Hybrid control of a hydro-pneumatic tractor suspension

International audienceWe consider the set-point regulation of a non-standard hydro-pneumatic suspension architecture used in commercial tractors, which allows regulating both the stroke and the pressure in the suspension. The model reveals an affine dynamic comprising two single integrators whose actuation is performed by way of suitably switching constant input selections. We design the switching input by way of a hybrid representation, providing necessary and sufficient conditions for the global stabilizability, and proposing two constructive hybrid control laws. The first control law solves the stabilization problem, while the second one can be used to suitably reduce the number of switches of the input, thereby reducing the aging of the actuators. Both control laws are tested in simulation, and assessed in terms of performance and robustness in the presence of parametric uncertainties. I. INTRODUCTION Despite the traditional attention to mechanical topics and issues, agricultural vehicles design has recently started to wink at electronic control systems in order to improve vehicle dynamics performances, see [3]. Besides automatic guidance works, which date back to early noughties (see e.g. [2], [10]), driver comfort is one of the main subject addressed in the recent literature, [8], [9], [13], [14], [16]. Particular attention has been given to vehicle vertical dynamics and vibrations, as typical tractor working scenarios involve uneven soil and irregular roads. Among the several possibilities, the hydro-pneumatic suspension technology is an interesting suspension one since it allows, with a relatively simple mechanical architecture, to actively produce forces to counteract the effect of road roughness on the sprung masses. Such technology can be beneficially employed on tractors, being capable of sustaining significant loads and exploit already installed hardware (oil-pump and circuits, which are typically present on tractors for the use of implements). However, when agricultural applications are considered, slower actuation dynamics (w.r.t. the mentioned car counterpart) are to be expected, given the increased volumes and oil flows required. With this limitation, the control objective is usually to centre the suspension position in the available stroke during standard operations, in order to minimize possible collisions with the end-strokes; moreover the suspension can be controlled to set different vehicle chassis geometry and change weights distribution, which can increase the efficiency of specific agricultural processes: such problem is usually called suspension levelling. Suspension levelling is presented and discussed in the scientific literature. The most common control approach to the problem is presented in [6], [7], [11], [17], [18], where a continuous control action (coming from classical PID or sliding mode controllers) is approximated by means of a PWM actuation of on-off valves, usually flanked by heuristic and fuzzy logic rules to handle uncertainties or application specific issues. In the recent work, [15] a hybrid model of an air-suspension system is proposed and an MPC control strategy is employed to regulate the suspension. In the present work a non-standard hydro-pneumatic suspension architecture is considered, that allows also to actively change the suspension stiffness by properly regulating the air-spring pressure: thus the control problem becomes multi-objective: the hereby proposed solution lies within the hybrid system framework presented by [5]. Moreover a specific design parameter is also introduced to moderate the number of switches. To overcome the typical implementation and computational burden of MP