Output tracking via sliding modes in causal systems with time delay modeled by higher order pade approximations

Output tracking in a SISO causal uncertain nonlinear system with an output subject to a time delay is considered using sliding mode control. A higher order Pade approximation to a delay function with a known time delay is used to construct a model of a transformed system without a time delayed output and is employed in a feedback sliding mode control. This model functions as a predictor of the plant states and the plant output, but is of nonminimum phase due to the application of the Pade approximation. The method of the stable system center is used to stabilize the internal dynamics of this plant model, and a control is developed using a sliding surface to allow the plant to track an arbitrary reference profile given by an exogenous system with a known characteristic equation. Simulations of the system are performed for the plant model using a first, second and third order Pade approximations and a controller in plant feedback mode. Numerical examples for Pade approximations of increasing order are considered and compare

Stabilisation of Time Delay Systems with Nonlinear Disturbances Using Sliding Mode Control

This paper focuses on a class of control systems with delayed states and nonlinear disturbances using sliding mode techniques. Both matched and mismatched uncertainties are considered which are assumed to be bounded by known nonlinear functions. The bounds are used in the control design and analysis to reduce conservatism. A sliding function is designed and a set of sufficient conditions is derived to guarantee the asymptotic stability of the corresponding sliding motion by using the Lyapunov-Razumikhin approach which allows large time varying delay with fast changing rate. A delay dependent sliding mode control is synthesised to drive the system to the sliding surface in finite time and maintain a sliding motion thereafter. Effectiveness of the proposed method is demonstrated via a case study on a continuous stirred tank reactor system

Second-order SM approach to SISO time-delay system output tracking

A fully linearizable single-input-single-output relative-degree n system with an output time delay is considered in this paper. Using the approach of Pade approximation, system center approach, and second-order sliding-mode (SM) control, we have obtained good output tracking results. The Smith predictor is used to compensate the difference between the actual delayed output and its approximation. A second-order supertwisting SM observer observes the disturbance in the plant. A nonlinear example is studied to show the effect of this methodology

Observer-based sliding mode control for stabilization of a dynamic system with delayed output feedback

This paper considers the sliding mode control problem for a kind of dynamic delay system. First by utilizing Lyapunov stability theory and a linear matrix inequality technique, an observer based on delayed output feedback is constructed. Then, an integral sliding surface is presented to realize the sliding mode control for the system with the more available stability condition. Finally, some numerical simulations are implemented to demonstrate the validity of the proposed control method.Bo Wang, Peng Shi, Hamid Reza Karimi, and Cheng Chew Li

Sliding Mode Control of Time-Delay Systems with Delayed Nonlinear Uncertainties

This paper considers a class of time delay systems with delayed states and non-linear uncertainties using sliding mode techniques. In order to improve robustness, matched and mismatched disturbances are considered and assumed to be nonlinear functions of system states and delayed states. A sliding function is designed and a set of su?cient conditions is derived to guarantee the stability of the corresponding sliding motion by using Lyapunov-Razumikhin approach which allows large time varying delay with fast changing rate. A delay dependent sliding mode control is synthesized to drive the system to the sliding surface in ?nite time and maintain a sliding motion thereafter. E?ectiveness of the proposed method is tested via a case study on a continuous stirred tank reactor system

Linear parameter-varying sliding mode control of state delayed systems with application to delta wing vortex coupled dynamics

In this thesis a new linear parameter-varying sliding mode control (LPVSMC) approach is developed for linear parameter-varying time-delayed systems (LPVTDS). This approach combines sliding mode control (SMC), linear parameter-varying (LPV) control theory, and time delay stability analysis to solve an LPVTDS control problem. A new linear parameter-varying sliding surface is proposed to achieve the control objectives. The time-varying parameters of the sliding surface are calculated according to a parameter-dependent Lyapunov-Krasovskii functional analysis which ensures asymptotic stability of the closed-loop system. It is anticipated that this method will lead to significant improvement over existing SMC approaches in aerospace applications with parameter variations

Higher accuracy output feedback sliding mode control of sampled-data systems

(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.This is the author version of a work accepted for publication in IEEE Transactions on Automatic Control. The definitive version is available via the publisher at 10.1109/TAC.2015.2505303The problem of output feedback sliding mode control for sampled-data systems in the presence of external disturbances is considered. The proposed output feedback control strategy helps obtain a quasi sliding mode with an O(T3) boundary layer, where T is the sampling period. This outperforms the O(T2) result induced by the one-step delayed disturbance approximation method. The proposed scheme is applicable to linear systems which are relative degree one and minimum phase. An example is given to illustrate the efficacy of the new method

Stabilizing Unstable Periodic Orbit of Unknown Fractional-Order Systems via Adaptive Delayed Feedback Control

This paper presents an adaptive nonlinear delayed feedback control scheme for stabilizing the UPO of unknown fractional-order chaotic systems. The proposed control scheme uses the Lyapunov approach and sliding mode control technique to ensure that the closed-loop control system is asymptotically stable on a periodic trajectory sufficiently close to the UPO of the fractional-order chaotic system. It is guaranteed that the closed-loop system will be robust to external disturbances with unknowable bounds. Finally, the proposed method is used to stabilize the UPO of the fractional-order Duffing and Gyro systems, and extensive simulation results are used to evaluate its performance