Keywords: First Order Sliding Mode, Higher Order Sliding Mode, Adaptive Sliding Mode
Abstract: An overview of control design for uncertain systems based on transforming and combining adaptive control and sliding-mode control techniques is presented. Output-feedback controllers with global stability and convergence properties are thereby developed for linear and nonlinear systems with general relative degree. Real-world applications illustrate the performance of the controllers designed using the described approach. A bridge between parameter-adaptive systems and sliding-mode control systems is formulated as a controller that combines the desirable features and avoids the drawbacks. Global exact tracking controllers utilizing higher-order sliding-mode compensators are discussed. A scheme for adaptive sliding-mode control with guaranteed transient and steady-state performance based on monitoring functions and gain switching is described. Chattering alleviation by means of a prediction error loop for classical and modern sliding-mode controllers is presented.

Keywords: First Order Sliding Mode, Higher Order Sliding Mode, Application of Sliding Mode Control to other theoretical problems
Abstract: In this paper, the concepts of equivalent control and real motions in non ideal sliding mode are considered and discussed through an example that uses together a first-order sliding mode strategy and a second-order Super-Twisting algorithm.

Keywords: First Order Sliding Mode, Higher Order Sliding Mode
Abstract: Very often in sliding mode (SM) control design, the control function is defined as the sum of the equivalent and discontinuous (or Lipschitz-discontinuous) control. This control arrangement is referred to in the present paper as the regeneration of the equivalent control. It is shown in the present paper that the regeneration of the equivalent control results in the plant input-output dynamics reduced to those of an integrator. This property holds for all linear plant dynamics as well as some nonlinear plant dynamics.

Keywords: Higher Order Sliding Mode, Homogeneity Methods for Variable Structure Systems & Sliding Mode Control, First Order Sliding Mode
Abstract: This work investigates the use of the Locus of Perturbed Relay System (LPRS) to analyze oscillations in homogenous sliding mode controllers in the condition of absence of parasitic dynamics. The homogenous sliding mode controllers produce either finite time convergence or non-vanishing oscillations under different combinations of system and controller parameters. The undertaken LPRS analysis reveals that multiple frequency solutions exist for the systems of different relative degrees. Solutions of the nonlinear equations of the LPRS are computed numerically to determine these frequency points. Simulations are done to see the behavior of these solution frequencies, which shows that some of these are stable frequency points while others are unstable.

Keywords: First Order Sliding Mode, Adaptive Sliding Mode, Lyapunov Methods for Variable Structure Systems & Sliding Mode Control
Abstract: This paper presents a new theoretical analyses and a condition regarding to an algorithm, based on Linear Matrix Inequalities (LMIs), for finding a constant output feedback matrix Ko and a constant output tandem matrix F such that the controlled system {A − BKoC, B, F C} is Strictly Positive Real (SPR). The number of output variables of the plant {A, B, C} is supposed to be greater than or equal to the number of its input variables. The main result offers a more general necessary condition to specify the matrix F that can offer a solution for this problem, that works when a known condition holds and also in some case where this known solution does not hold.

Keywords: Lyapunov Methods for Variable Structure Systems & Sliding Mode Control, Automotive Systems, Electric Drives And Actuators
Abstract: A state feedback design for linear uncertain systems is proposed. To attenuate the effect of disturbances on the output of the system two performance indexes are included in the control design. For L_2 disturbances the results ensures that the closed loop system has an H_infty guaranteed cost and for L_infty disturbances a L_1 performance index is achieved. The stabilization conditions are given in terms of LMIs. To improve the control performance and relax the LMI conditions a switched controller which avoids chattering is proposed. A numerical example illustrates the efficiency of the stabilizing conditions.

Keywords: Homogeneity Methods for Variable Structure Systems & Sliding Mode Control, Application of Sliding Mode Control to other theoretical problems, Electric Drives And Actuators
Abstract: In this article a general method, based on Geometric Algebra (GA), is presented for the synthesis of sliding mode (SM) controllers in SISO switched nonlinear systems. The method, addressed as the {em invariance control method}, rests on a natural reinterpretation of the necessary and sufficient conditions for the local existence of a sliding regime on a smooth manifold. The interpretation leads to a decomposition of the SM control scheme into a feedback invariance controller feeding a Delta-Sigma modulator that provides the required switched input to the plant. The results are used to explain a second order sliding regime algorithm, through a limiting process on first order sliding regimes. For switched flat systems, the method is found to be coincident with the Active Disturbance Rejection Control scheme in combination with a Delta-Sigma modulator. A non-trivial application example is presented using digital computer simulations.

Keywords: First Order Sliding Mode, Mobile Robots
Abstract: This paper demonstrates the implementability of a linear parameter varying control scheme which aims to prevent actuator saturation. The control scheme is based on a model reference sliding mode controller with control allocation. To prevent saturation the reference model is optimised on-line through a computationally-light bisection-like algorithm which aims to give the best performance possible within actuator constraints. The scheme's efficacy is demonstrated via implementation and flight tests of a parrot rolling spider mini-drone.

Keywords: First Order Sliding Mode, Mobile Robots
Abstract: This paper is concerned with the robust guidance and control of fully actuated mobile robots subject to velocity and control constraints in dynamic environments involving external disturbances. The overall method consists of an outer-loop guidance based on the acceleration-velocity-obstacles strategy and a stabilizing control loop based on a global sliding mode policy. The guidance strategy generates velocity commands aiming to reach a target position while avoiding collision with moving obstacles and respecting velocity and acceleration bounds. On the other hand, the global sliding mode ensures that the velocity commands are, in theory, exactly tracked all the time. The proposed method is numerically evaluated using two-dimensional robots and shows to be effective.

Keywords: Higher Order Sliding Mode, Mobile Robots
Abstract: This paper provides a perspective on the problem of trajectory tracking of a hexacopter in the presence of wind disturbances. Aiming to generate a smooth and robust control law, a Modified Smooth Sliding Control (MSSC) is introduced, which is derived from the earlier Smooth Sliding Control (SSC) designed for linear time-invariant uncertain plants and based on an appropriate predictor. This modification is obtained by allowing the smoothing filter and the predictor to be time varying. Generally speaking, robustness with respect to wind disturbances in closed-loop trajectory tracking can be observed. In addition, a clear connection between the MSSC and the Super-Twisting Algorithm (STA) is provided. Experimental results with the MSSC and STA control are obtained for trajectory tracking of a commercial hexacopter.

Keywords: Mobile Robots, Adaptive Sliding Mode, Higher Order Sliding Mode
Abstract: This paper present the control of an aerial manipulator composed of a quadrotor and a manipulator with two degrees of freedom (2 DOF). There is a strong physical coupling between the dynamics of the UAV and the manipulator arm. This coupling along with external perturbations (e.g. wind gusts), considerably affect the stability of the drone's motion in flight which, consequently, affects the desired accuracy of the end effector with respect to its final task. The work presented here is based on super-twisting sliding mode control with adaptive gain. It is a continuation of previous study on sliding mode control with adaptive gain. The effectiveness of the controller and its robustness against perturbations are verified and analyzed using numerical simulation.

Keywords: Mobile Robots, First Order Sliding Mode
Abstract: This paper is concerned with the design of a predefined-time sliding mode control law suitable for the attitude control of a quadrotor aerial vehicle. Using the Newton-Euler approach, the modeling of the rotation kinematics and dynamics of the quadrotor is formulated in terms of the control errors and put in the regular state-space form. Then, a multi-input predefined-time first-order sliding mode control law is designed so that, under reasonable conditions, the settling-time bound of the tracking error can be directly specified by a unique parameter independently of the initial conditions. The proposed control law is evaluated through numerical simulations where the results have confirmed that the tracking errors in fact converge to zero within the predefined time.

Keywords: Higher Order Sliding Mode, Lyapunov Methods for Variable Structure Systems & Sliding Mode Control, Application of Sliding Mode Control to other theoretical problems
Abstract: We propose an output feedback High-Order Sliding Mode (HOSM) controller for a class of uncertain SISO Linear Time Invariant systems. It is able to nullify the output of the system globally and in finite-time, despite of the uncertainty in the (constant) coefficients of the system and in presence of matched non-vanishing perturbations, that can grow linearly with the state of the system. This improves the possibilities of the classical High-Order Sliding Mode controllers, which are not able to deal globally with linear system's vector fields. The result is obtained by using control laws and injection terms of observers composed of classical linear terms and the homogeneous terms of the classical HOSM. The stability of the closed-loop dynamics is proved using non-homogenous explicit Lyapunov functions. The results are illustrated by some simulations.

Keywords: Higher Order Sliding Mode, Lyapunov Methods for Variable Structure Systems & Sliding Mode Control, Homogeneity Methods for Variable Structure Systems & Sliding Mode Control
Abstract: We propose a novel MIMO Super-Twisting control algorithm based on passivity properties. The differences with most known MIMO algorithms are: the control terms are not of unity-type, the control matrix may be uncertain and the gain matrices can be full, instead of the usual scalar gains. A smooth Lyapunov function is used instead of the usual non-smooth one. Two examples with uncertain control matrices are presented to illustrate the unique properties of the proposed controllers, together with a comparison with other known schemes.

Keywords: Sliding Mode based Observation, Discrete Time Sliding Mode, Higher Order Sliding Mode
Abstract: It is well-known that implicit-based and projector-based differentiator schemes offer better performances, like reducing high frequency oscillations, compared to the corresponding explicit schemes. To keep the advantages of such implicit Euler approximations, when this approximation is applied in case of homogeneous differentiators, a semi-implicit Euler approximation has been recently proposed for second-order systems. In this paper, a generalization to third order semi-implicit differentiation is proposed taking into account the attenuation of the noise considering advanced iterative projectors definition. Validation on experimental data is conducted to highlight the well-founded of the proposed differentiation strategy.

Keywords: Sliding Mode based Observation, Higher Order Sliding Mode, Automotive Systems
Abstract: This paper proposes a delayed sliding mode observer (DSMO) for the robust estimation of linear systems with bounded unknown inputs and measurement delays. In the DSMO, a static proportional minus delay output feedback loop is artificially incorporated, and an addictive switching delayed sliding mode injection is also introduced to achieve the convergence of estimation errors. The proposed DSMO permits both periodic and aperiodic measurements in output feedback loops, which improves the design flexibility with low-cost sensors. In simulation, an example of a magnetic levitation system is used to illustrate the merits of DSMOs.

Keywords: Lyapunov Methods for Variable Structure Systems & Sliding Mode Control, Higher Order Sliding Mode, Automotive Systems
Abstract: In this paper an artificial delay based impedance controller is proposed for robotic manipulators with uncertainty in dynamics. The control law unites the time delayed estimation (TDE) framework with a second order switching controller of super twisting algorithm (STA) type via a novel generalized filtered tracking error (GFTE). While time delayed estimation framework eliminates the need for accurate modelling of robot dynamics by estimating the uncertain robot dynamics and interaction forces from immediate past data of state and control effort, the second order switching control law in the outer loop provides robustness against the time delayed estimation (TDE) error that arises due to approximation of the manipulator dynamics. Thus, the proposed control law tries to establish a desired impedance model between the robot end effector variables i.e. force and motion in presence of uncertainties, both when it is encountering smooth contact forces and during free motion. Simulation results for a two link manipulator using the proposed controller along with convergence analysis are shown to validate the proposition.