Selected Topics in Structronics and Mechatronic Systems

The following sections are included:

• Preface

• Contents

Robots generally represent Multi Body Systems with apparently simple topology (mostly a topological chain). Design elements are typically motor-gear-arm units or, in case of stiff gears, single arms (rigid bodies) with may be looked at as subsystems. The obviously easiest access to subsystem dynamics is the use of cartesian velocities (a first set of nonholonomic variables). When combining the subsystems to the model under consideration, these are constrained by the actual design requirements leading to a second set of velocities, denoted as minimal velocities according to the minimal (constrained) state. These are nonholonomic if nonholonomic constraints arise but they may also be nonholonomic for the holonomic case. A first look on the available methods leads to the use of the Projection Equations for simplest procedure. Next, specifying reference frames yields a recursive scheme for kinematics as well for kinetics which avoids the total mass matrix inversion. Finally, one may ask why to inspect the constraints at all instead of to confine oneself on minimal state space considerations. The answer is simply that constraints may become active or remain passive which typically arises in mobile robots (friction at the contacts with the environment in wheeled robots, closing and opening contacts along with impact and friction in legged locomotion). Here, correponding motion equations lead directly to an adequate formulation of the Gauss Principle. Having these backgrounds in mind, the main question to be investigated in this contribution is wether the use of nonholonomic variables offers advantages even in the holonomic case.

Fluid borne noise is a problem in hydraulics. Most conventional devices for the attenuation of fluid flow pulsations are either too expensive, build too long or have poor attenuation characteristics. Furthermore, all conventional devices but multi-volume resonators fail to attenuate frequencies which are integer multiples of a base harmonic. In this publication several devices, such as multi-body mass-spring oscillators, multi-volume Helmholtz resonators, compact λ/4 side branch resonators, as well as systems based on various arrangements of plate/shell elements, will be investigated. Besides that, a novel concept for the frequency tuning of chain-structure mass-spring spring oscillators will be presented which places the natural frequencies ω₁ … ω_N at a base harmonic Ω₁ and N − 1 integer multiples Ω₂ … Ω_N. The usefulness of the presented concepts will be evaluated on a simulation study of two real world hydraulic systems (one low pressure system with p_Sys = 40 bar and one conventional system with p_Sys = 200 bar). Although the results appear promising, especially for multi DOF mass-spring compensators and λ/4 side-branch resonators, experimental work is required to confirm the results.

A nonlinear planar centrifugally excited oscillatory system was studied in its steady-state domain. The integral of the correlation dimension and Lyapunov exponents were used to describe the motion of the model in the phase space. Power spectral and bispectral analyses have further been used to analyse the behaviour of the model in the frequency domain. The experimental work has been undertaken on the washing-machine washing complex dynamics to verify the theoretical approach.

Hydraulic actuators are used in a wide range of industrial applications but hydraulic systems are nonlinear in their nature. The steadily rising demands for tighter thickness tolerances in rolling mills gave the motivation for the development of a nonlinear controller based on the exact Input–Output–Linearization. In this contribution it will be shown that the dynamical behavior of a hydraulic adjustment system can be improved by such a nonlinear control concept. One can also find a detailed root locus analysis of the linearized system of such a plant as well as an FFT–identification of a rolling mill.

This contribution is devoted to the mathematical description of a temper rolling mill and a nonlinear controller design based on physical considerations. The plant consists of a four-high mill stand, unwinder, rewinder, and bridle rolls in the entry and exit section of the mill. Special emphasis is laid on the mathematical modelling of the rollgap, since it establishes the interconnection between the strip tensions, the elongation coefficient, the roll force and the slip conditions. The nonlinear control concept is characterized by the fact that the torques of the bridle rolls are intended as control inputs for the elongation and master speed control, whereas the hydraulic adjustment system and the main mill drive are used to take effect on the strip tensions.

It is shown that the high frequency dynamics is a low frequency limit of thermodynamics and a high frequency limit of structural dynamics. It allows one to apply the conventional methods of mechanics and thermodynamics to description of complex engineering structures at high frequencies. The local principle in the vibrational conductivity approach to high frequency dynamics is suggested. The aim of the analysis is to demonstrate a way of combining Statistical Energy Analysis for modelling local dynamics of a structural member and the vibrational conductivity approach to high frequency dynamics for an integral description of complex engineering structures. The study has shown that all parameters of the present method can be determined in terms of the overall mechanical properties of the structure and local properties of the structural member attached to the complex structure.

Mechanical structures in engineering often undergo large rigid body motion together with small elastic deformation. Early observations concerning satellites showed that the purely rigid body modeling is sometimes insufficient for the simulation of mechanical systems. The present work deals with the analysis and simulation of flexible multibody systems with plastic deformation. The existing theory of plane and beam-type multibody systems is extended with respect to nonlinear material behavior, including moderately large deformation, as well. The floating frame of reference formulation is used, which fits best to the small strain plasticity formulation. The single bodies of a multibody system are connected via nodes, which allow a very general formulation of the equations of motion. A short section concerning numerics describes the numerical strategy, which is built up on implicit Runge Kutta schemes. A computational program has been developed and it is used to verify the implementability of the proposed theory. Several examples and comparisons are performed to verify the accuracy of the proposed methods. A damage model is included into the formulation. An example shows the accuracy of the proposed method.

The following sections are included:

• Introduction

• Some Basic Notions of Dynamical Systems

• Disturbance Rejection Using State Feedback

• Linear Quadratic Control and Optimal Noise Rejection
  • Continuous-Time Linear Quadratic Regulation (LQR)
  • Linear Quadratic Gaussian Regulation (LQG) and Kalman Filtering
  • Singlerate Sampled-Data LQG Control
  • Multirate Sampled-Data LQG Control
  • Sampled-Data LQG Control Based on Multirate-Output Controllers
  • Sampled-Data LQG Control Using Two-Point Multirate Controllers
  • Noise Rejection Using Generalized Sampled-Data Hold Functions

• Robust Nonlinear Control

• H^∞-Robust Control Design
  • Continuous-Time State Feedback H^∞-Disturbance Attenuation
  • Discrete-Time State Feedback Minimum H^∞-Norm Regulation
  • Alternative Discrete-Time H^∞-Control Strategies: Dynamic Output Feedback vs. Multirate Output Controllers

• Structural Modelling: Principles and Applications

• Application Examples
  • Example I (Seismic disturbance rejection of shear-type frame)
  • Example II (Optimal noise rejection in steel frame structures using GSHF control)
  • Example III (LQR vs. H^∞ control for seismic excited buildings)
  • Example IV (Robust nonlinear controller design for an aseismic base isolated structure)
  • Example V (Discrete-time state-feedback H^∞ control of an operational self propelled sprayer)
  • Example VI (Discrete H^∞ control of a hollow beam using MROCs)
  • Example VII (Singlerate vs. Multirate LQ control of the hollow beam)

• Conclusions

• References

The fundamentals of Ionic Polymer-Conductor Composites (IPCC's) as biomimetic sensors/transducers/actuators and artificial muscles are briefly reviewed in this short paper. Briefly, the current state-of-the art IPCC manufacturing techniques, governing phenomenological laws, and mechanical and electrical characteristics are described.

The following sections are included:

• Index