PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Series A, OF THE ROMANIAN ACADEMY Volume 5, Number 1/2004, pp.000 - 000 _____________________________ Recommended by Radu P.VOINEA, Member of the Romanian Academy CONTROL SYNTHESIS METHODOLOGY RELATED TO AN ADVANCED NONLINEAR ELECTROHYDRAULIC SERVO SYSTEM Ioan URSU, Florica POPESCU, Felicia URSU “Elie Carafoli” National Institute for Aerospace Research-Bucharest e-mail: iursu@aero.incas.ro The obtaining of control law for an advanced four-dimensional, nonlinear electrohydraulic servo mathematical model is the main contribution of the paper. This control law ensures the asymptotic stability of references tracking by constructing a Control Lyapunov Function (CLF) on the errors concerning the state variables and theirs desired values. An approach based on partitioning the state system into two subsystems − a first one internal stable, and a second one taken as framework of control synthesis − was developed; this is another main contribution of the present paper. The paper's interest derives also from illustrating the key idea of CLFs synthesis by using of celebrated Barbalat's Lemma. Numerical simulations were reported from viewpoint of assessing the servo time constant performance. Key words: nonlinear control synthesis, backstepping, Control Lyapunov Function, Barbalat's Lemma, electrohydraulic servo. 1. INTRODUCTION This paper develops control strategies for the electrohydraulic servo (EHS) control synthesis using the concept of Control Lyapunov Function (CLF), concept introduced by Artstein [1] and Sontag [2], and based on the backstepping approach [3] of building these functions. In the beginning, Lyapunov's stability theory deals with dynamic systems without inputs. For this reason, it has traditionally been applied only to closed loop control systems, that is, to systems for which the input has been eliminated through the substitution of a predetermined feedback control. Recently, some authors started using Lyapunov function candidates in feedback design itself by making the Lyapunov function derivative negative when choosing the control. Such idea has been made precise with the introduction of the CLF concept. The building of a CLF is not a unique matter, and the Jurdjeviæ-Quinn's approach [4] and Sontag's approach [5] are only two such examples. Another approach is just backstepping methodology [3], a recursive type control design brought out in 1990's. Its initial limitation to a class of strict feedback systems [3] stimulated the development of various recursive procedures, applicable to more general nonlinear systems, as feedforward systems, adaptive systems and systems with structured uncertainty [3], [6] and [7]. In the following, the backstepping [3], [8], [11] is applied to position control synthesis for an EHS four- dimensional mathematical model, whose equation belongs to a general class of nonlinear systems ( f & means the derivative of the function ( ) t f with respect to the time t) ( ) ( ) u x G x F + = x & (1) where x ∈ R n is the state vector, u ∈ R m is the control vector and F and G are smooth vector fields of appropriate dimensions. The key idea in certifying the CLF building is using of the Barbalat's Lemma.