Active Control of Smart Structures using Port Controlled Hamiltonian Systems

Sprache des Vortragstitels:

Englisch

Original Tagungtitel:

IUTAM Symposium on Dynamics of Advanced Materials and Smart Structures

Sprache des Tagungstitel:

Englisch

Original Kurzfassung:

Smart structures based on piezoelectric composites have turned out to be excellent actuators and sensors for active and passive damping in vibration control. In the case of small displacements a linear approach suffices [8], if hysteresis or depolarization of the active material are negligible [7]. This contribution presents a unifying way for the mathematical modeling of smart structures based on Port Controlled Hamiltonian Systems, see [3]. It is well known that the generalized Hamiltonian formulation is extremely useful for lumped parameter control systems, where the mathematical model includes nonlinear algebraic and ordinary differential equations. As a result of this development the interest in the PCH formulation of distributed parameter control systems, the mathematical model includes also nonlinear partial differential equations, is strongly increasing. Some successfully solved examples lead us to suppose that in the latter case the Hamitonian approach is even more important than in the first one [6]. Recently, a PCH formulation of Maxwell's equations has been presented [3]. The presented contribution is organized as follows. In the next section we draw together the mathematical notation required for the subsequent investigation, see [1], [5]. The third section presents an introductory example of a PCH system together with its rigorous geometric picture. The fourth section generalizes this approach to lumped and distributed parameter systems of the Lagrangian and Hamiltonian type. The general mathematical model of peizeoelectric structure is presented in the fifth section. In the sixth section we give some remarks concerning the controller design and close this contribution with some final remarks.

Sprache der Kurzfassung:

Englisch

Englischer Vortragstitel:

Active Control of Smart Structures using Port Controlled Hamiltonian Systems

Englischer Tagungstitel:

IUTAM Symposium on Dynamics of Advanced Materials and Smart Structures

Englische Kurzfassung:

Smart structures based on piezoelectric composites have turned out to be excellent actuators and sensors for active and passive damping in vibration control. In the case of small displacements a linear approach suffices [8], if hysteresis or depolarization of the active material are negligible [7]. This contribution presents a unifying way for the mathematical modeling of smart structures based on Port Controlled Hamiltonian Systems, see [3]. It is well known that the generalized Hamiltonian formulation is extremely useful for lumped parameter control systems, where the mathematical model includes nonlinear algebraic and ordinary differential equations. As a result of this development the interest in the PCH formulation of distributed parameter control systems, the mathematical model includes also nonlinear partial differential equations, is strongly increasing. Some successfully solved examples lead us to suppose that in the latter case the Hamitonian approach is even more important than in the first one [6]. Recently, a PCH formulation of Maxwell's equations has been presented [3]. The presented contribution is organized as follows. In the next section we draw together the mathematical notation required for the subsequent investigation, see [1], [5]. The third section presents an introductory example of a PCH system together with its rigorous geometric picture. The fourth section generalizes this approach to lumped and distributed parameter systems of the Lagrangian and Hamiltonian type. The general mathematical model of peizeoelectric structure is presented in the fifth section. In the sixth section we give some remarks concerning the controller design and close this contribution with some final remarks.