Control of port-hamiltonian systems. Observer design and alternate passive input-output pairs

Promotie: dhr. A. Venkatraman, 16.15 uur, Academiegebouw, Broerstraat 5, Groningen

Proefschrift: Control of port-hamiltonian systems. Observer design and alternate passive input-output pairs

Promotor(s): prof .dr. A. van der Schaft

Faculteit: Wiskunde en Natuurwetenschappen

Contact: Aneesh Venkatraman, tel. 050-363 3972, e-mail: aneesh.82@gmail.com

Control of port-hamiltonian systems. Observer design and alternate passive input-output pairs

We focus on two control related problems in the context of port-Hamiltonian systems with dissipation:

1. Observer design and output feedback stabilization: We identify a special class of mechanical systems which can be partially linearized in the pseudo-momenta via a change of coordinates and study their physical and differential geometric properties. We study the problem of velocity observer design using position measurements for these systems. We then consider a general class of mechanical systems with kinematic constraints and address the problem of velocity observer design for them by using only position measurements. As expected, the observer design simplifies when the system is affine in the (unmeasured) momenta.

We next provide a different viewpoint on observer design by considering a special class of port-Hamiltonian systems with dissipation and constructing observers for them by using a passivity based approach. The essential idea is to make the augmented system consisting of the plant and the observer dynamics to become strictly passive with respect to an invariant manifold defined on the extended state space, on which the state estimation error is zero. In view of the passivity properties, the observer is expected to show a certain amount of robustness.

We finally prove the separation principle for the above observers when used in combination with an asymptotically stabilizing full-state feedback control law which is obtained using passivity based control design techniques.

2. Energy shaping of PHSD by using alternate passive input-output pairs: We explore the possibility of generating new passive input-output pairs for a PHSD and investigate their role in shaping the system's energy via the control by interconnection method. We show that by changing the passive input-output pair of the PHSD, the underlying Dirac structure also changes. We characterize the set of all achievable Casimirs for this new Dirac structure by providing certain necessary conditions. These conditions can be used to check a priori whether the proposed new passive input-output pair, when used for interconnection with the controller, would help in shaping the system's energy along the desired coordinate.