Global practical stabilisation of large-scale hydraulic networks

Abstract

Proportional feedback control of a large scale hydraulic network which is subject to structural changes is considered. Results regarding global practical stabilization of the non-linear hydraulic network using a set of decentralized proportional control actions are presented. The results show that closed loop stability of the system is maintained when structural changes are introduced to the system.

Global stabilisation of large‐scale hydraulic networks with quantised and positive proportional controls

“…The results presented here represents an important extension of the analytical results presented in [2][3][4][5]. In [3], it was shown that semi-global practical output regulation is achievable using the proposed control architecture with constrained proportional control actions.…”

“…In the work presented here, a set of decentralised proportional control actions will be in the focus. The control strategy has previously been introduced in [2][3][4][5]. The individual control signal relies only on information obtained at the individual end-user.…”

“…In [2], this proposition was extended to a logarithmic quantised version of the control actions. Whereas, in [4] it was shown that with no quantisation of the control signals and with no assumption of actuation constraints, that a global asymptotically stable equilibrium point of the closed-loop system exists. The analysis in [4] was extended in [5] to logarithmic quantised and unconstrained control signals, and existence of an attractor set with a global basin of attraction was shown.…”

“…Whereas, in [4] it was shown that with no quantisation of the control signals and with no assumption of actuation constraints, that a global asymptotically stable equilibrium point of the closed-loop system exists. The analysis in [4] was extended in [5] to logarithmic quantised and unconstrained control signals, and existence of an attractor set with a global basin of attraction was shown. In the analysis presented here, global stability properties of the closed-loop system with quantised and constrained proportional control signals are given.…”

Global Stabilization of Large-Scale Hydraulic Networks Using Quantized Proportional Control

“…4. Contrary to the result with the continuous proportional control actions (Jensen and Wisniewski, 2010), it is evident from Fig. 4 that a single unique equilibrium point can generally not be achieved when the quantized version of the proportional control actions are used.…”