Chih-Chiang Cheng

A decentralized model reference adaptive variable structure controller for large-scale time-varying delay systems

In this note, the problem of decentralized model reference adaptive variable structure control for a class of perturbed large-scale systems with varying time-delay interconnections is investigated. Based on the Lyapunov stability theorem, an adaptive variable structure control strategy for solving the robust tracking problem without the knowledge of upper bound of perturbations is developed. The use of adaptive technique is to adapt the unknown upper bound of perturbations so that the objective of globally asymptotical stability is achieved. Once the system enters the sliding manifold, the dynamics of controlled systems are insensitive to matching perturbations. Finally, an example is given to demonstrate the feasibility of the proposed control scheme.

Design of adaptive variable structure controllers for perturbed time-varying state delay systems

Abstract The problem of stabilizing a class of perturbed linear dynamic systems with time-varying state delay is investigated in this paper. By applying the Lyapunov stability theorem, we develop a delay-independent adaptive variable structure controller to drive the states of system to zero. Based on the variable structure control (VSC) technique, the proposed controller can drive the system into a pre-specified sliding hyperplane to obtain the desired dynamic performance. Once the dynamics of system reach the sliding plane, the proposed controlled system is insensitive to perturbations. The use of adaptive technique is to overcome the unknown upper bound of perturbations so that the reaching condition (or sliding condition) can be satisfied. Furthermore, the globally asymptotic stability is guaranteed for the proposed control scheme under certain conditions. Finally, an example is given to illustrate the feasibility of the proposed control methodology.

Design of sliding surface for mismatched uncertain systems to achieve asymptotical stability

The design of an adaptive sliding mode control (SMC) scheme is proposed in this paper for stabilizing a class of dynamic systems with matched and mismatched perturbations. Two methods for designing a novel sliding surface function are introduced first. By utilizing a pseudocontrol input in the sliding surface function, one cannot only suppress the mismatched perturbations in the sliding mode, but also obtain the property of asymptotical stability. Then a sliding mode controller is designed to drive the controlled systems to the designated sliding surface in a finite time. Adaptive mechanism is also embedded in the controller as well as in the sliding surface function designed from the second method to overcome the perturbations, so that the informations of upper bound of perturbations are not required. An application of flight control and experimental results of controlling a servomotor are also given for demonstrating the applicability of the proposed control scheme.

A unifying design of sliding mode and classical controllers

A theory is given to unify output sliding-mode control and classical control. The idea is based on defining the sliding variable in such a way that once the system begins to slide, the classical controller transfer function is realized. This idea leads to the development of a hybrid sliding-and-classical controller which retains the merits of both types of controllers but eliminates their respective limitations. The proposed method is robust and applies to non-minimum-phase single-input, single-output (SISO) systems. No state measurement is required. >

DESIGN OF MIMO INTEGRAL VARIABLE STRUCTURE CONTROLLERS

Abstract The MIMO integral variable structure control (MIMOIVSC) scheme is proposed for a class of linear MIMO dynamic systems with nonlinear matched perturbations. This scheme is composed of two types of controllers. One is variable structure controller, which gives robust stability for system in the presence of parameter variations, uncertainties, and/or disturbances. The other is integral controller, which can eliminate steady-state error for step tracking. When the system is in the sliding mode, the dynamic equations of the closed-loop system can be reduced to a linear form and its eigenvalues can be arbitrarily assigned. In addition, an observer can be employed for state estimation, so that the state variables need not be measured. The fulfillment of sliding condition, including the case when estimated states are used, is verified. Two numerical examples are given to demonstrate the applicability of the proposed control scheme.

Design of decentralised adaptive sliding mode controllers for large-scale systems with mismatched perturbations

Based on the Lyapunov stability theorem, a methodology for designing a decentralised adaptive sliding mode control scheme is proposed in this paper. This scheme is implemented for a class of large-scale systems with both matched and mismatched perturbations. The perturbations and the interconnection terms are assumed to be norm bounded under certain mild conditions. The decentralised sliding surfaces with adaptive mechanisms embedded are specially designed for each subsystem, so that when each subsystem enters the sliding mode, the mismatched perturbations and the effects of interconnections can be effectively overcome and achieve asymptotic stability. The decentralised controller with embedded adaptive mechanisms is capable of driving the controlled state trajectories into the designated sliding surface in finite time. This is also achieved without the knowledge of upper bounds of the perturbations except those of the uncertainties in the input channels. A numerical example is included to demonstrate the feasibility of the proposed control scheme.

Block backstepping control of multi-input nonlinear systems with mismatched perturbations for asymptotic stability

Based on the Lyapunov stability theorem, a methodology of designing the block backstepping controller for a class of multi-input systems with matched and mismatched perturbations is proposed in this article. Some adaptive mechanisms are embedded both in the virtual input controller and in the backstepping controllers so that not only are the mismatched perturbations suppressed, but also part knowledge of the upper bound of perturbation is not required. Finally, an example of stabilising the control-moment-gyro devices is presented to demonstrate the feasibility of the proposed methodology.

Design of adaptive sliding mode tracking controllers for chaotic synchronization and application to secure communications

Abstract Synchronization of two identical chaotic systems with matched and mismatched perturbations by utilizing adaptive sliding mode control (ASMC) technique is presented in this paper. The sliding surface function is specially designed based on the Lyapunov stability theorem and linear matrix inequality (LMI) optimization technique. The designed tracking controller can not only suppress the mismatched perturbations when the controlled dynamics (master–slave) are in the sliding mode, but also drive the trajectories of synchronization errors into a small bounded region whose size can be adjusted through the designed parameters. Adaptive mechanisms are employed in the proposed control scheme for adapting the unknown upper bounds of the perturbations, and the stability of overall controlled synchronization systems is guaranteed. The comparison of the proposed chaotic synchronization technique with an existing generalized chaotic synchronization (GCS) method as well as application of the proposed control method to secure communications is also demonstrated in this paper.

Decentralized model following variable structure control for perturbed large-scale systems with time-delay interconnections

The problem of decentralized model following variable structure control for a class of perturbed large-scale systems with time-delay interconnections is investigated in this paper. Based on the variable structure control technique, we develop a control strategy for solving the robust tracking problems. The proposed control law will drive the systems dynamics into a chosen sliding manifold, then exhibit the desired behavior. Furthermore, this control strategy can guarantee globally asymptotic stability for the composite system. Finally, an illustrative example is given to demonstrate the proposed strategy.

Design of adaptive sliding mode controllers for systems with mismatched uncertainty to achieve asymptotic stability

Based on the Lyapunov stability theorem, an adaptive sliding mode control scheme is proposed in this paper for a class of mismatched, perturbed dynamic systems to solve regulation problems. This method is an extension of the existing methods where n ≤ 2 m has to be fulfilled (n is the dimension of the system, m is the number of inputs). It means that the proposed method in this paper can be used for the case n > 2 m. The sliding surface function is firstly designed by treating some state variables as pseudo controllers to stabilize the rest of state variables. The second step is to design the controllers so that the trajectories of the controlled systems are able to reach sliding surface in a finite time. The advantages of the existing methods, for instance, suppressing the perturbations without requiring their upper bounds when designing the sliding surface function and controllers, are still preserved. Once the controlled system enters the sliding mode, the property of asymptotic stability is achieved under certain conditions. A numerical example is given to demonstrate the feasibility of the proposed design technique.