Robust Measurement Feedback Control of an Inclined Cable

Abstract

Considering the partial differential equation model of the vibrations of an inclined cable, we are interested in applying robust control technics to stabilize the system with measurement feedback when it is submitted to external disturbances. This paper focuses indeed on the construction of a standard linear infinite dimensional state space system and an H ∞ feedback control of vibrations with partial observation of the state. The control and observation are performed using an active tendon.

Robust Control of a Cable From a Hyperbolic Partial Differential Equation Model

“…Similar H ∞ -approaches have been considered in [9] to suppress vibrations in flexible structures, but only in the finite dimensional setting. A preliminary version of the present study has been published in [10]. L Besides giving a theoretical robust control study based on a realistic model from civil engineering, the contribution of this paper is also to illustrate a theoretical result presented in [11] or [12] that gives the H ∞ -robust control of infinite dimensional systems in terms of solvability of two coupled Riccati equations.…”

Optimal dynamic inversion‐based boundary control design for two‐dimensional heat equations

“…In control design problems, the control action can be defined in one of two ways: either distributed (in-domain) or boundary control. The distributed control action appears explicitly in the system of equations [12,13,15,21], whereas the boundary control actuates the system implicitly through the boundary conditions [19,[23][24][25][26][27][28][29]. For implementation purposes, the boundary actuation is practically more relevant as compared with the in-domain actuation.…”

“…The boundary control could be defined in more than one way as per the system's spatial dimension. A one-dimensional (1D) system can be actuated through the boundary condition [19,20,27] when a point action is used. In a two-dimensional (2D) system, the system can be controlled by either defining a distributed control over the boundary or utilising a point control with an influence function [23].…”