This paper proposes a finite time control for a class of linear time invariant multi-input continuous-time (CT) and discrete-time (DT) controllable systems. The main idea is to reduce the system order to zero, by using higher sliding control which drives states to origin in finite time. The control scheme is fully decentralized and differentiators are not needed for control realization. The CT reaching control uses the quasi-continuous control. For DT systems a new type of order reducing control named multi-step equivalent control is proposed. This control annihilates both the switching functions and states in a finite number of discrete time units, resulting in a dead-beat control.

This paper proposes a design method of the discrete-time integral sliding manifold that minimizes linear systems sensitivity to unmatched constant or slowly-varying external disturbances. The impact of unmatched disturbances is evaluated by a steady-state dependent quadratic criterion. An efficient design procedure is derived that easily finds the optimal sliding manifold that minimizes a criterion in discrete-time integral sliding mode control system. The suggested approach has been verified on numerical examples and computer simulations.

This paper considers a hybrid approach to control of linear dynamic and impulse controllable continuous-time disturbed linear descriptor systems. The first step in control is a design of continuous state feedback that makes system impulse-free. The obtained system is represented as a state space system of relative order zero. Based on this model, a full order discrete-time sliding mode control providing given pole placement is designed. The reaching control is completely decentralized and chattering-free. Simulations show a very good suppression of slow disturbances. All design steps and simulations require only standard MATLAB Toolbox.

This work presents a new approach to high performance velocity servo system design. The approach is based on a discrete-time sliding mode (DSM) control with disturbance compensation. For the purpose of design, the controlled plant is approximated by first-order model. The traditional, as well as the integral type of DSM control is considered. The disturbance compensator is based on the fact that the matched disturbances are directly reflected in the previous value of the switching function. In this paper, slow varying disturbances are estimated by a parallel connection of first- and second-order estimators. The integral type of DSM velocity servo system with such combined compensator can track references and significantly reject bounded disturbances, both up to cubic parabola type. The proposed control system is chattering-free. Theoretically obtained results are verified by simulations and experiments.

This paper presents a new approach to Direct Power Control (DPC) strategy using Space Vector Modulation (SVM) for the three-phase grid connected Voltage Source Converter (VSC) in the Renewable Energy Sources (RESs). The proposed DPC strategy is based on the Sliding Mode Control (SMC) and it is implemented in the dq reference frame. The active and reactive powers are directly controlled by VSC switching states selection based on the instantaneous value of the delivered power error. This strategy may be implemented to various VSC topologies. Moreover, linear controllers and modulators are not necessary. The aim of the control strategy is to inject maximal available active power and a controlled amount of reactive power into grid. The strategy is tested on a simulation model of a multilevel VSC (ML-VSC). Simulation results of the tested VSC topology and harmonic analysis of the output signals are presented at the end.

This paper considers design in state space of reduced and integral sliding mode having either desired spectrum or optimal behavior in LQR sense. Due to the operator representation of system equation a separate consideration of discrete time and continuous time is not needed. The obtained sliding subspace enables a fully decentralized design of reaching control. Four very simple algorithms are the paper's outcome. Examples of their implementation in MATLAB are given at the end.

This paper proposes a new approach for slow and matched disturbance suppression in digital sliding mode. The previous value of disturbance is extracted from switching function and used to make disturbance estimation, and later used in control to cancel disturbance effects. The control function is linear in state and in disturbance estimate. It may be considered chattering free since its value is zero in equilibrium if there are no disturbances.

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.

This paper presents a design of digitally controlled positional systems with Euler velocity estimation within the framework of the discrete-time sliding mode (DSM). The effects of quantization and simple velocity estimation on DSM quality are analyzed. It is shown that the introduced and amplified quantization noise degrades sliding motion into the quasi-sliding mode and threatens to provoke chattering. Furthermore, a new DSM control algorithm is proposed, featuring a two-scale reaching law and a supplemental integral action. This algorithm avoids chattering and provides excellent performance. The developed DSM controller has been experimentally tested in an induction motor position control.

A new way of induction-motor position control for high-performance applications is developed in this paper using discrete-time sliding-mode (DSM) control. In addition to the main DSM position controller, the proposed control structure includes an active disturbance estimator (ADE), in which a passive filter is replaced by another DSM-controlled subsystem, in order to improve system robustness and accuracy. Furthermore, the application of an ADE makes possible the design of both controllers using the knowledge of the nominal system only. Experiments have verified high efficiency of the proposed servo system under the influence of large parameter perturbations and external disturbances in the presence of unmodeled dynamics.

This paper investigates the effects of signal quantization and velocity estimation on the quality of the discrete-time sliding mode (DSM) in a positional servo-system. Velocity estimation is based on a simple backward finite difference method using the measured quantizied discrete-time position samples. It is shown that such introduced and amplified measurement noise degrades sliding motion into the quasi-sliding mode and threatens to provoke chattering. Furthermore, a DSM control algorithm is proposed, which provides satisfactory performance under these conditions. To avoid chattering, system trajectories are slowed down near the sliding surface by dividing the state space into the fast and slow convergence zones. In the slow zone an additional integral action is employed to secure convergence under action of disturbances. The proposed DSM controller has been experimentally tested in an induction motor position control.