Sliding mode control in the presence of input delay: A singular perturbation approach (original) (raw)
Related papers
On the Design of Sliding-Mode Static-Output-Feedback Controllers for Systems With State Delay
IEEE Transactions on Industrial Electronics, 2000
This paper considers the development of sliding-5 mode-based output-feedback controllers for uncertain systems 6 which are subject to time-varying state delays. A novel method 7 is proposed for design of the switching surface. This method 8 is based on the descriptor approach and leads to a solution in 9 terms of linear matrix inequalities (LMIs). When compared to 10 existing methods (even for systems without delays), the proposed 11 method is efficient and less conservative than other results, giving 12 a feasible solution when the Kimura-Davison conditions are not 13 satisfied. No additional constraints are imposed on the dimensions 14 or structure of the reduced order triple associated with design of 15 the switching surface. The magnitude of the linear gain used to 16 construct the controller is also verified as an appropriate solution 17 to the reachability problem using LMIs. A stability analysis for 18 the full-order time-delay system with discontinuous right-hand 19 side is formulated. This paper facilitates the constructive design 20 of sliding-mode static-output-feedback controllers for a rather 21 general class of time-delay systems. A numerical example from the 22 literature illustrates the efficiency of the proposed method. 23 Index Terms-Linear matrix inequalities (LMIs), sliding-mode 24 control (SMC), static output feedback (SOF), time delay. 25 I. INTRODUCTION 26 S LIDING-MODE control (SMC) [1] is known for its com-27 plete robustness to so-called matched uncertainties (which 28 can include time delays that satisfy matching conditions) and 29 disturbances [2]-[4]. The control technique has been applied in 30 many industrial areas [5]-[7]. Many early theoretical develop-31 ments in SMC assume that all the system states are accessible. 32 In the case where only a subset of states are measurable, which 33 is relevant to a range of practical applications, either output 34 feedback control or the observer-based method are required. 35 Some work has considered implementation of SMC schemes 36 using observers [8]-[10]. In [11], a sliding-mode observer has 37 been shown to give a significant increase in performance in esti-38 mation of the unknown variables of a boost converter compared
State estimation and sliding mode control for non-linear singular systems with time-varying delay
IFAC-PapersOnLine, 2020
This paper deals with the sliding mode control (SMC) problem for a class of nonlinear discrete-time singular systems with external disturbances and time-varying delay. The main contribution of this paper is to design an observer-based sliding mode control scheme for the system under consideration. First, a delay dependent criterion is built to guarantee the closed-loop system to be robustly admissible. Then, a (SMC) law is synthesized to guarantee the state trajectories of the closed-loop systems to be stable, to and ensure the reachability of the specified sliding surface in a short time interval. An illustrative example is given to numerically demonstrate the effectiveness of the proposed control scheme.
Static Output Feedback Sliding Mode Control Design via an Artificial Stabilizing Delay
IEEE Transactions on Automatic Control, 2009
It is well known that for linear, uncertain systems, a static output feedback sliding mode controller can only be determined if a particular triple associated with the reduced order dynamics in the sliding mode is stabilisable. This paper shows that the static output feedback sliding mode control design problem can be solved for a broader class of systems if a known delay term is deliberately introduced into the switching function. Effectively the reduced order sliding mode dynamics are stabilized by the introduction of this artificial delay.
Computacion Y Sistemas, 2005
This paper presents the optimal regulator for a linear system with time delay in control input and a quadratic criterion. The optimal regulator equations are obtained using the duality principle, which is applied to the optimal filter for linear systems with time delay in observations. Performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulator available for linear systems without delays. Simulation graphs and comparison tables demonstrating better performance of the obtained optimal regulator are included. The paper then presents a robustification algorithm for the obtained optimal regulator based on integral sliding mode compensation of disturbances. The general principles of the integral sliding mode compensator design are modified to yield the basic control algorithm oriented to time-delay systems, which is then applied to robustify the optimal regulator. As a result, the sliding mode compensating control leading to suppression of the disturbances from the initial time moment is designed. The obtained robust control algorithm is verified by simulations in the illustrative example.
International Journal of Electrical and Computer Engineering (IJECE), 2022
Novel results on complex interconnected time-delay systems with single phase second order sliding mode control is investigated. First, a reaching phase in traditional sliding mode control (TSMC) is removed by using a novel single phase switching manifold function. Next, a novel reduced order sliding mode observer (ROSMO) with lower dimension is suggested to estimate the unmeasurable variables of the plant. Then, a new single phase second order sliding mode controller (SPSOSMC) is established based on ROSMO tool to drive the state variables into the specified switching manifold from beginning of the motion and reduce the chattering in control input. Then, a stability condition is suggested based on the well-known linear matrix inequality (LMI) method to ensure the asymptotical stability of the whole plant. Finally, an illustrated example is simulated to validate the feasible application of the suggested technique.
Stability Analysis of a Class of Second Order Sliding Mode Control Including Delay in Input
Mathematical Problems in Engineering, 2013
This paper deals with a class of second order sliding mode systems. Based on the derivative of the sliding surface, sufficient conditions are given for stability. However, the discontinuous control signal depend neither on the derivative of sliding surface nor on its estimate. Time delay in control input is also an important issue in sliding mode control for engineering applications. Therefore, also sufficient conditions are given for the time delay size on the discontinuous input signal, so that this class of second order sliding mode systems might have amplitude bounded oscillations. Moreover, amplitude of such oscillations may be estimated. Some numerical examples are given to validate the results. At the end, some conclusions are given on the possibilities of the results as well as their limitations.
Asian Journal of Control, 2008
This paper presents the optimal regulator for a linear system with multiple time delays in control input and a quadratic criterion. The optimal regulator equations are obtained using the duality principle, which is applied to the optimal filter for linear systems with multiple time delays in observations. Performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulator available for linear systems without delays. Simulation graphs and comparison tables demonstrating better performance of the obtained optimal regulator are included. The paper then presents a robustification algorithm for the obtained optimal regulator based on integral sliding mode compensation of disturbances. The general principles of the integral sliding mode compensator design are modified to yield the basic control algorithm oriented to time-delay systems, which is then applied to robustify the optimal regulator. As a result, the sliding mode compensating control leading to suppression of the disturbances from the initial time moment is designed. The obtained robust control algorithm is verified by simulations in the illustrative example.
International Journal of Robust and Nonlinear Control, 2010
In this paper, a robust stabilization problem for a class of linear time-varying delay systems with disturbances is studied using sliding mode techniques. Both matched and mismatched disturbances, involving time-varying delay, are considered. The disturbances are nonlinear and have nonlinear bounds. A sliding surface is designed and the stability of the corresponding sliding motion is analysed based on the Razumikhin Theorem. Then a static output feedback sliding mode control with time-delay is synthesized to drive the system to the sliding surface in finite time. Simulation results show the effectiveness of the proposed approach.
Optimal and Robust Sliding Mode Regulator for Linear Systems with Delayed Control
Computación Y Sistemas, 2005
This paper presents the optimal regulator for a linear system with time delay in control input and a quadratic criterion. The optimal regulator equations are obtained using the duality principle, which is applied to the optimal filter for linear systems with time delay in observations. Performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulator available for linear systems without delays. Simulation graphs and comparison tables demonstrating better performance of the obtained optimal regulator are included. The paper then presents a robustification algorithm for the obtained optimal regulator based on integral sliding mode compensation of disturbances. The general principles of the integral sliding mode compensator design are modified to yield the basic control algorithm oriented to time-delay systems, which is then applied to robustify the optimal regulator. As a result, the sliding mode compensating control leading to suppression of the disturbances from the initial time moment is designed. The obtained robust control algorithm is verified by simulations in the illustrative example.
2 3 Robust sliding mode control for a class of nonlinear systems using inertial delay control
Nonlinear Dynamics
Your article is protected by copyright and all rights are held exclusively by Springer Science +Business Media Dordrecht. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".