Peter C. Müller

Calculation of Lyapunov exponents for dynamic systems with discontinuities

Abstract The model based algorithm for the calculation of the spectrum of Lyapunov exponents is generalized for nonlinear dynamical systems with discontinuities. As the main result, the required linearized equations have to be supplemented by certain transition conditions at the instants of discontinuities.

State estimation of dynamical systems with nonlinearities by using proportional-integral observer

In this paper the application of a PI observer technique to dynamical systems with nonlinearities is proposed. The PI observer has two feedback loops, a proportional loop and an integral loop of the estimation error. In this way the PI observer combines the structures of the practical orientated nonlinearity observer developed by the third author and the classical Luenberger observer. The structure and the estimation performance of the PI observer are discussed and analysed. The results show that the PI observer can estimate the states not only of linear systems, but also, more significantly, of systems with any arbitrary external input which appear as unknown input, nonlinearity or unmodelled dynamics. It is shown that the PI observer works with weak assumptions, which can be fulfilled by many classes of systems to be observed. Owing to the weak assumptions it can improve many observer-based technical solutions as diagnosis or control based on observers. In the paper the conditions are given and proved. ...

Optimal positioning of dampers in multi-body systems

Abstract An important aspect of the passive and/or active damping of vibrations of multi-body systems is the optimal positioning of the dampers, actuators and sensors. This study is concerned with the problem of finding the optimal positioning of a viscous damper for a linear conservative mechanical system on the basis of an energy criterion. The results obtained are applied to homogeneous oscillating chains.

Linear mechanical descriptor systems: Identification, analysis and design.

Abstract Describing mechanical multibody systems with holonomic and/or nonholonomic constraints by Lagranges equations of first kind, then the system is represented in descriptor form. Recent progress of dealing with descriptor systems allows the complete analysis and the design of linear mechanical descriptor systems. Controllability, observability, stability, descriptor state feedback, observers, and parameter identification of such systems are discussed in detail. It is shown that todav efficient tools are available to deal with mechanical descriptor systems.

Chaotic motions and fault detection in a cracked rotor

Applying the theory of Lyapunov exponents for nonsmooth dynamical systems, chaotic motions and strange attractors are found in the case of a cracked rotor. To detect the crack and establish a clear relation between shaft cracks in turbo rotors and induced phenomena in vibrations measured in bearings, a model-based method is applied. Based on a fictitious model of the time behaviour of the nonlinearities, a state observer of an extended dynamical system is designed resulting in estimates of the nonlinear effects.

Design of decentralized linear state function observers

Abstract Based on an extended result of unknown-input observers, an easy and systematic procedure is presented for the design of decentralized linear state function observers. The problem formulation permits a general class of interconnected large-scale linear systems to be taken into consideration. Three different class of interconnection patterns are discussed. When these proposed observers are used within decentralized dynamical feedback controllers, the desired separation property of the overall closed-loop system is guaranteed.

A Global Asymptotic Stable Output Feedback PID Regulator for Robot Manipulators

In this paper, we provide an answer to the long-standing question of designing global asymptotically stable proportional-integral-derivative (PID) regulators with only position feedback for uncertain robots. Our main contribution is to establish the global asymptotic stability of the controlled system by using Lyapunov direct method and LaSalles invariance principle. We provide explicit conditions on the regulator gains to ensure global asymptotic stability. The proposed controller does not utilize the modeling information in the control formulation, and thus permits easy implementation. Simulations performed on a planar two degrees-of-freedom robot manipulator demonstrate the effectiveness of the proposed approach.

Global stabilization for constrained robot motions with constraint uncertainties

In this paper, the global stability problem for constrained robot motions in the presence of constraint uncertainties is investigated. We focus on the uncertainties in the constraint functions and their effects on the global stability. PD type controllers are used and conditions for global stability are developed using Lyapunovs direct approach. In the presence of the constraint uncertainties under investigation, the desired position and constraint force can be guaranteed with global asymptotic convergence. The developed conditions for feedback gain selections clearly show the effects of the constraint uncertainties. For the case when the velocity measurements are not available, conditions for global stability regulation are also established and the robot controller uses only the measurements of the position angles. Finally, we consider the case where the robot joints are flexible and global stability conditions are given.

Independent joint control: Estimation and compensation of coupling and friction effects in robot position control

The method of independent joint control has been widely used in the position control of industrial robots. In order to improve the control performance of this type of controllers, the concept of nonlinearity-estimation and-compensation is introduced. With this extended method comparable results can be obtained as with the method of exact linearization. Especially by the treatment of unmodeled or inaccurate effects, e.g., friction, load variation or parameter inaccuracy, the presented control concept shows great advantages.

Position Control of Robots by Nonlinearity Estimation and Compensation: Theory and Experiments

To improve the performance of position controllers of robots, a designapproach using the method of nonlinearity estimation and compensation ispresented. The controller designed has a similar structure to that of thelinear independent joint control. Nonlinearities in the robot dynamics areestimated by a state observer based on approximate linear models of thesystem, and then compensated by an appropriate feedback. The paper presentsthe theory how to design such a controller as well as the experimentalresults verifying its performance.