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 socalled 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 finitedimensional systems certain extensions of the analysis and control concepts to the infinitedimensional 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 LowDimensional Manifolds. Nonlinear Feedback (Linearizations, Zero Dynamics, Stabilization, Disturbance Decoupling). Tracking and Feedback Regulation. Global Feedback Design (L2Gains and Disturbance Attenuation, Nonlinear H_{∞}Theory) 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 infinitedimensional Systems
Tracking control of finitedimensional nonlinear systems. The analysis is focused on control structures comprising trajectory planning, feedforward, and feedback control. The concepts of differential flatness, passivitybased control, and backstepping are introduced. Besides a sophisticated theoretical analysis, the application of the introduced concepts is illustrated for various examples.
Tracking control of infinitedimensional structural systems. The concepts differential flatness, passivity, and backstepping as introduced for finitedimensional nonlinear systems are extended to 1dimensional distributedparameter 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 EulerBernoulli 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 1dimensional structural systems, certain further extensions to the design of tracking controllers for 2dimensional 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 infinitedimensional 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 costate variables. We consider finite dimensional systems, which depend linearly or nonlinearly on the control variables. In the first case usually nonsmooth “bangbang” 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, semiactive 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 SaxeCoburg 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.
HannsPeter 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 (Hinfinity 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 , email:
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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 
9:4510:30 
Flockerzi 
Flockerzi 
Rega 
Troger 
Jörgl 
Coffee Break 
11:0011:45 
Flockerzi 
Kugi 
Kugi 
Rega 
Jörgl 
11:4512:30 
Flockerzi 
Kugi 
Kugi 
Rega 
Jörgl 
Lunch 
14:3015:15 
Kugi 
Kugi 
Flockerzi 
Lacabonara 
Troger 
15:1516:00 
Kugi 
Kugi 
Flockerzi 
Lacabonara 
Discussion 
Coffee Break 
16:3017:15 
Steindl 
Steindl 
Kugi 
Gattulli 
Closure 
17:1518:00 
Steindl 
Troger 
Kugi 
Gattulli 

