An improved Wien bridge oscillator (original) (raw)

ESAIM: Control, Optimisation and Calculus of Variations, 2003

We study the large-time behaviour of the nonlinear oscillator m x + f (x) + k x = 0 , where m, k > 0 and f is a monotone real function representing nonlinear friction. We are interested in understanding the long-time effect of a nonlinear damping term, with special attention to the model case f (x) = A |x | α−1 x with α real, A > 0. We characterize the existence and behaviour of fast orbits, i.e., orbits that stop in finite time.

Feedback linearization and driftless systems

Mathematics of Control, Signals, and Systems, 1994

The problem of dynamic feedback linearization is recast using the notion of dynamic immersion. We investigate here a "generic" property which holds at every point of a dense open subset, but may fail at some points of interest, such as equilibrium points. Linearizable systems are then systems that can be immersed into linear controllable ones. This setting is used to study the linearization of driftless systems : a geometric sufficient condition in terms of Lie brackets is given ; this condition is shown to be also necessary when the number of inputs equals two. Though non invertible feedbacks are not a priori excluded, it turns out that linearizable driftless systems with two inputs can be linearized using only invertible feedbacks, and can also be put into chained form by (invertible) static feedback. Most of the developments are done within the framework of differential forms and Pfaffian systems.

On damped second-order gradient systems

Journal of Differential Equations, 2015

Using small deformations of the total energy, as introduced in [28], we establish that damped second order gradient systems u ′′ (t) + γu ′ (t) + ∇G(u(t)) = 0, may be viewed as quasi-gradient systems. In order to study the asymptotic behavior of these systems, we prove that any (non trivial) desingularizing function appearing in KL inequality satisfies ϕ(s) O( √ s)) whenever the original function is definable and C 2 . Variants to this result are given. These facts are used in turn to prove that a desingularizing function of the potential G also desingularizes the total energy and its deformed versions. Our approach brings forward several results interesting for their own sake: we provide an asymptotic alternative for quasi-gradient systems, either a trajectory converges, or its norm tends to infinity. The convergence rates are also analyzed by an original method based on a one dimensional worst-case gradient system.

Oscillations analysis in nonlinear variable-structure systems with second-order sliding-modes and dy

Proceedings of the 16th IFAC World Congress, 2005, 2005

A class of uncertain systems nonlinear in the input variable and driven by a dynamic actuator device is dealt with. We give sufficient conditions under which the feedback controller based on the "Sub-optimal" second-order slidingmode control algorithm can guarantee the attainment of a boundary layer of the sliding manifold. The relationship between the actuator parameters and the size of the boundary layer is investigated. We discuss about the possible ways for estimating, or even shaping, the parameters of the periodic limit cycles that may occur in the steady-state within the boundary layer. A simulation example is given that confirm the results of the proposed analysis

OSCILLATIONS ANALYSIS IN NONLINEAR VARIABLE-STRUCTURE SYSTEMS WITH SECOND-ORDER SLIDING-MODES AND DYNAMIC ACTUATORS

An improved Wien bridge oscillator (original) (raw)

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