Euler-Bernoulli beam flatness based control with constraints

Abstract

Abstract-The control of infinite dimensional systems with constraints is a notoriously difficult task. We consider a general class of linear systems governed by partial differential equations with boundary control. This problem is here treated in a quite natural manner through the freeness property, the analogue of differential flatness for linear systems. Any variable is then expressed as infinite order differential operators applied to the basis components, the analogue of the flat output components. The specialisation of the basis components are functions which are both of Gevrey regularity (in order for the infinite order differential operators to be convergent) and pertaining the flexibility of polynomial splines. An illustration is made through an Euler Bernoulli beam example.

Flatness-based longitudinal vehicle control with embedded torque constraint

“…In (Löwis and Rudolph, 2003), no optimisation technique is used, but the flat output trajectory is not known on advance; thus, the trajectory is built step by step, by concatenating pieces The only work partially related to our approach is (Ruppel et al, 2011), where the constraints appear solely on derivatives of the flat output, which is specialised to piecewise polynomial functions. Preliminary results related to the present one have been presented for linear systems with delays in (Bekcheva et al, 2017), and for an Euler Bernoulli beam in (Bekcheva et al, 2015). Other works related to the present theme include differential flatness based techniques for longitudinal and lateral vehicle dynamics (Menhour et al, 2014).…”