Adaptive control of uncertain port-controlled Hamiltonian systems subject to actuator saturation

Abstract

This paper deals with the problem of adaptive control of uncertain nonlinear port-controlled Hamiltonian systems subject to actuator saturation, and proposes a number of results on the control design. Firstly, the adaptive stabilization problem is studied, and a control design method is developed by using both the dissipative Hamiltonian structural and saturated actuator properties. Secondly, for the case that there are both parametric uncertainties and external disturbances in the AS systems, an adaptive H ∞ control design approach is presented. Finally, study of an example of power systems with simulations shows that the adaptive controller proposed in this paper is effective.

Port-Hamiltonian Systems in Adaptive and Learning Control: A Survey

“…Combining (24) -(29), the closed-loop for (2) is Model-based methods (Section II-B) Learning methods (Section IV-VII) Stabilization Energy shaping and damping injection (ES-DI) [9], Interconnection and damping assignment (IDA)-PBC [12], power based method [30], Canonical transformation (CT) [8], Control by interconnection (CbI) or energy-casimir methods [7], [9], [10] Energy balancing actor-critic (EBAC) [31], Iterative feedback tuning (IFT) [32], Evolutionary strategy (ES-IDA-PBC) [33], Adaptive control (AC) [34]- [37] Tracking Modified IDA-PBC [38], Canonical transformation [39] Iterative learning control (ILC) [14], Repetitive control (RC) [40], Adaptive control [35] is the closed-loop Hamiltonian, withθ =θ − θ . One can use the closed-loop Hamiltonian for the stability analysis.…”

“…Because of the above advantages the adaptive framework for PH systems has been used in various applications. Notable examples include power system stabilization [34], adaptive tracking control and disturbance rejection [18], [30], [35], simultaneous stabilization of a set of uncertain PH systems [36], [37], and stabilization of time-varying PH systems [42].…”

Hamiltonian stabilization additional L 2 adaptive control and its application to hydro turbine generating sets

“…There are five state variables and two controls are expressed in seven equations, thus the solution is unique. Dynamic equation of system (22) at constant control v * can be described as:…”

“…Remark 3: The (22) or (26) is the HTGS Hamiltonian model with rigid water column hydro turbine model and the third order generator model. The model will be built in the controller to calculate the stabilization control v * .…”

“…Many approaches, such as H ∞ theory [9][10][11][12][13], L 2 disturbance attenuation theory [14][15][16][17][18][19] and other adaptive methods [20][21][22][23], are developed to handle the robustness of the Hamiltonian system. The L 2 method, investigating system robustness directly from model error and parameters disturbance, is the most direct approach.…”