribological aspects of all friction regimes are modeled utilizing the elasto-plastic friction model. This model can reflect the linear spring damper behavior of the elastic friction domain as well as velocity depending friction behavior of the plastic friction domain. The parameters are separately identified through specific experiments referring to their physical equivalents. Therefore, two testing benches are developed in order to capture the different effects in the direct current motor.

Dynamical friction modelling and adaptive compensation on the nanometer scale

The presented work concerns the modelling and compensation of highly nonlinear friction effects on nanometer scale. Experiments in the pre-rolling and rolling friction regimes are conducted on a high precision positioning stage. Two selected dynamical friction models were identified as well as validated and this analysis shows, that the system behaviour of the experimental set-up is highly position dependent. Hence the identified models are not valid over the whole operating range and online parameter adaption mechanisms are presented, which ensure precise friction estimations over the positioning range of 200 mm. Finally, the models are utilized as an adaptive feed-forward friction compensator in a trajectory tracking control scheme. Using this adaptive control approach the tracking error is reduced significantly. Both adaptive models showed a similar performance but differ noticeably relating to consumption of calculating time.

Maxwell Slip based adaptive friction compensation in high precision applications

In this work an adaptive approach for friction compensation based on the Generalized Maxwell Slip (GMS) Model is presented. The model is utilized in a feed-forward controller in combination with a standard feedback controller to improve the dynamical performance of a two dimensional high precision positioning stage with a working range of 200 mm. The GMS model is extended to be used as an inverse system model. The parameter identification shows, that the identified model does not represent the system behavior at every position. On this account the linear model parameters are adapted online to ensure precise friction compensation. Experiments show that this approach can improve the dynamical behavior of the system significantly. In combination with a feedback controller the adaptive GMS model based friction compensation is robust against disturbances and reduces the tracking error while moving over the whole operating range.

Model based control of a linear stage using a contactless optical sensor system

In this paper, we present a model-based tracking control of a positioning stage using laser trackers as contactless position feedback sensor. The laser trackers follow the stage in the complete working range and the position of the stage is determined with the laser triangulation method. Based on this very precise position information a trajectory tracking controller with friction compensation was developed. The dynamical behavior of the stage without friction is modeled as a differential equation second order and the model parameters are identified by experiment. Based on this model a PD controller is designed using pole placement method. In the feedforward path of the trajectory tracking controller a Basic Maxwell-Slip friction model is utilized for friction cancellation. In order to identify the parameters of the friction model the Dynamic NonLinear Regression with direct application of eXcitation (DNLRX) identification algorithm is used. It is shown by experiment that the proposed control approach reduces the tracking error significantly.