Decentralised sliding mode control for nonlinear interconnected systems with uncertainties

With the advances in science and technology, nonlinear large-scale interconnected systems have widely appeared in the real life. Traditional centralised control methods have inevitable disadvantages when they are used to deal with complex nonlinear interconnected systems with uncertainties. In connection with this, people desire to develop the novel control strategy which can be applied to complex interconnected systems. Therefore, decentralised sliding mode control (SMC) for interconnected systems has attracted great attention in related fields due to its advantages, for instance, simple structure, low cost of calculation, fast response, reduced-order sliding mode dynamics and insensitivity to matched variation of parameters and disturbances in systems. This thesis focuses on the development of decentralised SMC for nonlinear interconnected systems with uncertainties under certain assumptions. Several methods and different techniques have been considered in design of the controller to improve the robustness. The main contributions of this thesis include: • The state feedback decentralised SMC is developed for nonlinear interconnected systems with matched uncertainty and mismatched unknown interconnections. A state feedback decentralised SMC strategy, under the assumption that all system states are accessible, is proposed to attenuate the impact of the uncertainties by using bounds on uncertainties and interconnections. The bounds used in the design are fully nonlinear which provide higher applicability for different complex interconnected systems. Especially, for this fully nonlinear system, the proposed method does not need to use the technique of linearisation, which is widely used in existing work to deal with nonlinear interconnected systems with uncertainties. • The dynamic observer is applied to complex nonlinear interconnected systems with matched and mismatched uncertainties. This dynamic observer can estimate the system states which can not be achieved during the controller design. The proposed method has great identification ability with small estimated errors for the states of nonlinear interconnected systems with matched and mismatched uncertainties. It should be pointed out that the considered uncertainties of nonlinear interconnected systems have general forms, which means that the proposed method can be effectively used in more generalised nonlinear interconnected systems. • A variable structure observer-based decentralised SMC is proposed to control a class of nonlinear interconnected systems with matched and mismatched uncertainties. Based on the designed dynamic observer, a dynamic decentralised output feedback SMC using outputs and estimated states is presented to control the interconnected systems with matched and mismatched uncertainties. The nonlinear interconnections are employed in the control design to reduce the conservatism of the developed results. The bounds of the uncertainties are relaxed which are nonlinear and take more general forms. Moreover, the limitation for the interconnected system is reduced when compared with the existing results in which the proposed strategies adopt the full-order observer. Besides that, the presented method improves the robustness of nonlinear interconnected systems to be against the effects of uncertainties. This thesis also provides several numerical and practical simulations to demonstrate the effectiveness of the proposed decentralised SMC for nonlinear interconnected systems with matched uncertainty, mismatched uncertainty and nonlinear interconnections

Decentralised sliding mode control for a class of nonlinear interconnected systems

In this paper, a decentralised control strategy based on sliding mode techniques is proposed for a class of nonlinear interconnected systems. Both matched uncertainties in the isolated subsystems and mismatched uncertainties associated with the interconnections are considered. Under mild conditions, sliding mode controllers for each subsystem are designed in a decentralised manner by only employing local information. Conditions are determined which enable information on the interconnections to be employed in decentralised controller design to reduce conservatism. The developed results are applied to an automated highway system. Simulation results pertaining to a high-speed following system are presented to demonstrate the effectiveness of the approach

Sliding mode and shaped input vibration control of flexible systems

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the vibration reduction problem is investigated for a flexible spacecraft during attitude maneuvering. A new control strategy is proposed, which integrates both the command input shaping and the sliding mode output feedback control (SMOFC) techniques. Specifically, the input shaper is designed for the reference model and implemented outside of the feedback loop in order to achieve the exact elimination of the residual vibration by modifying the existing command. The feedback controller, on the other hand, is designed based on the SMOFC such that the closed-loop system behaves like the reference model with input shaper, where the residual vibrations are eliminated in the presence of parametric uncertainties and external disturbances. An attractive feature of this SMOFC algorithm is that the parametric uncertainties or external disturbances of the system do not need to satisfy the so-called matching conditions or invariance conditions provided that certain bounds are known. In addition, a smoothed hyperbolic tangent function is introduced to eliminate the chattering phenomenon. Compared with the conventional methods, the proposed scheme guarantees not only the stability of the closed-loop system, but also the good performance as well as the robustness. Simulation results for the spacecraft model show that the precise attitudes control and vibration suppression are successfully achieved

Finite-time control for uncertain systems and application to flight control

In this paper, the finite-time control design problem for a class of nonlinear systems with matched and mismatched uncertainty is addressed. The finite-time control scheme is designed by integrating multi power reaching (MPR) law and finite-time disturbance observer (FTDO) into integral sliding mode control, where a novel sliding surface is designed, and the FTDO is applied to estimate the uncertainty. Then the fixed-time reachability of the MPR law is analyzed, and the finite-time stability of the closed-loop system is proven in the framework of Lyapunov stability theory. Finally, numerical simulation and the application to the flight control of hypersonic vehicle (HSV) are provided to show the effectiveness of the designed controller

Adaptive Backstepping Controller Design for Stochastic Jump Systems

In this technical note, we improve the results in a paper by Shi et al., in which problems of stochastic stability and sliding mode control for a class of linear continuous-time systems with stochastic jumps were considered. However, the system considered is switching stochastically between different subsystems, the dynamics of the jump system can not stay on each sliding surface of subsystems forever, therefore, it is difficult to determine whether the closed-loop system is stochastically stable. In this technical note, the backstepping techniques are adopted to overcome the problem in a paper by Shi et al.. The resulting closed-loop system is bounded in probability. It has been shown that the adaptive control problem for the Markovian jump systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions. A numerical example is given to show the potential of the proposed techniques

Disturbance Observer-based Robust Control and Its Applications: 35th Anniversary Overview

Disturbance Observer has been one of the most widely used robust control tools since it was proposed in 1983. This paper introduces the origins of Disturbance Observer and presents a survey of the major results on Disturbance Observer-based robust control in the last thirty-five years. Furthermore, it explains the analysis and synthesis techniques of Disturbance Observer-based robust control for linear and nonlinear systems by using a unified framework. In the last section, this paper presents concluding remarks on Disturbance Observer-based robust control and its engineering applications.Comment: 12 pages, 4 figure

Hierarchical robust fuzzy sliding mode control for a class of simo under-actuated systems with mismatched uncertainties

The development of the algorithms for single input multi output (SIMO) under-actuated systems with mismatched uncertainties is important. Hierarchical sliding-mode controller (HSMC) has been successfully employed to control SIMO under-actuated systems with mismatched uncertainties in a hierarchical manner with the use of sliding mode control. However, in such a control scheme, the chattering phenomenon is its main disadvantage. To overcome the above disadvantage, in this paper, a new compound control scheme is proposed for SIMO under-actuated based on HSMC and fuzzy logic control (FLC). By using the HSMC approach, a sliding control law is derived so as to guarantee the stability and robustness under various environments. The FLC as the second controller completely removes the chattering signal caused by the sign function in the sliding control law. The results are verified through theoretical proof and simulation software of MATLAB through two systems Pendubot and series double inverted pendulum

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