Kurt Schlacher

Nonlinear H/sub /spl infin// controller design for a DC-to-DC power converter

We present a state feedback controller for the Cuk converter. It is shown that a special type of DC-DC switched mode power supply can be handled by the theory of affine-input systems. The controller design is based on the H/sub /spl infin//-theory of nonlinear systems. Using an appropriate exogenous system, the stationary control error can be made arbitrarily small. Furthermore, this design method leads to a simple controller and the stability of the closed loop can be guaranteed in the sense of Lyapunov. The implementation for a laboratory model shows a good tracking and disturbance behavior, which proves the feasibility of the proposed procedure.

Shaping of Piezoelectric Sensors/Actuators for Vibrations of Slender Beams: Coupled Theory and Inappropriate Shape Functions

Flexural vibrations of smart slender beams with integrated piezoelectric actuators and sensors are considered. A spatial variation of the sensor/actuator activity is achieved by shaping the surface electrodes and/or varying the polarization profile of the piezoelectric layers, and this variation is characterized by shape functions. Seeking shape functions for a desired purpose is termed a shaping problem. Utilizing the classical lamination theory of slender composite beams, equations for shaped sensors and actuators are derived. The interaction of mechanical, electrical and thermal fields is taken into account in the form of effective stiffness parameters and effective thermal bending moments. Self-sensing actuators are included. From these sensor/actuator equations, shaping problems with a practical relevance are formulated and are cast in the form of integral equations of the first kind for the shape functions. As a practical interesting aspect of these inverse problems, shape functions which fail to measure or to induce certain structural deformations are investigated in the present paper. Such inappropriate shape functions are termed nilpotent solutions of the shaping problems. In order to derive an easy-to-obtain class of such nilpotent solutions, the homogeneous versions of the integral equations for the shaping problems are compared to orthogonality relations valid for redundant beams. Hence, by analogy, the presented nilpotent solutions are shown to correspond to solutions of the basic theory of thermoelastic structures, namely to thermally induced static bending moment distributions. This result beautifully reflects the close connection between the theory of thermally loaded structures and the theory of smart structures. A particular result for a nilpotent shape function previously investigated in the literature is explained in the context of the present theory, and examples of nilpotent shape functions for various structural systems are presented.

Modeling and simulation of a hydrostatic transmission with variable-displacement pump

The S-matic power split drive of Steyr Antriebstechnik is a drive box for vehicular drive systems which combines the advantages of hydrostatic and mechanical transmission. This paper is concerned with the mathematical modeling of the hydrostatic unit of the drive box with special emphasis on the swash-plate mechanism of the variable-displacement pump. For reasons of reliability no measurement device is planned for the variable swash-plate angle. Therefore, a simple discrete on-line simulator for the swash-plate angle is derived by simplifying gradually the mathematical model on the basis of physical considerations.

Active compensation of roll eccentricity in rolling mills

This paper is concerned with the active compensation of the roll eccentricity-induced periodic disturbances in the strip exit thickness of hot and cold rolling mills. The roll eccentricity may be caused by different reasons, like e.g. inexact roll grinding or nonuniform thermal expansion of the rolls. The increasing demands on the thickness tolerances require new methods for the active compensation of the contribution of the roll eccentricity to the final thickness deviation. The presented method is based on the factorization approach over the set of stable transfer functions in combination with an adaptive least mean squares algorithm derived from the projection theorem. Here we take advantage of the fact that the eccentricity caused disturbance is periodic with a frequency proportional to the measured angular velocity of the rolls. Furthermore, it turns out that the presented concept fits the conventional control circuit of automatic gauge control in an optimal way. Simulation results for a cold rolling mill and measurement results for a hot strip mill demonstrate the feasibility and the excellent performance of the design.

CONSTRUCTION OF FLAT OUTPUTS BY REDUCTION AND ELIMINATION

Abstract The construction of flat outputs for nonlinear lumped parameter systems is still an open problem in the general case. An algorithm, based on successive reduction of the number of variables and elimination of variables is presented. It is shown that the reduction requires a dynamic extension in general. The geometric interpretation of this fact is that certain vector fields become projectable on the manifold defined by the extended system. Finally some applications of this approach are presented.

Nonlinear Vehicle Dynamics Control - A Flatness Based Approach

The central issue of this contribution is the discussion of the differential flatness of the planar holonomic bicycle model. The components of a flat output are given as the lateral and the longitudinal velocity component of a distinguished point located on the longitudinal axis of the vehicle. This property is shown for the front-, rear- and all-wheel driven vehicle, without referring to particular representatives of the functions modelling the lateral tire forces. The clear physical meaning of the flat output is regarded as particularly useful for the control design task. The vehicle dynamics control design is accomplished following the flatness based control theory.

Mathematical modeling for nonlinear control: a Hamiltonian approach

Modern model-based nonlinear control requires a good mathematical description of the system we want to control, for both, the system analysis and the controller design. Obviously, the term nonlinear system is too broad, and one is interested in subclasses of nonlinear systems with at least two properties. These classes should cover real world problems, and there should exist controller design methods, powerful enough to admit a systematic design of the closed loop with certain properties. Now, classical Hamiltonian systems have a rich mathematical structure, which has been extended such that dissipative effects and inputs, outputs, or better ports, are included in this class. This contribution starts with a Hamiltonian description of linear time invariant lumped parameter systems to motivate the introduction of certain mathematical ideas, which will be exploited in the nonlinear case afterwards. After that the approach will be extended to the distributed parameter case. Finally, the applicability of the presented methods is shown with the help of a piezoelectric elastic structure.

Non-linear control in rolling mills: a new perspective

This paper is concerned with the application of modern nonlinear control techniques to the thickness control in rolling mills. It turns out that the performance of the closed loop can be significantly improved by taking into account the essential nonlinearities of the to-be-controlled plant already in the controller design. These nonlinear control strategies totally differ from the common approach of linearizing the nonlinear system around a nominal operating point because they are not limited to a more or less small neighborhood of the operating point, but are valid all over the operating range. Practically, these nonlinear control concepts are a possible answer to the trend of modern rolling mills towards tighter thickness tolerances, thinner final strip thicknesses, faster production rates and shorter off-gauge lengths. However, a straightforward application of the well established nonlinear control theory does not always lead to a control concept that is practically feasible. It is rather unavoidable to consider all the special features and properties of the plant. By means of the gap control of a mill stand with a hydraulic positioning system, the authors show in detail the advantages of a nonlinear control approach. Finally, simulation and measurement results demonstrate the feasibility and the excellent performance of the proposed design.

Brief paper: On the observability of discrete-time dynamic systems - A geometric approach

A coordinate-free description for dynamic systems described by explicit (nonlinear) difference equations in one independent variable via a differential geometric framework is presented. Based on this covariant approach suitable geometric objects for discrete-time dynamics are introduced. Especially, the observability along a trajectory is discussed and transformations to normal forms are derived. In addition, the obtained (local) observability criteria can be checked by computer algebra algorithms. Some examples illustrate the proposed approach.

Modelling of piezoelectric structures–a Hamiltonian approach

This contribution is dedicated to the geometric description of infinite-dimensional port Hamiltonian systems with in- and output operators. Several approaches exist, which deal with the extension of the well-known lumped parameter case to the distributed one. In this article a description has been chosen, which preserves useful properties known from the class of port controlled Hamiltonian systems with dissipation in the lumped scenario. Furthermore, the introduced in- and output maps are defined by linear differential operators. The derived theory is applied to the piezoelectric field equations to obtain their port Hamiltonian representation. In this example, the electrical field strength is assumed to act as distributed input. Finally it is shown, that distributed inputs, that are in the kernel of the input map act similarly on the system as certain boundary inputs.