Output to input saturation transformation: Demonstration and application to disturbed linear systems

Abstract

In the case of linear systems, control law design is often performed so that the resulting closed-loop meets specific frequency requirements. However, in many cases, it may be observed that the obtained controller does not enforce timedomain requirements amongst which the objective of keeping an output variable in a given interval. In this article, a transformation is proposed to convert expected bounds on an output variable into time-varying saturations on the synthesized linear control law. It is demonstrated that the resulting closedloop is stable and satisfies time-domain constraints in the presence of unknown bounded disturbance. An application to a linear ball and beam model is presented.

Attitude tracking control of a flexible spacecraft under angular velocity constraints

“…Goodwin and de Dona (2004), Glattfelder and Schaufelberger (2003), a popular idea consists of modifying a nominal controller whenever the constraints are about to be violated. Following this line, the Output to Input Saturation Transformation (OIST) approach was recently proposed in Burlion (2012); Chambon, Burlion, and Apkarian (2015a) to replace the state constraints by some state-dependent control saturations. Such an approach is attractive because it enables use of the vast literature on control saturation problems and may especially lead to consider anti-windup loops which are now well understood (see e.g Galeani, Tarbouriech, Turner, and Zaccarian (2009); Tarbouriech and Turner (2009)).…”

Time-response shaping using output to input saturation transformation

“…Using this method along with some assumptions, it is possible to obtain guarantees on the fulfilment of the time-domain constraints when an unsatisfactory control law has already been designed. This article is an extension of the work presented in Chambon, Burlion, and Apkarian (2015a). It gives a comprehensive description of the method for minimum-phase linear systems with unknown finite-energy bounded disturbances.…”

UAV obstacle avoidance scheme using an output to input saturation transformation technique

“…For instance, the anti-windup framework [13], [14] can be applied in combination with the OIST technique (see e.g. [15]). In this paper, we propose to show how the OIST technique can be applied to the problem of UAV obstacle avoidance.…”