Synchronization of Unified Chaotic System by Robust H∞/Sliding Mode Control

2010 ◽  
Author(s):  
Omolbanin Yazdanbakhsh ◽  
Saeid Hoseinia
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Optimization Technique ◽  
Linear Matrix ◽  
External Disturbances ◽  
Switching Surface ◽  
Lmi Optimization ◽  
Mode Control ◽  
Sliding Motion ◽  
Synchronization Problem

This paper investigates the chaos synchronization problem for a class of uncertain unified chaotic systems with external disturbances. Based on the proportional-integral (PI) switching surface, a sliding mode controller (SMC) is derived to not only guarantee the occurrence of a sliding motion of error states, but also reduce the effect of external disturbances to an H∞-norm performance. Also, a new reaching law is introduced to reduce the chattering problem that is produced by traditional sliding mode control. The parameters necessary for constructing both PI switching surface and the SMC can be found by the linear matrix inequality (LMI) optimization technique. Finally, a numerical simulation is presented to show the effectiveness of the proposed method.

New results on robust sliding mode control for linear time-delay systems

2020 ◽  
Author(s):  
Jothiappan Palraj ◽  
Kalidass Mathiyalagan ◽  
Peng Shi
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Linear Time ◽  
Lyapunov Stability Theory ◽  
Delay Systems ◽  
Linear Matrix ◽  
Switching Surface ◽  
Mode Control ◽  
Short Time ◽  
Robust Asymptotic Stability

Abstract This work focuses on the sliding mode control (SMC) for a family of linear systems with uncertainties and time-varying delays. First, an integral switching surface is constructed to verify the robust asymptotic stability of the considered system and the results are extended to analyse the mixed $\mathscr{H}_{\infty }\big /$Passivity performance index. Thereafter, a suitable SMC law is developed to force the system state onto the predefined switching surface in short time. By using Lyapunov stability theory, some novel results are obtained, and the required stability conditions are established in terms of linear matrix inequalities which can be solved by standard Matlab toolbox. Finally, the results are validated over a Chua’s circuit model, which describes the practical application of the developed results.

Stabilization of a Class of Fractional-Order Chaotic Systems via Direct Adaptive Fuzzy Optimal Sliding Mode Control

2018 ◽  
pp. 289-304
Author(s):  
Bachir Bourouba
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Optimization Technique ◽  
External Disturbances ◽  
Control Approach ◽  
Adaptive Fuzzy ◽  
Mode Control ◽  
Fuzzy Control Strategy

In this chapter a new direct adaptive fuzzy optimal sliding mode control approach is proposed for the stabilization of fractional chaotic systems with different initial conditions of the state under the presence of uncertainties and external disturbances. Using Lyapunov analysis, the direct adaptive fuzzy optimal sliding mode control approach illustrates asymptotic convergence of error to zero as well as good robustness against external disturbances and uncertainties. The authors present a method for optimum tuning of sliding mode control system parameter using particle swarm optimization (PSO) algorithm. PSO is a robust stochastic optimization technique based on the movement and intelligence of swarm, applying the concept of social interaction to problem solving. Simulation examples for the control of nonlinear fractional-order systems are given to illustrate the effectiveness of the proposed fractional adaptive fuzzy control strategy.

A Novel Global Sliding Mode Control Based on Exponential Reaching Law for a Class of Underactuated Systems With External Disturbances

2015 ◽  
Vol 11 (2) ◽  
Author(s):  
Saleh Mobayen
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Linear Matrix ◽  
Underactuated Systems ◽  
Robust Controller ◽  
External Disturbances ◽  
Mode Control ◽  
Global Sliding Mode Control ◽  
Suggested Technique ◽  
Exponential Reaching Law

This paper is concerned with the control of underactuated systems with external disturbances. Using the global sliding mode control (GSMC) technique, a new robust controller is presented to improve the robustness and stability of the system. The conditions of asymptotic stability are presented by linear matrix inequalities (LMIs). Our purpose is to build a control law so that it would enforce the states of the system to exponentially verge the sliding surface. The suggested controller has a simple structure because it is derived from the associated first-order differential equation and is able to handle the external disturbances and system nonlinearities. The efficiency of the proposed scheme is observed through simulations in an illustrative example. Simulation results demonstrate the considerable performance of the suggested technique.

scholarly journals Zero-Width Quasi-Sliding Mode Band in the Presence of Non-Matched Uncertainties

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3011
Author(s):  
Paweł Latosiński ◽  
Andrzej Bartoszewicz
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Control Strategies ◽  
Relative Degree ◽  
Band Width ◽  
Representative Point ◽  
Mode Control ◽  
Sliding Motion ◽  
Selection Of

Sliding mode control strategies are well known for ensuring robustness of the system with respect to disturbance and model uncertainties. For continuous-time plants, they achieve this property by confining the system state to a particular hyperplane in the state space. Contrary to this, discrete-time sliding mode control (DSMC) strategies only drive the system representative point to a certain vicinity of that hyperplane. In established literature on DSMC, the width of this vicinity has always been strictly greater than zero in the presence of uncertainties. Thus, ideal sliding motion was considered impossible for discrete-time systems. In this paper, a new approach to DSMC design is presented with the aim of driving the system representative point exactly onto the sliding hyperplane even in the presence of uncertainties. As a result, the quasi-sliding mode band width is effectively reduced to zero and ideal discrete-time sliding motion is ensured. This is achieved with the proper selection of the sliding hyperplane, using the unique properties of relative degree two sliding variables. It is further demonstrated that, even in cases where selection of a relative degree two sliding variable is impossible, one can use the proposed technique to significantly reduce the quasi-sliding mode band width.

scholarly journals New Time-Varying Sliding Surface for Switching Type Quasi-Sliding Mode Control

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3811
Author(s):  
Katarzyna Adamiak ◽  
Andrzej Bartoszewicz
Keyword(s):  
Sliding Mode Control ◽  
Continuous Time ◽  
Sliding Mode ◽  
Representative Point ◽  
Time Varying ◽  
Sliding Surface ◽  
External Disturbances ◽  
Mode Control ◽  
Switching Type ◽  
Time Systems

This study considers the problem of energetical efficiency in switching type sliding mode control of discrete-time systems. The aim of this work is to reduce the quasi-sliding mode band-width and, as follows, the necessary control input, through an application of a new type of time-varying sliding hyperplane in quasi-sliding mode control of sampled time systems. Although time-varying sliding hyperplanes are well known to provide insensitivity to matched external disturbances and uncertainties of the model in the whole range of motion for continuous-time systems, their application in the discrete-time case has never been studied in detail. Therefore, this paper proposes a sliding surface, which crosses the system’s representative point at the initial step and then shifts in the state space according to the pre-generated demand profile of the sliding variable. Next, a controller for a real perturbed plant is designed so that it drives the system’s representative point to its reference position on the sliding plane in each step. Therefore, the impact of external disturbances on the system’s trajectory is minimized, which leads to a reduction of the necessary control effort. Moreover, thanks to a new reaching law applied in the reference profile generator, the sliding surface shift in each step is strictly limited and a switching type of motion occurs. Finally, under the assumption of boundedness and smoothness of continuous-time disturbance, a compensation scheme is added. It is proved that this control strategy reduces the quasi-sliding mode band-width from O(T) to O(T3) order from the very beginning of the regulation process. Moreover, it is shown that the maximum state variable errors become of O(T3) order as well. These achievements directly reduce the energy consumption in the closed-loop system, which is nowadays one of the crucial factors in control engineering.

scholarly journals Reaching Law Based Sliding Mode Control of Sampled Time Systems

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1882
Author(s):  
Piotr Leśniewski ◽  
Andrzej Bartoszewicz
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Rate Of Change ◽  
Reaching Law ◽  
Mode Control ◽  
Sliding Motion ◽  
Control Precision ◽  
Continuous Time Systems ◽  
Time Systems

In this paper, discrete time reaching law-based sliding mode control of continuous time systems is considered. In sliding mode control methods, usually the assumption of bounded absolute values of disturbances is used. However in many cases, the rate of change of the disturbance is also bounded. In the presented approach, this knowledge is used to improve the control precision and reduce the undesirable chattering. Another advantage of the proposed method is that the disturbance does not have to satisfy the matching conditions. In the paper two new reaching laws are analyzed, one of them ensures the switching quasi-sliding motion and the other the non-switching motion. For both of them, the robustness is assessed by calculating the quasi-sliding mode band width, as well as the greatest possible state error values. Specifically, the state errors are not considered only at the sampling instants, as is usual for discrete time systems, but the bounds on the continuous values “between” the sampling instants are also derived. Then, the proposed approaches are compared and analyzed with respect to energy expenditure of the control signal.

Nonlinear observer based sliding mode control and oxygen fraction estimation for diesel engine

2017 ◽  
Vol 40 (7) ◽  
pp. 2227-2239 ◽  
Author(s):  
Haoping Wang ◽  
Qiankun Qu ◽  
Yang Tian
Keyword(s):  
Diesel Engine ◽  
Sliding Mode Control ◽  
Oxygen Concentration ◽  
Control Method ◽  
Sliding Mode ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Linear Matrix ◽  
Model Based ◽  
Mode Control

In this paper, a nonlinear observer based sliding mode control (NOSMC) approach for air-path and a model-based observer for oxygen concentration in the diesel engine equipped with a variable geometry turbocharger and exhaust gas recirculation is introduced. We propose a less conservative observer design technique for Lipschitz nonlinear systems using Ricatti equations. The observer gains are obtained by solving the linear matrix inequality (LMI). Then a robust nonlinear control method, sliding mode control is applied for the states of intake and exhaust manifold pressure and compressor mass flow rate for the sake of the minimization of emissions. The proposed NOSMC controller is applied on a mean value model of turbocharged diesel engine. Besides this, a model-based observer is developed to estimate the oxygen concentration in the intake and exhaust manifolds owing to its significance in reducing emissions of diesel engines. The validation and efficiency of the proposed method are demonstrated by AMESim and Matlab/Simulink co-simulation results.

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