This paper describes a new method, proposed for the control of objects with a stable finite zero, using sliding mode control strategies. The method is a combination of the conventional linear control and the sliding mode approach with an observer structure. The proposed structure looks like a reference model control system. The object control signal has two components: the first one is integral of the sliding mode controller output signal, and the second is a linear combination of observer error signal and its derivative. Such a control signal has not switching nature, i.e. the process control is chattering-free. The stability of the proposed control structure is analyzed and some recommendations for controller synthesis are given. The effectiveness of the proposed control strategy is demonstrated by simulation on an example.

Sampled-data (SD) variable structure control systems (VSCS) with quasi-sliding mode (QSM) are treated in this paper as a logical extension of VSCS with ideal sliding mode (SM). The most of well-known SD QSM control algorithms are derived by starting from reaching law approach. The problems of robustness to uncertainties, loads and unmodeled inertial dynamics are considered and some methods to solve these problems are presented. An example that illustrates SD QSM VSCS properties is given.

This paper considers the design of robust servo system for accurate tracking of complex referent signals in the presence of internal and external disturbances. Discrete-time sliding mode tracking controller is employed in servo-system design. In order to improve tracking accuracy, application of active disturbance estimator is suggested. The same sliding mode controller, designed for reference tracking of nominal system, is identically implemented in the control subsystem within the estimator. The overall servo-system exhibits high tracking accuracy under action of parameter uncertainties and external disturbances. Experimental results confirm the effectiveness of the proposed servo-system structure

The output tracking is considered for discrete-time causal SISO n th order linear time invariant system with unstable zero dynamics (nonminimum phase zeros) via discrete-time variable structure control. The stable system center method that originally was developed for controlling the output in continuous time nonminimum phase causal system using sliding mode (variable structure) control is extended to the discrete-time systems. The developed discrete-time stable system center technique transforms an output tracking problem to a corresponding state variable tracking problem by asymptotically identifying the ideal internal dynamics for the unstable internal states of a discrete-time system. The causal disturbances and output tracking profiles are assumed to obey a linear exogenous system with known characteristic polynomial. The theoretical results are confirmed by robust to matched disturbances discrete variable structure control design for the track parabolic-type signal problem in the third order nonminimum phase systems

The paper deals with the design of digital sliding mode controllers using only input and output sequences of plant. Two approaches are considered. The first one is based on the sliding mode based generalized minimum variance control implemented on the linearized plant model, whereas the second one utilizes the similar idea from the previous method modified for and applied on the discrete-time nonlinear model of the plant. The proposed algorithms are presented and tested by digital simulation on an example of inverted pendulum control

This chapter reviews some basic results obtained in the study of discrete-time (DT) variable structure control systems (DVSCS) theory during its twenty-five year history. For this purpose, the chapter is organised as follows: in Section 5.1 basic defini tions, assumptions and remarks are introduced that are necessary for the connection with continuous-time (CT) variable structure control systems (CVSCS) and form an introduction of terminologies for DVSCS. Section 5.2 is a brief overview of the more notable works in DVSCS. Section 5.3 gives the definition of a quasi-sliding mode (QSM) and a DT sliding mode (DSM). In Section 5.4, the Lyapunov stability concept is used to define invariant sets in DVSCS. Section 5.5 gives DSM existence conditions as a new motion phenomenon that is not possible in CVSCS. In Section 5.6, a basic concept of DVSCS, which is founded on the DT equivalent control method and a boundary layer concept for the system with nominal parameters, is presented, while Section 5.7 introduces some disturbance estimation methods. Section 5.8 describes two methods of DVSCS with sliding sectors. In Section 5.9 basic properties of DVSCS are given. Design methods to establish sliding surfaces are summarised in Section 5.10. Section 5.11 gives numerical examples that illustrate the properties of some DVSCS algorithms. Some issues in the practical realisation of DVSCS are given in Section 5.12 and Section 5.13 contains a list of published papers and other work that has been used for the preparation of this chapter.

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.

The paper considers the problem of ensuring synchronized movement of two pneumatic cylinders. The control system for synchronization was designed by applying the theory of control system with variable structure. The algorithm of control is based on digital sliding regime. Measuring coordinates of state (positions and speeds) directly on the cylinders is supposed to be possible. It is shown that such a system ensures quick synchronization of cylinders under different initial conditions. The applied algorithm was compared with conventional algorithms of control. The quality of work of the considered system was illustrated by computer simulation.

A systematic approach to the synthesis of a high-quality harmonic oscillator, based on a conservative harmonic oscillator created by means of three operational amplifiers, is presented in this paper. Amplitude stabilization is accomplished using sliding mode design technic. Proposed control algorithm eliminates or reduces chattering problem.

This paper proposes a synchronization method of two-phase harmonic oscillators, based on amplitude and phase control, employing variable structure control approach. Synchronization between referent and controlled oscillator is achieved using variable structure controller, which organizes sliding mode along the intersection of two sliding surfaces. Mathematical analysis and experimental results are presented.

On the basis of the theory of variable structure systems, a new method for the synthesis of high-quality triangular wave oscillators has been proposed. The proposed oscillator features a finite oscillation build-up time, and the negative influence of the high-frequency control signal on the quality of output signals, chattering, is eliminated.