New stabilization and tracking control laws for electrohydraulic servomechanisms

Some nonlinear control laws for a fifth order mathematical model, representative for an electrohydraulic servomechanism (EHS), are presented in the paper. Intrinsically, the EHS mathematical model has several shortcomings: critical case for stability, relative degree defect, and switching type nonsmooth nonlinearity. First, the control synthesis is approached, in the framework of the so-called Malkin canonical form for a critical case in the stability theory, from the perspective of the two paradigms: the regulator, or stabilization problem, and the tracking problem. In the first part of the paper, the stabilization problem is solved and a stabilizing control law, of geometric type, is designed and then illustrated by numerical simulations. Further on, the solution of the stabilizing control is extended as a geometric control for the EHS tracking problem, but given the extreme difficulty of the problem, the proposed solution works only as a conjecture, well confirmed by numerical simulations. In this context, the importance of the electrohydraulic servovalve dynamic response, defined by the time constant, to ensure a reasonable parametric robustness of the control law, has been established. Leaving apart the geometric control approach, the EHS tracking problem was finally solved by appealing to the backstepping synthesis, also validated by numerical simulations.