Energy-based Control and Observer Design for higher-order infinite-dimensional Port-Hamiltonian Systems

Abstract

In this paper, we present a control-design method based on the energy-Casimir method for infinite-dimensional, boundary-actuated port-Hamiltonian systems with two-dimensional spatial domain and second-order Hamiltonian. The resulting control law depends on distributed system states that cannot be measured, and therefore, we additionally design an infinite-dimensional observer by exploiting the port-Hamiltonian system representation. A Kirchhoff-Love plate serves as an example in order to demonstrate the proposed approaches.

Figures (7)

• Figure 3: Force distribution of the actuators over $z^{1}$.
• Figure 4: Final plate deflection $w(z^{1},z^{2},T_{end})$ over $\mathcal{B}$.
• Figure 5: Simulation result for the deflection $w$ of the edge $\partial\mathcal{B}_{2}$ over time $t$ and coordinate $z^{1}$.
• Figure 6: Comparison of the measurement $w(L_{1},\frac{L_{2}}{2},t)$ and the observer state $\hat{w}(L_{1},\frac{L_{2}}{2},t)$.
• Figure 7: Final plate deflection $w(z^{1},z^{2},T_{end})$ over $\mathcal{B}$.

Theorems & Definitions (14)

• Example 3: Boundary-actuated Kirchhoff-Love plate
• Remark 4
• Theorem 5: Structural Invariants
• Remark 6
• Example 7: Casimir-based Controller for Ex. 2
• Theorem 8: Observer Design
• Example 9: Observer Design for Ex. 2
• Example 10: Boundary-actuated Kirchhoff-Love plate
• Remark 11
• Theorem 12: Structural Invariants