Stabilization Of port-Hamiltonian Systems Research Articles

Stabilization of port-Hamiltonian systems with discontinuous energy densities

<p style='text-indent:20px;'>We establish an exponential stabilization result for linear port-Hamiltonian systems of first order with quite general, not necessarily continuous, energy densities. In fact, we have only to require the energy density of the system to be of bounded variation. In particular, and in contrast to the previously known stabilization results, our result applies to vibrating strings or beams with jumps in their mass density and their modulus of elasticity.</p>

Asymptotic stability of port-hamiltonian systems with constant inputs

In this paper, the asymptotic stability of Port-Hamiltonian (PH) systems with constant inputs is studied. Constant inputs are useful for stabilizing systems at their nonzero equilibria and can be realized by step signals. To achieve this goal, two methods based on integral action and comparison principle are presented in this paper. These methods change the convex Hamiltonian function and the restricted damping matrix of the previous results into a Hamiltonian function with a local minimum and a positive semidefinite matrix, respectively. Due to common conditions of Hamiltonian function and damping matrix, the proposed method asymptotically stabilizes more classes of PH systems with constant inputs than the existing methods. Finally, the validity and advantages of the presented methods are shown in an example.

Stabilization of port-Hamiltonian systems by nonlinear boundary control in the presence of disturbances

In this paper, we are concerned with the stabilization of linear port-Hamiltonian systems of arbitrary orderN∈ ℕ on a bounded 1-dimensional spatial domain (a,b). In order to achieve stabilization, we couple the system to a dynamic boundary controller, that is, a controller that acts on the system only via the boundary pointsa,bof the spatial domain. We use a nonlinear controller in order to capture the nonlinear behavior that realistic actuators often exhibit and, moreover, we allow the output of the controller to be corrupted by actuator disturbances before it is fed back into the system. What we show here is that the resulting nonlinear closed-loop system is input-to-state stable w.r.t. square-integrable disturbance inputs. In particular, we obtain uniform input-to-state stability for systems of orderN= 1 and a special class of nonlinear controllers, and weak input-to-state stability for systems of arbitrary orderN∈ ℕ and a more general class of nonlinear controllers. Also, in both cases, we obtain convergence to 0 of all solutions ast→∞. Applications are given to vibrating strings and beams.

New Results on Stabilization of Port-Hamiltonian Systems via PID Passivity-Based Control

In this article, we present some new results for the design of PID passivity-based controllers (PBCs) for the regulation of port-Hamiltonian (pH) systems. The main contributions of this article are: (i) new algebraic conditions for the explicit solution of the partial differential equation required in this design; (ii) revealing the deleterious impact of the dissipation obstacle that limits the application of the standard PID-PBC to systems without pervasive dissipation; (iii) the proposal of a new PID-PBC which is generated by two passive outputs, one with relative degree zero and the other with relative degree one. The first output ensures that the PID-PBC is not hindered by the dissipation obstacle, while the relative degree of the second passive output allows the inclusion of a derivative term. Making the procedure more constructive and removing the requirement on the dissipation significantly extends the realm of application of PID-PBC. Moreover, allowing the possibility of adding a derivative term to the control, enhances its transient performance.

Casimir-Based Control Beyond the Dissipation Obstacle

A prevailing trend in the stabilization of port-Hamiltonian systems is the assumption that the plant and the controller are both passive. In the standard approach of control by interconnection based on the generation of Casimir functions, this assumption leads to the dissipation obstacle, which essentially means that dissipation is admissible only on the coordinates of the closed-loop Hamiltonian that do not require shaping and thus severely restricts the scope of applications. In this contribution, we show that we can easily go beyond the dissipation obstacle by allowing the controller to have a negative semi-definite resistive structure, while guaranteeing stability of both the closed-loop and the controller.