Adaptive Control of Active Balancing System for a Fast Speed-varying Jeffcott Rotor with Actuator Time Delay

Due to actuator time delay existing in an adaptive control of the active balancing system for a fast speed-varying Jeffcott rotor, if an unsynchronized control force (correction imbalance) is applied to the system, it may lead to degradation in control efficiency and instability of the control system. In order to avoid these shortcomings, a simple adaptive controller was designed for a strictly positive real rotor system with actuator time delay, then a Lyapunov-Krasovskii functional was constructed after an appropriate transform of this sys-tem model, the stability conditions of this adaptive control system with actuator time delay were derived. After adding a filter function, the active balancing system for the fast speed-varying Jeffcott rotor with actuator time delay can easily be converted to a strictly positive real system, and thus it can use the above adaptive controller satisfying the stability conditions. Finally, numerical simulations show that the adaptive controller proposed works very well to perform the active balancing for the fast speed-varying Jeffcott rotor with actuator time delay.

Adaptive control for a class of discrete-time time-delay systems with regard to delay parameter

The memory state feedback control problem for a class of discrete-time systems with input delay and unknown state delay is addressed based on LMIs and Lyapunov-Krasovskii functional method. Under the action of our designed adaptive control law, the unknown time-delay parameter is included in memory state feedback controller. Using LMI technique, delay-dependent sufficient conditions for the existence of the feedback controller are obtained. Finally, the effectiveness of the proposed design method is demonstrated by a numerical example.

Novel Adaptive Learning Control of Linear Systems with Completely Unknown Time Delays

A novel output-feedback adaptive learning control approach is developed for a class of linear time-delay systems. Three kinds of uncertainties： time delays, number of time delays, and system parameters are all assumed to be completely unknown, which is dfferent from the previous work. The design procedure includes two steps. First, according to the given periodic desired reference output and the allowed bound of tracking error, a suitable finite Fourier series expansion （FSE） is chosen as a practical reference output to be tracked. Second, by expressing the delayed practical reference output as a known time-varying vector multiplied by an unknown constant vector, we combine three kinds of uncertainties into an unknown constant vector and then estimate the vector by designing an adaptive law. By constructing a Lyapunov-Krasovskii functional, it is proved that the system output can asymptotically track the practical reference signal. An example is provided to illustrate the effectiveness of the control scheme developed in this paper.

Robust adaptive control for interval time-delay systems

This paper focuses on the robust adaptive control problems for a class of interval time-delay systems and a class of large-scale interconnected systems. The nonlinear uncertainties of the systems under study are bounded by high- order polynomial functions with unknown gains. Firstly, the adaptive feedback controller which can guarantee the stability of the closed-loop system in the sense of uniform ultimate boundedness is proposed. Then the proposed adaptive idea is extended to robust stabilizing designing method for a class of large-scale interconnected systems. Here, another problem we address is to design a decentralized feedback adaptive controller such that the closed-loop system is stable in the sense of uniform ultimate boundedness for all admissible uncertainties and time-delay. Finally, an illustrative example is given to show the validity of the proposed approach.

Adaptive control of uncertain time-delay chaotic systems

This work investigates adaptive control of a large class of uncertain time-delay chaotic systems （UTCSs） with unknown general perturbation terms bounded by a polynomial （unknown gains）, Associated with the different cases of known and unknowl system matrices, two corresponding adaptive controllers are proposed to stabilize unstable fixed points of the systems by means of Lyapunov stability theory and linear matrix inequafities （LMI） which can be solved easily by convex optimization algorithms, Two examples are used for examining the effectiveness of the proposed methods.

New type of adaptive control for a class of distributed time-delay systems with adaptation regard to delay parameter

The problem on stabilization for the system with distributed delays is researched. The distributed time-delay under consideration is assumed to be a constant time-delay, but not known exactly. A design method is proposed for a memory proportional and integral （PI） feedback controller with adaptation to distributed time-delay. The feedback controller with memory simultaneously contains the current state and the past distributed information of the addressed systems. The design for adaptation law to distributed delay is very concise. The controller can be derived by solving a set of linear matrix inequalities （LMIs）. Two numerical examples are given to illustrate the effectiveness of the design method.

Observer-based adaptive control of uncertain time-delay switched systems with stuck actuator faults

This paper concerns the observer-based adaptive control problem of uncertain time-delay switched systems with stuck actuator faults. Under the case where the original controller cannot stabilize the faulty system, multiple adaptive controllers are designed and a suitable switching logic is incorporated to ensure the closed-loop system stability and state tracking. New delay-independent sufficient conditions for asymptotic stability are obtained in terms of linear matrix inequalities based on piecewise Lyapunov stability theory. On the other hand, adaptive laws for on-line updating of some of the controller parameters are also designed to compensate the effect of stuck failures. Finally, simulation results for reference [1] model show that the design is feasible and efficient.

A Systematic Analysis Approach to Discrete-time Indirect Model Reference Adaptive Control

这份报纸论述间接模型引用的设计和分析有为分离时间的系统的一个类的规范的适应法律的适应控制(MRAC ) 。主要工作包括三部分。第一，构造工厂参数评价算法不仅拥有传统的评价算法的象那些的一样的性质而且在零避免分割的可能性。第二，由发现在工厂参数之间的关系，估计和控制器参数估计并且用工厂参数的性质估计，控制器参数估计的类似的性质也被建立。第三，基于关系，在使正常化之间的性质发信号并且在靠近环的系统并且在分离时间的系统上的一些重要数学工具上的所有信号作为在连续时间的盒子中，到分离间接 MRAC 计划的系统的稳定性和集中分析途径严厉地被开发。

Discrete-time Direct Model Reference Adaptive Control： A Systematic Approach

为直接模型引用的分离时间的系统，设计和分析的一个类，有规范的适应法律的适应控制(MRAC ) 被调查。我们责骂在输入和产量之间的 p 和 2 个关系性质上的分离时间的结论，和分离时间的交换词根 1 和 2。我们也建立分离时间的适应法律的性质，定义使正常化的信号，并且联系有在靠近环的系统的所有信号的信号。因此，分离时间的 MRAC 计划的稳定性和集中性质作为在连续时间的案例中以一种系统的方式严厉地被分析。

DISCRETE VARIABLE STRUCTURE CONTROL OF LINEAR TIME-INVARIANT SYSTEMS WITH TIME DELAY

A discrete variable structure control(DVSC) method for the linear time invariant systems with time delay was presented. The continuous time delay systems are first transformed into the standard discrete form which contains no time delay by augmenting the state variables. Then the switching surface is determined by using the ideal quasi sliding mode. As it is difficult for the state trajectory to reach the switching surface exactly, the reaching condition in the form of approach law is used to design the controller. The deduced switching surface and controller contain not only the current step of state feedback but also some former steps of controls. Stability analysis with and without time delay information is also investigated in this paper. Numerical simulation was carried out to demonstrate the effectiveness and feasibility of the presented control method.

Delay-Dependent Robust Passive Control for Uncertain Discrete-Time Systems with Time Delays

This paper considers the problem of robust passive control for uncertain discrete systems with time-varying delays. We pay attention to designing a state feedback controller which guarantees the passivity of the closed-loop system for all admissible uncertainties. In terms of a linear matrix inequality, a sufficient condition for the solvability of this problem is presented and the explicit expression of the desired state feedback controller is given.

Adaptive Robust Control of Multi-Machine Power Systems with Control Time Delay

The adaptive H_∞ control problem of multi-machine power system in the case of disturbances and uncertain parameters is discussed,based on a Hamiltonian model.Considered the effect of time delay during control and transmission,a Hamilton model with control time delay is established.Lyapunov-Krasovskii function is selected,and a controller which makes the system asymptotically stable is got.The controller not only achieves the stability control for nonlinear systems with time delay,but also has the ability to suppress the external disturbances and adaptive ability to system parameter perturbation.The simulation results show the effect of the controller.

Robustness Analysis of Discrete-time Indirect Model Reference Adaptive Control with Normalized Adaptive Laws

For a class of discrete-time systems with unmodeled dynamics and bounded disturbance, the design and analysis of robust indirect model reference adaptive control （MRAC） with normalized adaptive law are investigated. The main work includes three parts. Firstly, it is shown that the constructed parameter estimation algorithm not only possesses the same properties as those of traditional estimation algorithms, but also avoids the possibility of division by zero. Secondly, by establishing a relationship between the plant parameter estimate and the controller parameter estimate, some similar properties of the latter are also established. Thirdly, by using the relationship between the normalizing signal and all the signals of the closed-loop system, and some important mathematical tools on discrete-time systems, as in the continuous-time case, a systematic stability and robustness analysis approach to the discrete indirect robust MRAC scheme is developed rigorously.

Adaptive control method for nonlinear time-delay processes

Two complex properties, varying time-delay and block-oriented nonlinearity, are very common in chemical engineering processes and not easy to be controlled by routine control methods. Aimed at these two complex properties, a novel adaptive control algorithm the basis of nonlinear OFS （orthonormal functional series） model is proposed. First, the hybrid model which combines OFS and Volterra series is introduced. Then, a stable state feedback strategy is used to construct a nonlinear adaptive control algorithm that can guarantee the closed-loop stability and can track the set point curve without steady-state errors. Finally, control simulations and experiments on a nonlinear process with varying time-delay are presented. A number of experimental results validate the efficiency and superiority of this algorithm.

Robust adaptive control for uncertain systems with discrete and distributed delays

In this paper, a robust adaptive control scheme is proposed for the stabilization of uncertain linear systems with discrete and distributed delays and bounded perturbations. The uncertainty is assumed to be an unknown continuous function with norm-bounded restriction. The perturbation is sector-bounded. Combining with the liner matrix inequality method, neural networks and adaptive control, the control scheme ensures the exponential stability of the closed-loop system for any admissible uncertainty.

Stability of stochastic switched epidemic systems with discrete or distributed time delay

Stochastic switched epidemic systems with a discrete or distributed time delay are constructed and investigated. By the Lyapunov method and lto＇s differential rule, the existence and uniqueness of global positive solution of each system is proved. And stability conditions of the disease-free equilibrium of the systems are obtained. Numerical simulations are presented to illustrate the results.

The Lotka-Volterra Competition System with Discrete and Distributed Time Delays

In this paper, the Lotka-Volterra competition system with discrete and distributed time delays is considered. By analyzing the characteristic equation of the linearized system, the local asymptotic stability of the positive equilibrium is investigated. Moreover, we discover the delays don＇t effect the stability of the equilibrium in the delay system. Finally, we can conclude that the positive equilibrium is global asymptotically stable in the delay system.

Mixed sensitivity H_∞ control for LTI systems with varying time delays

Designing a robust controller for a system with timevarying delays poses a major challenge. In this paper, we propose a method based on mixed sensitivity H∞ for the control of linear time invariant（LTI） systems with varying time delays. The time delay is assumed bounded and the upper bound is known. In the technique we propose, the delay affecting the plant to be controlled is treated as an unmodeled uncertainty（in form of multiplicative uncertainty）. That uncertainty is approximated and then an H∞based controller, for the plant represented by the multiplicative uncertainty and the nominal model, is calculated. The obtained H∞controller is used to control the LTI systems with varying time delays. Simulation examples are given to illustrate the effectiveness of the proposed method.

Stability analysis of the active control system with time delay using IHB method

In this paper, the incremental harmonic balance method is employed to solve the periodic solution that a vibration active control system with double time delays generates, and the stability analysis of which is achieved by the Poincare theorem. The system stability regions can be obtained in view of time delay and feedback gain, the variation of which is also studied. It turns out that along with the increase of time delay, the active control system is not always from stable to unstable, and the system can be from stable to unstable state, whereas the system can be from unstable to stable state. The extent that the two times delays impact to the relative magnitude of the two feedback gains. the condition of the well-matched feedback gains. control strategy of time-delayed feedback.