This note offers an integral sliding manifold design method for linear systems that minimizes the impact of unmatched constant external disturbances. System sensitivity upon an unmatched disturbance vector is assessed by the steady-state dependent criterion function. The derived procedure easily finds a unique integral sliding manifold that minimizes a quadratic optimization criterion. Applicability of this method in case of slowly-varying disturbances is supported by determining disturbance frequency limit that guarantees satisfactory performance. The proposed approach has been demonstrated on a numerical example and verified by simulations.

This paper deals with the synchronization problem of harmonic oscillatory systems, such as two- and three-phase harmonic oscillators. Synchronization between referent and controlled harmonic oscillators, based on amplitude and phase control, is pursued by employing a variable structure control system. Synchronization is achieved by organizing sliding mode along the intersection of two appropriate nonlinear sliding surfaces, individually providing amplitude and phase identity. In case of three-phase harmonic oscillator synchronization an additional symmetry condition arises, which is handled by introduction of another sliding surface. Parameter perturbations and external disturbances are taken into consideration in control system design. Variable structure controllers for two- and three-phase synchronization are designed, which provide sliding mode along the intersection of sliding surfaces in finite time in spite of present disturbances. Ideal sliding dynamics is proved to be insensitive to internal and external disturbances resulting in an ideal harmonic response. Mathematical analysis as well as experimental and simulation results are presented.

Model-based control techniques have been gaining more and more interest these days. These complex control systems are mostly based on theories, such as feedback linearization, model predictive control, adaptive and robust control. In this paper the latter approach is investigated, in particular, sliding mode (SM) control is analyzed. While several works on the description and application of SM control on single-input single-output systems can easily be found, its application on multi-input multi-output systems is not examined in depth at the same level. Hence, this work aims at formalizing some theoretical complements about the necessary conditions for the feasibility of the SM control for multi-input-multi-output systems. Furthermore, in order to obtain the desired performance from the control system, a method for parameter tuning is proposed in the particular case in which the relative degree of the controlled channels is equal to one. Finally, a simple control problem example is shown with the aim of stressing the benefits derived from the application of the theoretical complements described here.

The paper studies sliding mode (SM) features in systems characterized by the presence of unmatched disturbances. Although it is possible to establish a SM in such systems, the unmatched part of disturbances has impact on the SM dynamics. Under these circumstances system trajectory does not converge to the origin but wanders in its neighborhood along the sliding manifold. This paper offers a sliding hyperplane design method to minimize the effects of the unmatched disturbances upon the SM dynamics, for a class of linear systems. The optimization criterion is minimization of the steady state vector norm. The suggested approach has been demonstrated on a numerical example.