Markus Burkhardt

A Comprehensive Fuzzy Uncertainty Analysis of a Controlled Nonlinear System With Unstable Internal Dynamics

Fuzzy uncertainty analyses disclose a deeper insight and provide a better understanding of complex systems with highly interdependent parameters. In contrast to probability theory, fuzzy arithmetic is concerned with epistemic uncertainties, which originate from a lack of knowledge or from idealizing assumptions in the modeling process. Direct fuzzy arithmetic can be used to illustrate how parameter uncertainties propagate through a system. In contrast, inverse fuzzy arithmetic can be used to identify admissible parameter uncertainties that obey defined error bounds. In addition, fuzzy arithmetic is capable of providing global sensitivity analyses. Therefore, an improved formulation for inverse analyses as well as a new concept for the computation of global sensitivities is presented. These tools are used here to assess the model-based feed-forward control of a nonlinear system with unstable internal dynamics.This article is available in the ASME Digital Collection at http://dx.doi.org/10.1115/1.4030810.

Trajectory Control of Serial and Parallel Flexible Manipulators Using Model Inversion

Traditional manipulator designs are based on maximized stiffness to suppress undesired elastic vibrations. This results in high accuracy in end-effector trajectory tracking, while it usually includes a drastic mass increase, a poor weight-to-payload ratio and high energy consumption. In contrast, modern light weight designs result in low energy consumption and allow often high working speeds. However, due to the light weight design the bodies have a significant flexibility which yields undesired vibrations. Therefore, in the control design these flexibilities must be taken into account. In this chapter feedforward control designs based on inverse models are presented and applied to serial and parallel flexible manipulators. Thereby, for a given system output the inverse model provides the control input for exact reproduction of the desired output trajectory and the trajectories of the generalized coordinates.

Control of vibrations for a parallel manipulator with flexible links — concepts and experimental results

A comprehensive control approach is presented to reduce the vibrations of a parallel manipulator with a kinematic loop and two flexible links whereof the longer one can show significant oscillations. The control objectives are end-effector trajectory tracking and active vibration control. The system is modeled as a flexible multibody system and exact feedforward control based on the full dynamic flexible multibody system is applied to improve the end-effector trajectory tracking performance. Furthermore, the effect of different position control concepts for the two linear drives, such as gain scheduling for the utilized cascade control and a model based friction compensation, on the movers themselves as well as on the end-effector are discussed, which can be conflicting. Experimental results are presented illustrating the achievable accuracy of the end-effector tracking for different trajectories while showing significant error reductions for a feedforward control based on an elastic model in contrast to a rigid one. Finally, a model based curvature controller is utilized which actively controls the occurring oscillations of the parallel manipulator. Here, a proportional controller as well as a linear-quadratic regulator are applied and the impact of an additional curvature control on the end-effector tracking performance is investigated.

Friction compensation, gain scheduling and curvature control for a flexible parallel kinematics robot

For a parallel manipulator with a kinematic loop and a highly flexible link, a comprehensive control approach including friction compensation for the drive train, gain scheduling and active oscillation damping is considered. Friction compensation based on the Stribeck as well as the LuGre models and gain scheduling are used to improve the position control. A curvature controller, which is based on a nonlinear flexible multibody system and on an accurate position control, actively damps the oscillations of the parallel manipulator. First experimental results are presented to confirm the utility of the implemented concepts.

Servo-Constraints for Control of Flexible Multibody Systems With Contact

This paper presents inversion based feedforward control design for flexible multibody systems with kinematic loops and end-effector contact. The inverse model provides for a given desired output trajectories, e.g. end-effector point and contact force, the required control inputs for exact output reproduction. A very appealing and efficient model inversion approach for such multibody systems is the use of so-called servo-constraints. These can be seen as an extension of classical mechanical constraints and yield a set of differential-algebraic equations. This allows an efficient numerical solution without burdensome symbolic manipulations. In addition, the use of servo-constraints allows the straight-forward treatment of flexible multibody systems with various topologies. The arising set of differential-algebraic equations describes the inverse model. The inverse model might be purely algebraic or include a dynamical part, which is called internal dynamics in nonlinear control theory. For its numerical solution it is advisable to transform the set of differential-algebraic equations to its underlying set of ordinary differential equations. The solution method for this internal dynamics depends then on its stability. For systems with unstable internal dynamics, as considered in this paper, a solution can be computed from a boundary-value problem. The efficiency of this approach is demonstrated for a flexible multibody system with a kinematic loop and a closed end-effector contact.© 2013 ASME

Inversion Based End-Effector Trajectory Tracking of Passive-Joint Manipulators

End-effector trajectory tracking of manipulators with passive joints is a challenging task since classical approaches known from fully actuated systems cannot be applied. The paper presents the inversion based control design for manipulators with passive joints, whereby the complexity of the inverse model highly depends on the stability properties of the internal dynamics. For the inverse model the control problem is included here by servo-constraints. For minimum phase systems the internal dynamics can be solved by forward time integration. For non-minimum phase systems a bounded solution is found by solving the internal dynamics as a boundary value problem. The example of a three-arm manipulator with one passive joint is used as application, whereby minimum phase and non-minimum phase designs are considered. The obtained inverse models are used in experiments to control the real system.Copyright