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To avoid the chattering problem in the reaching-law-based discrete-time sliding mode control (DSMC) and the generation of over-large control action in the equivalent-control-based DSMC, a new DSMC method based on non-smooth control is proposed in this paper. Since there is no use of any switching term in the proposed DSMC, it is a chattering-free SMC method. Meanwhile, it is shown that the newly proposed non-smooth control-based DSMC can guarantee the same level of accuracy for the sliding mode motion as that of an equivalent control-based DSMC. To demonstrate the effectiveness of the proposed approach, a simulation example is presented. [ABSTRACT FROM AUTHOR]

Abstract: In conventional sliding-mode control systems, the sliding-mode motion is of reduced order. Two main problems hindering the application of the sliding-mode control are the singularity in terminal sliding-mode control systems and the chattering in both the conventional linear sliding-mode and the terminal sliding-mode control systems. This paper proposes a chattering-free full-order terminal-sliding-mode control scheme. Since the derivatives of terms with fractional powers do not appear in the control law, the control singularities are avoided. A continuous control strategy is developed to achieve the chattering free sliding-mode control. During the ideal sliding-mode motion, the systems behave as a desirable full-order dynamics rather than a desirable reduced-order dynamics. A systematic design method of full-order sliding-mode control for nonlinear systems is presented, which allows both the chattering and singularity problems to be resolved. Simulations validate the proposed chattering free full-order sliding-mode control. [Copyright &y& Elsevier]

Abstract: The main obstacles for application of Sliding Mode Control are two interconnected phenomena: chattering and high activity of control action. It is well known that the amplitude of chattering is proportional to the magnitude of discontinuous control. These two problems can be handled simultaneously if the magnitude is reduced to a minimal admissible level defined by the conditions for the sliding mode to exist. In this paper an adaptation methodology is developed for searching the minimum possible value of control based on evaluations of the, so-called, equivalent control by a low-pass filter. It is based on direct measurements of the, so-called, equivalent control by a first-order low-pass filter. The application of this methodology to the Super-Twist control enables reducing the control action magnitude to the minimum possible value keeping the property of a finite-time convergence. [Copyright &y& Elsevier]

Abstract: This paper analyzes features and problems related to the application of the simplex sliding mode control to systems with mono-directional actuators and integrators in the input channel. The plain use of the method formulated in previous contributions results in unacceptable behaviors, such as control laws (the output of the mono-directional actuators), which increase without bounds. A nontrivial modification of the original algorithm is proposed; the new simplex strategy allows the fulfillment of the control objectives by means of bounded inputs from the actuators. [Copyright &y& Elsevier]

Abstract: This paper considers the stabilization problem of a one-dimensional unstable heat conduction system (rod) modeled by a parabolic partial differential equation (PDE), powered with a Dirichlet type actuator from one of the boundaries. By applying the Volterra integral transformation, a stabilizing boundary control law is obtained to achieve exponential stability in the ideal situation when there are no system uncertainties. The associated Lyapunov function is used for designing an infinite-dimensional sliding manifold, on which the system exhibits the same type of stability and robustness against certain types of parameter variations and boundary disturbances. It is observed that the relative degree of the chosen sliding function with respect to the boundary control input is zero. A continuous control law satisfying the reaching condition is obtained by passing a discontinuous (signum) signal through an integrator. [ABSTRACT FROM AUTHOR]

Abstract: The simplex sliding mode control method is further developed by considering uncertain control systems non-affine in the control law. In order to reduce chattering effects, a set of integrators is added in the input channels. The augmented system is then controlled by a switching logic based on the simplex control method. As a result, the original control vector turns out to be continuous. A second order sliding mode observer is used when the sliding output is not available. Explicit conditions are identified about systems uncertainties and the simplex geometry in order to guarantee the convergence of the proposed methodology. [Copyright &y& Elsevier]

Abstract: A frequency-domain method of the input–output analysis of a class of relay feedback systems is proposed. The approach is based on the notion of the locus of a perturbed relay system (LPRS). The proposed LPRS is defined as a characteristic of the response of a linear part to an unequally spaced pulse control of variable frequency in a closed-loop system. Consequently, the LPRS comprises oscillatory and transfer properties of the relay system. Formulas for computing the LPRS are derived. An example of input–output analysis is given. [Copyright &y& Elsevier]

A chattering-free full-order terminal sliding mode control scheme has been recently proposed (Automatica 50 (2014) 1310–1314). In this correspondence, we point out a serious error in the paper. [ABSTRACT FROM AUTHOR]