Marie Curie Europe

TC2: Nonlinear Dynamics and Control of Structural and Mechanical Systems

TC2: Nonlinear Dynamics and Control of Structural and Mechanical Systems

A training course coordinated by Hans Troger
time:  18-22 February 2008
location: Institute of Mechanics and Mechatronics, Vienna University of Technology, (HS 5)
address: Wiedner Hauptstrasse 8-10,  A-1040 Wien


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The steadily growing demand on the performance of complex mechanical systems and engineering structures such as, for example, large aerospace structures or even railway cars, which are modeled as a system of coupled  rigid and flexible components, cannot be achieved only by passive system components, but requires active control. However, accurate modeling yields nonlinear control problems for which the standard linear control theory must be properly extended or new concepts must be introduced. Moreover the progress in computing and actuation – we only mention the concept of so-called smart structures – has opened up new technical possibilities which must be taken into account.

The course will focus on the connection between nonlinear control and nonlinear dynamics by presenting the fundamentals of the theory of nonlinear control systems with special emphasis on the differential geometric approach. This on one side is based on concepts like invariant manifolds, for example Center Manifolds presented in the Course TC1, and on the other hand on the fundamental tools in the analysis of nonlinear control systems, for example, invariant distributions. Besides finite-dimensional systems certain extensions of the analysis and control concepts to the infinite-dimensional case will be considered in order to account for the flexible components in complex mechanical systems.

In two basic series of lectures a general introduction into the mathematical concepts of nonlinear control both for finite and infinite dimensional systems will be given. Here the concepts of nonlinear control theory are introduced from an applied mathematical (Flockerzi) and from a more engineering (Kugi) point of view. The amount of these two series of lectures will be approximately half of the Course. Further the theoretical concepts of optimal steering by means of Pontriyagin's Maximum Principle (Steindl) and the use of chaos control (Rega) will be presented.

Various applications will be given in the remaining lectures applying the theoretical concepts, as can be seen from the detailed listing of the Contents.


 
 
Invited Lecturers

Dietrich Flockerzi - Max Planck Institute Magdeburg, Germany

8 lectures on:  Integral Manifolds for Model Reduction and Nonlinear Control

Integral Manifolds and Singular Perturbations with a critical view on Intrinsic Low-Dimensional Manifolds. Nonlinear Feedback (Linearizations, Zero Dynamics, Stabilization, Disturbance Decoupling). Tracking and Feedback Regulation. Global Feedback Design (L2-Gains and Disturbance Attenuation, Nonlinear HTheory)  or Decompositions of Control Systems - A Differential Geometric Point of View

Andreas Kugi, Thomas Meurer - Technische Universität Wien, Austria

10 lectures on:  Introduction into Tracking Control of finite- and infinite-dimensional Systems

Tracking control of finite-dimensional nonlinear systems. The analysis is focused on control structures comprising trajectory planning, feedforward, and feedback control. The concepts of differential flatness, passivity-based control, and backstepping are introduced. Besides a sophisticated theoretical analysis, the application of the introduced concepts is illustrated for various examples.

Tracking control of infinite-dimensional structural systems. The concepts differential flatness, passivity, and backstepping as introduced for finite-dimensional nonlinear systems are extended to 1-dimensional distributed-parameter systems with boundary control input. For this, certain applications are considered such as a gantry crane, i.e. a heavy chain with payload attached to a driven trailer, and a cantilevered piezoelectric Euler-Bernoulli beam, which serves as a micropositioning device. Experimental results for these examples will be shown in order to illustrate the performance of the designed tracking controllers. Besides 1-dimensional structural systems, certain further extensions to the design of tracking controllers for 2-dimensional structural systems are presented.

Giuseppe Rega - University of Roma, La Sapienza, Italy

4 lectures on:  Bifurcation, chaos, dynamic integrity and their control in mechanical/structural systems

Invariant manifolds and global bifurcations. Controlling nonlinear dynamics and chaos. A unified framework for optimal control of bifurcations and chaos. Analytical treatment and numerical validation. Finite- and infinite-dimensional systems. System dynamical integrity and its control. Paradigmatic models and applications to various mechanical and structural systems.  

Alois Steindl - Technische Universität Wien, Austria

3 lectures on: Optimal Control

Optimal Control problems. Using Pontrijagin's Maximum principle we derive the Hamiltonian equations and boundary conditions for the state and co-state variables. We consider finite dimensional systems, which depend linearly or nonlinearly on the control variables. In the first case usually non-smooth “bang-bang” control histories occur, whereas in the nonlinear case the control variables are continuous under certain regularity assumptions. Also different kinds of inequality constraints on the control and state variables are investigated. Application of Optimal Control theory to the deployment of tethered satellite systems is presented.

Vincenzo Gattulli - University of L'Aquila, Italy

3 lectures on: Advanced control strategies in cable dynamics

Introduction to cable dynamics (suspended cables, stays, mooring cables). Control strategies for cable vibration suppression: longitudinal control, transversal control. Passive, semi-active and active configuration. Control design procedures: theoretical development, experimental and actual implementation.

(The material of the lectures is partially presented in the chapter titled "Advanced control strategies in cable dynamics," by V. Gattulli, published in the hardback volume of Saxe-Coburg Publications, which includes the invited lectures presented at: The Eleventh International Conference on Civil, Structural and Environmental Engineering Computing, CC2007, Malta).

Walter Lacarbonara - University of Roma, La Sapienza, Italy

2 lectures on: Parametric instabilities and cancellation in nonlinearly viscoelastic structures

Introduction to modelling of nonlinearly viscoelastic beams and shells (spherical and cylindrical) subject to parametric forcing. Mechanical phenomena arising from the parametric instabilities of various kinds. Active cancellation of parametric instabilities: theoretical investigation and experimental verification. 

Hanns-Peter Jörgl - Technische Universität Wien, Austria

3 lectures on: Smart structural actuation

Active damping in smart structures using piezo actuators with an application to rail vehicles will be given. Optimal sensor/actuator placement and robust control (H-infinity control) of bending and torsional modes will be performed. Simulation results and their validation in a scaled down experiment will be presented.

Hans Troger - Technische Universität Wien, Austria 

3 lectures on: Application of Center Manifold Theory to control of nonlinear systems

Control of periodic motion of a simple robot and station keeping of a tethered satellite system using center manifold theory is presented. In addition to A.  Steindl's presentation of the optimally controlled deployment of a tethered satellite this problem is treated using alternative approaches such as chaos control presented by G.Rega. For a simple nonholonomic system (sledge) the optimal control strategy (presented by A.Steindl) is applied.

 

Preliminary Readings

  • A.Kugi, Nichtlineare Systeme I and II (in German)

  • Alberto Isidori, Nonlinear Control Systems, Springer Verlag, Berlin 1989

  • Shankar Sastry, Nonlinear Systems, Analysis, Stability and Control, Springer Verlag New York 1999

 

Hosting Institution

Institute of Mechanics and Mechatronics, Vienna University of Technology

 

For further information please contact:

Vincenzo Gattulli - SICON General Secretary -
Piazzale E. Pontieri 2 - 67040 Monteluco di Roio (Italy)
tel. +39 0862 434511, fax +39 0862 434548
http://www.sicon.ing.univaq.it , e-mail: This e-mail address is being protected from spam bots, you need JavaScript enabled to view it

 

Event Time Table

 

Time

Monday

Tuesday

Wednesday

Thursday

Friday

 

February 18

February 19

February 20

February 21

February 22

9:00 ­ 9:45

Opening

Flockerzi

Rega

Flockerzi

Gattulli

9:45-10:30

Flockerzi

Flockerzi

Rega

Troger

Jörgl

Coffee Break

11:00-11:45

Flockerzi

Kugi

Kugi

Rega

Jörgl

11:45-12:30

Flockerzi

Kugi

Kugi

Rega

Jörgl

Lunch

14:30-15:15

Kugi

Kugi

Flockerzi

Lacabonara

Troger

15:15-16:00

Kugi

Kugi

Flockerzi

Lacabonara

Discussion

Coffee Break

16:30-17:15

Steindl

Steindl

Kugi

Gattulli

 Closure

17:15-18:00

Steindl

Troger

Kugi

Gattulli

 

       
 
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