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A class of second order sliding mode control systems is studied in terms of its transfer properties, which allows for investigating the system response to an external signal representing either a disturbance, which the system is supposed to reject, or the reference input, which the system is supposed to track. An approach based on the Locus of a Perturbed Relay System (LPRS) is developed making reference to linear plant/actuator/sensor dynamics and to the "generalized sub-optimal" second-order sliding mode control algorithm in the closed loop. A thoroughly discussed example shows the feasibility of the presented procedure and confirms the theoretical results. Index Terms--Frequency-domain techniques, second-order sliding-mode control.

This paper presents a novel scheme for the speed/ position control of permanent-magnet (PM) dc motor drives. A cascade-control scheme, based on multiple instances of a second-order sliding-mode-control (2-SMC) algorithm, is suggested, which provides accurate tracking performance under large uncertainty about the motor and load parameters. The overall control scheme is composed of three main blocks: 1) a 2-SMC-based velocity observer which uses only position measurements; 2) a 2-SMC-based velocity control loop that provides a reference command current; and 3) a 2-SMC-based current control loop generating the reference voltage. The proposed scheme has been implemented and tested experimentally on a commercial PM dc motor drive. The experimental results confirm the precise and robust performance and the ease of tuning and implementation, featured by the proposed scheme. Index Terms--Cascade control, dc motor drives, second-order sliding-mode (2-SM) control (2-SMC), SM differentiators.

A systematic approach to the chattering analysis in systems with second-order sliding modes is developed. The neglected actuator dynamics is considered to be the main cause of chattering in real systems. The magnitude of oscillations in nonlinear systems with unmodeled fast nonlinear actuators driven by second-order sliding-mode control generalized suboptimal (2-SMC G-SO) algorithms is evaluated. Sufficient conditions for the existence of orbitally stable periodic motions are found in terms of the properties of corresponding Poincare maps. For linear systems driven by 2-SMC G-SO algorithms, analysis tools based on the frequency-domain methods are developed. The first of these techniques is based on the describing function method and provides for a simple approximate approach to evaluate the frequency and the amplitude of possible periodic motions. The second technique represents a modified Tsypkin's method and provides for a relatively simple, theoretically exact, approach to evaluate the periodic motion parameters. Examples of analysis and simulation results are given throughout this paper. Index Terms--Frequency-domain methods, limit cycles, Poincare map analysis, sliding-mode control.

This technical note discusses a finite-time stabilization problem in a nonlinear, uncertain, environment. The main result of the present note is presented making reference to a triple integrator affected by bounded uncertainties and subject to "hard" measurement nonlinearities such that the sign of the state variables is the only reliable information available for feedback. We propose a discontinuous control scheme guaranteeing the practical finite-time annihilation of the three state variables. Constructive proof and computer simulations, as well as guidelines for practical implementations, are provided throughout this technical note. Index Terms--Finite-time control, higher-order sliding modes, nonlinear uncertain systems.

The robustness of the second-order sliding-mode control (2-SMC) algorithm known as the "Generalized Sub-optimal" algorithm is analyzed with respect to the cascade introduction of a linear fast actuator. It is shown that if the actuator dynamics are sufficiently fast then the system trajectories converge to an invariant set that includes the second-order sliding domain s = [??] = 0. It is also shown that the size of the invariant set has quadratic dependence with respect to the actuator "small parameter" [mu] for the sliding variable s, and linear dependence for its derivative [??]. This means that in the steady state the system trajectories converge to an invariant domain described by the following conditions: [absolute value of s] [less than or equal to] O ([[mu].sup.2]) and [absolute value of s] [less than or equal to] O ([mu]). A simulation example is given to confirm the proposed analysis. Index Terms--Fast actuators, nonlinear systems, sliding-mode control (SMC), uncertain systems, variable structure systems.

In this note, the second-order sliding-mode control problem is tackled by explicitly taking into account the presence of measurement error with unknown upper bound [delta]. Under sensible assumptions regarding the uncertain dynamics of a broad class of nonlinear plants, a new switching controller is proposed guaranteeing a sliding accuracy of order [OMICRON] ([delta]). Simulations highlight the robustness and good performance of the proposed approach, and confirm the expected precision order. Index Terms--Measurement noise, nonlinear systems, second-order sliding modes, uncertain systems.