Adaptive sliding-mode load-torque observer

The extension of some of the results contained in Part I [1] to the case when only the plant outputs rather than all its state variables are accessible for measurement is discussed. A unified approach to the synthesis of an adaptive observer is presented whereby the plant state and parameters are simultaneously estimated. Uniform asymptotic stability of the scheme is proved using Lyapunov's direct method. The information provided by the adaptive observer is used to synthesize an adaptive controller for the plant. While all the principal results obtained here are for the case of a single-input single-output plant, extensions to special classes of multivariable systems is indicated.

In this paper, a class of nonlinear interconnected systems with uncertain time varying parameters (TVPs) is considered. Both the interconnections and the isolated subsystems are nonlinear. Sliding mode control method and adaptive techniques are employed together to design an observer to estimate the state variables of the systems in presence of unknown TVPs. The Lyapunov direct method is used to analysis the stability of the sliding motion and it is not required to solve the so‐called constrained Lyapunov problem (CLP). A set of conditions is developed under which the augmented systems formed by the error dynamical systems and the designed adaptive laws, are globally uniformly ultimately bounded. A simulation example is presented and the results show that the method proposed in this paper is effective.

In this study, a new adaptive sliding-mode observer is proposed to estimate the rotor position and speed for sensorless control of permanent-magnet synchronous motor (PMSM) in an electric vehicle drive system. This observer can effectively reduce the estimation errors caused by the inherent chattering phenomenon for a conventional sliding-mode observer and the stator resistance uncertainty due to the variation of motor temperature. This new sliding-mode observer is designed by using a hyperbolic tangent function instead of sign function together with a variable boundary layer, and the new adaptive law is constructed according to the back electromotive force model to reinforce dynamic performance and the robustness of system. Meanwhile, a stator resistance identification algorithm is raised and guaranteed to be stable by using a Lyapunov method. The performance of the developed observer is compared with the conventional sliding-mode controller. Both simulation and experimental results confirm that the chattering phenomenon is effectively eliminated and the estimation accuracy for position and velocity is apparently improved when applying the developed observer in the electric vehicle drive system

A design procedure for simultaneous position and force control is developed, using Lyapunov's direct method, for manipulators in contact with a rigid environment that can be described by holonomic constraints. Many manipulators that interact with their environment require taking into account the effects of these constraints in the control design. The forces of constraint play a critical role in constrained motion and are, along with displacements and velocities, to be regulated at specified values. Lyapunov's direct method is used to develop a class of position and force feedback controllers. The conditions for gain selection demonstrate the importance of the constraints. Force feedback has been shown not to be mandatory for closed-loop stabilization, but it is useful in improving certain closed-loop robustness properties.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A new approach is presented to improve power swings damping of nonlinear power system model based on direct Lyapunov method. The approach combines superconducting magnetic energy storage (SMES) system with static series synchronous compensator (SSSC). Considering the energy absorption/injection ability of SMES, in transient states the combination exchanges both active and reactive powers with power system. Since direct Lyapunov method implies time derivative of both active and reactive powers, prepares an effective control strategy for the integrated SSSC-SMES system to decrease power swings damping time. Using direct Lyapunov method for structure preserving model (SPM) of power system, dq components of SSSC injecting voltage are calculated. Decentralizing method is used to locally control the SSSC-SMES independent of state variables of synchronous generators which require wide area measurements. PSCAD/EMTDC simulations verify the effectiveness of proposed method.

This paper presents a sliding mode-based adaptive fault detection and emergency control algorithm for implementation in fail-safe systems of autonomous vehicles. The overall algorithm is comprised of a fault detection part and a fail-safe control part. For the former, sliding mode observer-based fault detection algorithms were developed for environment and chassis sensors, including LiDAR, Radar, and acceleration sensors. Unidentified fault signals from the sensors are reconstructed through the adaptive sliding mode observer. The reconstruction is based on the MIT rule through the use of an estimated sensitivity parameter. For the latter, a sliding mode control (SMC)-based emergency control method designed to respond to fault occurrences has been proposed to ensure the functional safety of autonomous vehicles. An adaptive gain parameter was designed, taking convergence time into consideration, to secure consistent and rapid responses from the controller. When the detection algorithm detects a fault, the appropriate control input is computed by a lower controller for the vehicle. This control input is calculated based on the last scene information obtained from an upper controller. The performance of the proposed fault detection and control algorithms has been evaluated through simulations and actual vehicle tests of various scenarios.

This paper proposes a new method of detection and reconstruction of the incipient fault of fixed-wing actuators based on an adaptive sliding-mode observer. First, a mathematical model of a fixed-wing aircraft is derived under certain assumptions, considering nonlinear terms and system disturbances. Second, by introducing a nonsingular coordinate transformation, the incipient faults are separated from the disturbances. For a subsystem with no disturbances, the Luenberger observer can estimate the incipient fault. For a subsystem with disturbances, the sliding-mode observer is robust against these disturbances. The Lyapunov stability theory guarantees dynamic error convergence and system stability. The evaluation function was designed to realize residual evaluation and threshold judgment. Third, based on the concept of equivalent output injection, an adaptive sliding-mode observer method is proposed to reconstruct actuator faults precisely under the condition of the uncertain system structure. The design steps of the proposed reconstruction method are introduced in the form of a linear matrix inequality problem, which provides an effective method for calculating the design parameters. Finally, the simulation results of the De Havilland DHC-2 “Beaver” aircraft demonstrate the correctness and effectiveness of the proposed method.

The positive output elementary super lift Luo (POESLL) converter is a dc–dc converter with a simple structure, which can increase input voltage with low ripples and high voltage gain. This study proposes an adaptive estimator-based sliding mode control scheme for the POSELL converter considering a reduced-order model of the converter with an unknown load and unknown input voltage. The proposed controller is composed of two parts: 1) an adaptive estimator, and 2) the sliding mode controller. At first, it is assumed that the state variables of the converter are available and adaptive estimator is proposed to facilitate the design of adaptive laws for estimating unknown parameters. Then, the sliding mode control input is designed based on the estimation of unknown parameters. Stability analysis of the proposed scheme is provided and σ-modification type robust adaptive laws for estimating the uncertain parameters are derived based on the Lyapunov direct method. Furthermore, one modification term is proposed to satisfy the sliding condition. Finally, the proposed scheme is experimentally implemented in real time using STM32F407VG discrete signal processor board interfaced with MATLAB. In addition, in order to compare and highlight the effective performance of the proposed scheme, the proportional-integral (PI) controller is designed and implemented. Experimental results are presented for both of the proposed approach and the PI one. The results verify the ability of the proposed scheme for voltage regulation as well as its robustness against parameter uncertainties. Additionally, comparison results demonstrate that the proposed controller has superior performance than the PI controller.

A novel sliding-mode control of induction motor using space vector modulation technique

For the four degrees of freedom (4‐DOF) trajectory tracking control problem of underwater vehicles in the presence of parametric uncertainties and external disturbances, a novel multivariable output feedback adaptive nonsingular terminal sliding mode control (ANTSMC) approach is proposed based on the equivalent output injection adaptive sliding mode observer (ASMO) and ANTSMC method. The ASMO is applied to reconstruct the full states in finite time and the ANTSMC method is designed to stabilize the trajectory tracking error to a small field in finite time. The proposed output feedback ANTSMC approach, using the adaptive technology, does not require the bound information of parametric uncertainties or external disturbances which successfully achieves the decrease of undesired chattering effectively. Corresponding stability analysis is presented. Comparative numerical simulation results are presented to validate the effectiveness of the proposed approach.

This paper deals with the problem of estimation of the topological entropy for non-autonomous systems of differential equations via the second (direct) Lyapunov method. The main result of the paper is illustrated by examples concerning the Lorenz system and Duffing oscillator.

Uniform asymptotic stability of impulsive differential-difference equations of neutral type by Lyapunov's direct method

In this paper, sufficient criteria for the existence of solutions to uniform asymptotic stability and boundedness problems associated with certain second order nonlinear non autonomous ordinary differential equation are established with the aid of Lyapunov's direct method. Furthermore, the appropriate complete Lyapunov function is given explicitly. Our results complement some well known results on the second order differential equations in the literature.

In this paper, the problem of controlling the relative pose between a robot camera and a rigid object of interest is solved using nonlinear system theory. The camera-object visual interaction model is derived in the state space form in terms of image points. Then it is shown that the image-based visual system is completely controllable. Moreover, as a consequence of nonlinear controllability, global uniform asymptotic stability of the image reference set-point is formally proved using Lyapunov's direct method. Active contours are used to track the 2-D projection of the visible object's surface in the image plane, and 3-D estimation procedure based on prediction errors is used to cope with the unknown depth of the object. Experimental results with a 6-DOF robot manipulator endowed with a camera on its wrist validate the framework.

Lyapunov's direct method has been applied extensively to the stability analysis of nonlinear systems. The method enables one to directly judge stability without solving the nonlinear differential equations representing motor involved. In the paper, the effect of important parameters on trasient stability of a three-phase reluctance motors have been assessed from the data obtained for load and applied voltage changes by applying the Lyapunov's direct method.