scholarly journals Integral Sliding Modes with NonlinearH∞-Control for Time-Varying Minimum-Phase Underactuated Systems with Unmatched Disturbances

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Roger Miranda-Colorado ◽  
Carlos Chavez ◽  
Luis T. Aguilar
Keyword(s):  
Nonlinear System ◽  
Sliding Mode ◽  
Robot Manipulator ◽  
Disturbance Attenuation ◽  
Underactuated Systems ◽  
Time Varying ◽  
Minimum Phase ◽  
Sliding Modes ◽  
Tracking Tasks ◽  
Disturbance Attenuation Level

This paper presents a methodology for controlling nonlinear time-varying minimum-phase underactuated systems affected by matched and unmatched perturbations. The proposed control structure consists of an integral sliding mode control coupled together with a global nonlinearH∞-control for rejecting vanishing and nonvanishing matched perturbations and for attenuating the unmatched ones, respectively. It is theoretically proven that, using the proposed controller, the origin of the free-disturbance nonlinear system is asymptotically stabilized, while the matched disturbances are rejected whereas theL2-gain of the corresponding nonlinear system with unmatched perturbation is less than a given disturbance attenuation levelγwith respect to a given performance output. The capability of the designed controller is verified through a flexible joint robot manipulator typically affected by both classes of external perturbations. In order to assess the performance of the proposed controller, an existing sliding modes controller based on a nonlinear integral-type sliding surface is also implemented. Both controllers are then compared for trajectory tracking tasks. Numerical simulations show that the proposed approach exhibits better performance.

scholarly journals NonlinearL2-Gain Analysis of Hybrid Systems in the Presence of Sliding Modes and Impacts

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
T. Osuna ◽  
O. E. Montano ◽  
Y. Orlov
Keyword(s):  
Sliding Mode ◽  
Numerical Study ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Sliding Modes ◽  
Time Dynamics ◽  
Attenuation Level ◽  
Disturbance Factor ◽  
Disturbance Attenuation Level ◽  
The Impact

TheL2-gain analysis is extended towards hybrid mechanical systems, operating under unilateral constraints and admitting both sliding modes and collision phenomena. Sufficient conditions for such a system to be internally asymptotically stable and to possessL2-gain less than ana priorigiven disturbance attenuation level are derived in terms of two independent inequalities which are imposed on continuous-time dynamics and on discrete disturbance factor that occurs at the collision time instants. The former inequality may be viewed as the Hamilton-Jacobi inequality for discontinuous vector fields, and it is separately specified beyond and along sliding modes, which occur in the system between collisions. Thus interpreted, the former inequality should impose the desired integral input-to-state stability (iISS) property on the Filippov dynamics between collisions whereas the latter inequality is invoked to ensure that the impact dynamics (when the state trajectory hits the unilateral constraint) are input-to-state stable (ISS). These inequalities, being coupled together, form the constructive procedure, effectiveness of which is supported by the numerical study made for an impacting double integrator, driven by a sliding mode controller. Desired disturbance attenuation level is shown to satisfactorily be achieved under external disturbances during the collision-free phase and in the presence of uncertainties in the transition phase.

scholarly journals Robust Stability for Nonlinear Systems with Time-Varying Delay and Uncertainties via theH∞Quasi-Sliding Mode Control

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yi-You Hou ◽  
Zhang-Lin Wan
Keyword(s):  
Nonlinear System ◽  
Robust Stability ◽  
Sliding Mode ◽  
Optimization Technique ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Switching Function ◽  
Time Varying ◽  
Time Varying Delay ◽  
Varying Delay

This paper considers the problem of the robust stability for the nonlinear system with time-varying delay and parameters uncertainties. Based on theH∞theorem, Lyapunov-Krasovskii theory, and linear matrix inequality (LMI) optimization technique, theH∞quasi-sliding mode controller and switching function are developed such that the nonlinear system is asymptotically stable in the quasi-sliding mode and satisfies the disturbance attenuation (H∞-norm performance). The effectiveness and accuracy of the proposed methods are shown in numerical simulations.

Event-based switching control for production inventory systems with time-varying delays

2019 ◽  
Vol 42 (9) ◽  
pp. 1585-1593
Author(s):  
Chen-Yu Wu
Keyword(s):  
Raw Materials ◽  
Sufficient Conditions ◽  
Switching Control ◽  
Inventory Systems ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Time Varying ◽  
Production Inventory ◽  
Disturbance Attenuation Level ◽  
Event Based

This paper investigates event-based switching control for production inventory systems with time-varying delays. The different subsystems are established to describe the fact that the different production rates are adjusted to meet the different customer needs, and the conditions of average dwelling time are used to constrain the switchings. The event-triggered scheme, where the event generates when the relative error between the current review-data and the last transmission review-data exceeds a certain threshold, depicts the transmission of raw materials (or finished products) in practice. Then, the sufficient conditions of exponentially stable with a prescribed disturbance attenuation level [Formula: see text] and controller synthesis are formulated as linear matrix inequalitiess for the production inventory switching systems. A numerical example is presented to illustrate the effectiveness of the proposed method.

scholarly journals Multicriteria Adaptive Observers for Singular Systems with Unknown Time-Varying Parameters

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Wookyong Kwon ◽  
Jaepil Ban ◽  
Soohee Han ◽  
Chong Soo Lee ◽  
Sangchul Won
Keyword(s):  
Singular Systems ◽  
Disturbance Attenuation ◽  
Estimation Accuracy ◽  
Time Varying ◽  
Varying Parameters ◽  
Integral Action ◽  
Attenuation Level ◽  
Adaptive Observers ◽  
Time Varying Parameters ◽  
Disturbance Attenuation Level

This paper proposes multicriteria adaptive observers for a class of singular systems with unknown time-varying parameters. Two criteria for theH∞disturbance attenuation level and the upper bound of an ultimate invariant set are scalarized into a single cost function and then it is minimized by varying the weight parameter, which creates the optimal trade-off curve or Pareto optimal points. The proposed multicriteria adaptive observers are shown to be able to easily include integral action for better robust performance. It is demonstrated with numerical simulations that the proposed multicriteria adaptive observers provide the good estimation accuracy and allow effective and compromising design by considering two different cost functions simultaneously.

Design of Controllers for Quadratic Stability and Disturbance Attenuation of Uncertain Systems

1997 ◽  
Vol 119 (3) ◽  
pp. 594-598
Author(s):  
Faryar Jabbari ◽  
I˙. Emre Ko¨se
Keyword(s):  
Output Feedback ◽  
Uncertain Systems ◽  
Disturbance Attenuation ◽  
Time Varying ◽  
Quadratic Stability ◽  
Structured Uncertainty ◽  
Attenuation Level ◽  
Convex Problem ◽  
Disturbance Attenuation Level ◽  
Two Stages

In this paper, we discuss the design of controllers that provide quadratic stability and a desirable disturbance attenuation level (through an appropriately small L2 gain) for systems with time varying, real and structured uncertainty. It is shown that for a class of systems, the problem of designing dynamic output feedback can be separated into two stages, each an easily solvable convex problem. This information could be used in system design and configuration. Two examples are presented to illustrate the proposed approach.

scholarly journals H∞ Robust T-S Fuzzy Design for Uncertain Nonlinear Systems with State Delays Based on Sliding Mode Control

2010 ◽  
Vol 5 (4) ◽  
pp. 592 ◽  
Author(s):  
Xizheng Zhang ◽  
Yaonan Wang ◽  
Xiaofang Yuan
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Sliding Mode ◽  
External Disturbance ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Mode Control ◽  
Disturbance Attenuation Level ◽  
Takagi Sugeno

This paper presents the fuzzy design of sliding mode control (SMC) for nonlinear systems with state delay, which can be represented by a Takagi-Sugeno (TS) model with uncertainties. There exist the parameter uncertainties in both the state and input matrices, as well as the unmatched external disturbance. The key feature of this work is the integration of SMC method with H∞ technique such that the robust asymptotically stability with a prescribed disturbance attenuation level γ can be achieved. A sufficient condition for the existence of the desired SMC is obtained by solving a set of linear matrix inequalities (LMIs). The reachability of the specified switching surface is proven. Simulation results show the validity of the proposed method.

scholarly journals Fault-Tolerant Control with Control Allocation for Time-Varying Linear Systems by Using Continuous Integral Sliding Modes

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Oziel Hernández-Durán ◽  
Rosalba Galván-Guerra ◽  
Juan Eduardo Velázquez-Velázquez ◽  
Benjamín A. Itzá-Ortiz
Keyword(s):  
Fault Tolerant ◽  
Sliding Mode ◽  
Linear Quadratic Regulator ◽  
Fault Tolerant Control ◽  
Control Allocation ◽  
Time Varying ◽  
Sliding Modes ◽  
Linear Quadratic ◽  
Time Varying Systems ◽  
Inversion Techniques

A fault-tolerant control algorithm based on sliding modes is proposed to ensure the tracking of the desired trajectory for time-varying systems even in the presence of actuator faults. The proposed algorithm uses a continuous integral sliding mode and a linear quadratic regulator, together with control allocation and system inversion techniques, resulting in both a finite-time exact compensation of the faults and the exponential tracking of the reference.

The design of a fractional-order sliding mode controller with a time-varying sliding surface

2020 ◽  
Vol 42 (16) ◽  
pp. 3196-3215
Author(s):  
Osman Eray ◽  
Sezai Tokat
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Robot Manipulator ◽  
Sliding Mode Controller ◽  
Sigmoid Function ◽  
Time Varying ◽  
Sliding Surface ◽  
Parameter Uncertainties ◽  
Improved Performance ◽  
System States

The novelty of this paper is the usage of a time-varying sliding surface with a fractional-order sliding mode controller. The objective of the controller is to allow the system states to move to the sliding surface and remain on it so as to ensure the asymptotic stability of the closed-loop system. The Lyapunov stability method is adopted to verify the stability of the controller. Firstly, by using the geometric coordinate transformation that is formerly defined for conventional sliding mode controller, a novel fractional-order sliding surface is defined. The time-varying fractional-order sliding surface is then rotated in the region in which the system state trajectories are stable. The adjustment of the sliding surface slope on the new coordinate axes is achieved by tuning a parameter defined as a sigmoid function. Then, a new control rule is derived. Numerical simulations are performed on the nonlinear mass-spring-damper and 2-DOF robot manipulator system models with parameter uncertainties and bounded external disturbances. The proposed controller is compared with the conventional sliding mode controller with a constant sliding surface and the fractional-order sliding mode controller with a constant sliding surface. Simulation results have shown improved performance of the proposed controller in terms of a decrease in the reaching and settling time, and robustness to disturbances as compared with the related controllers. Moreover, it is seen that the designed controller provides an improvement in the error state trajectories.

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