Relying on the possibility of generating a second-order sliding motion by using, as control, the first derivative of the control signal instead of the actual control, a new solution to the problem of chattering elimination in variable structure control (VSC) is presented. Such a solution, inspired by the classical bang-bang optimal control strategy, is first depicted and expressed in terms of a control algorithm by introducing a suitable auxiliary problem involving a second-order uncertain system with unavailable velocity. Then, the applicability of the algorithm is extended, via suitable modifications, to the case of nonlinear systems with uncertainties of more general types. The proposed algorithm does not require the use of observers and differential inequalities and can be applied in practice by exploiting such commercial components as peak detectors or other approximated methods to evaluate the change of the sign of the derivative of the quantity accounting for the distance to the sliding manifold.

Chattering avoidance by second-order sliding mode control

A solution to the problem of eliminating the chattering effect, which is always associated with practical implementations of variable structure control, is presented with reference to a class of uncertain multi-input nonlinear systems. The solution procedure relies on the application of an original control approach capable of enforcing a second-order sliding mode (i.e., a sliding regime on a surface s[x(t)]=0 in the system state space, with s/spl dot/[x(t)] identically equal to zero, a regime enforced by a control signal depending on s[x(t)], but directly acting only on s/spl uml/[x(t)]). Such an approach, in its original formulation, only applies to single-input nonlinear systems with particular types of uncertainties. In the present paper, its validity is extended to multi-input nonlinear systems characterized by uncertainties of more general nature, covering a wide class of real processes.

On multi-input chattering-free second-order sliding mode control

Output tracking control of uncertain nonlinear second-order systems

A control strategy proposed by the authors in previous works to reduce the effect of chattering led to the solution of a differential inequality involving the first and second derivatives of the control signal and a parameter for a first-order observer. The analysis was carried out assuming this parameter to be constant. In the present paper, this assumption is removed, thus allowing the solution of the differential inequality to be a function of a piecewise continuous first derivative of the control signal, without need for assuming a priori knowledge of bounds to the plant trajectories.

An improved, chattering free, VSC scheme for uncertain dynamical systems

In this paper, an optimal adaptive fuzzy sliding mode controller is presented for a class of nonlinear systems. In the proposed control, in the beginning, the boundaries of parametric uncertainties...

An optimal and intelligent control strategy for a class of nonlinear systems: adaptive fuzzy sliding mode

In this paper a new method for the solution of the asymptotic linearization of uncertain nonlinear systems by means of a continuous control law is presented. The main feature of this approach consists of a continuous first-order estimator and control laws with piecewise continuous derivatives. As an important by-product of this theory we can deal easily with the case of some uncertain systems which do not satisfy the matching condition, and with systems presenting first order unmodelled dynamics.

P. Pydynowski

Papers

Asymptotic linearization of uncertain nonlinear systems by means of continuous control