Control of open‐loop neutrally stable systems subject to actuator saturation and external disturbances

In this paper, we study the disturbance response of open‐loop neutrally stable linear systems with saturating linear feedback controller. It is shown that the closed‐loop states remain bounded if the disturbances consists of those signals that do not have large sustained frequency components corresponding to the system's eigenvalues on the imaginary axis (continuous‐time) or on the unit circle (discrete‐time). Copyright © 2011 John Wiley & Sons, Ltd.     

双线性自适应前馈控制及其应用

本文对存在可测干扰和界扰动的双线性系统提出了一种逢适应前馈控制算法，证明了算法的稳定性。     

Time-varying versus time-invariant compensation for rejection ofpersistent bounded disturbances and robust stabilization

It is shown that time-varying compensation does not improve the optimal rejection of persistent bounded disturbances. This result is obtained by exploiting a key observation that any time-varying compensator which yields a given degree of disturbance rejection must do so uniformly over time, thereby removing any advantage of time-variation. This key observation is exploited to show that time-varying compensation does not improve the optimal rejection of disturbances, regardless of the norm used to measure the disturbances. Thus, absolutely summable, finite-energy, or persistent bounded disturbances may be treated in the same manner. It is shown that time-varying compensation does not help in the bounded-input bounded-output robust stabilization of time-invariant plants with unstructured uncertainty. In doing so, it is also shown that the small-gain theorem is both necessary and sufficient for the bounded-input bounded-output stability of certain linear time-varying plants subject to unstructured linear time-varying perturbations     

Robust model predictive control of constrained linear systems with bounded disturbances

This paper provides a novel solution to the problem of robust model predictive control of constrained, linear, discrete-time systems in the presence of bounded disturbances. The optimal control problem that is solved online includes, uniquely, the initial state of the model employed in the problem as a decision variable. The associated value function is zero in a disturbance invariant set that serves as the ‘origin’ when bounded disturbances are present, and permits a strong stability result, namely robust exponential stability of the disturbance invariant set for the controlled system with bounded disturbances, to be obtained. The resultant online algorithm is a quadratic program of similar complexity to that required in conventional model predictive control.     

Asymptotic tracking control for a class of reference signals for linear differential inclusions

Tracking control for linear differential inclusions with disturbances is investigated in this paper. Based on the convex hull Lyapunov function, a feedback control law is designed such that the output of the closed-loop system without disturbances globally asymptotically tracks the desired reference signal. Under the bounded disturbances, the tracking error is bounded. An example is given to illustrate how to make the output of the closed-loop system track a sinusoidal signal, a cosine signal and a circular signal. The simulation shows the effectiveness of the proposed method.     

Robust continuous-time adaptive control by parameter projection

The problem of adaptive control of a continuous-time plant of arbitrary relative degree, in the presence of bounded disturbances as well as unmodeled dynamics, is addressed. The adaptation considered is the usual gradient update law with parameter projection, the latter being the only robustness enhancement modification employed. It is shown that if the unmodeled dynamics, which consists of multiplicative as well as additive system uncertainty, is small enough, then all the signals in the closed-loop system are bounded. This shows that extra modifications are not necessary for robustness with respect to bounded disturbances and small unmodeled dynamics. In the nominal case, where unmodeled dynamics and disturbances are absent, the asymptotic error in tracking a given reference signal is zero. Moreover, the performance of the adaptive controller is also robust     

Attitude Regulation With Bounded Control in the Presence of Large Disturbances With Bounded Moving Average

The attitude regulation problem with bounded control for a class of satellites in the presence of large disturbances, with bounded moving average, is solved using a Lyapunov-like design. The analysis and design approaches are introduced in the case in which the underlying system is an integrator and are then applied to the satellite attitude regulation problem. The performance of the resulting closed-loop systems are studied in detail and it is shown that trajectories are ultimately bounded despite the effect of the persistent disturbance. Simulation results on a model of a small satellite subject to large, but bounded in moving average, disturbances are presented.      

Robustness of an adaptive pole placement algorithm in the presenceof bounded disturbances and slow time variation of parameters

The robustness properties of a specific adaptive pole placement scheme in the presence of bounded disturbances and slow time variation of parameters are studied. It is shown that the least squares algorithm used in this scheme retains the global stability of the overall system in the presence of bounded disturbances of small magnitude and slow time variation of system parameters (within a compact set)     

State observer-based adaptive fuzzy output-feedback control for a class of uncertain nonlinear systems

This paper aims to develop state observer-based adaptive fuzzy control techniques for controlling a class of uncertain nonlinear systems with bounded external disturbances. An adaptive fuzzy observer is proposed to estimate the system state variables. It is shown that the observation errors obtained from the observer are uniformly ultimately bounded. Applying the estimated system state for design of an output-feedback controller, the uniformly ultimate boundedness of the tracking errors for the resulting closed-loop system can be guaranteed. A typical robot arm system is employed in our simulation studies, and the results demonstrate the usefulness and effectiveness of the proposed techniques for controlling nonlinear systems with bounded external disturbances.     

Robust adaptive quasi-sliding mode controller for discrete-time systems

In this paper, a discrete robust quasi-sliding mode adaptive controller is presented for the system with model uncertainties, unmodeled dynamics and bounded disturbances. The proposed method is adaptive control in conjunction with a sliding mode based controller design. The bounded motion of the state around the sliding surface and the stability of the global system in the sense that all signals remain bounded are guaranteed. In the proposed adaptive algorithms, the dead-zone method is employed even though the upper and lower bounds of the disturbances are unknown. Simulation results have shown the effectiveness of the proposed algorithms.     

A necessary and sufficient condition for input-to-state stability of quantised feedback systems

For zooming-out/in method used in the design of quantised feedback systems, the property of the duration of zoom-out mode (this duration is defined as capture time) is essential to input-to-state stability (ISS) of systems. This paper shows that a necessary and sufficient condition of achieving ISS with respect to external disturbances for quantised feedback systems is that capture time under the proposed coding scheme is uniformly bounded. It further shows that the coding scheme under which capture time is only bounded and not uniformly bounded cannot guarantee ISS of systems. A coding scheme is designed for uniformly bounded capture time and therefore achieves ISS of systems.     

Adaptive neural network control for a nonlinear Euler‐Bernoulli beam in three‐dimensional space with unknown control direction

In this paper, an adaptive neural network control system is developed for a nonlinear three‐dimensional Euler‐Bernoulli beam with unknown control direction. The Euler‐Bernoulli beam is modeled as a combination of partial differential equations (PDEs) and ordinary differential equations (ODEs). Adaptive radial basis function–based neural network control laws are designed to determine approximation of disturbances. A projection mapping operator is adopted to realize bounded approximation of disturbances. A Nussbaum function is introduced to compensate for the unknown control direction. The goal of this study is to suppress the vibrations of the Euler‐Bernoulli beam in three‐dimensional space. In addition, unknown control direction problem and bounded disturbances are considered to guarantee that the signals of the system are uniformly bounded. Numerical simulations demonstrate the effectiveness of the proposed method.     

具有降阶模型的多变量鲁棒自适应前馈控制器

本文提出了一种多变量鲁棒自适应前馈控制器。该控制器采用低阶模型来控制参数未知的高阶多变量系统时,在可测干扰和有界不可测干扰作用下能保证自适应系统稳定运行。当可测干扰与系统输出之间存在未建模动态时,它可以对可测干扰实行有效的动静态补偿。当只有有界干扰作用时,它能使有界干扰对系统产生的影响最小。本文还给出了采用所提出的控制器控制某钢厂间歇式余热锅炉的仿真结果。     

Discrete-time deadbeat model reference adaptive control of an adjustable-speed DC motor drive system

An imperfect model reference adaptive control for a DC motor drive system having bounded disturbances is proposed. The discrete-time model reference adaptive control algorithm proposed by Chiang and Chen (1987) with bounded disturbances is introduced to an Elettronica Veneta Mod. IBS-4/EV DC motor. This work shows that the adaptive controller can maintain good performance during startup, anticlockwise, or clockwise winding in the regulating reference signals.     

Control of a chain of integrators subject to actuator saturation and disturbances

In this paper, we study control of a chain of integrators under actuator saturation and non‐additive disturbances. We shall show that boundedness of the states can be ensured if the disturbances are matched and integral‐bounded, misaligned and magnitude‐bounded, or a combination of the two, using either a static or a dynamic low‐gain state feedback. This result is an extension of our earlier work on double integrator. Copyright © 2011 John Wiley & Sons, Ltd.     

Modeling,analysis and compensation of disturbances during task execution of a wheeled inverted pendulum type assistant robot using a unified controller

This paper presents the modeling and analysis of disturbances caused by model changes, unknown dynamics, and external forces during task execution of a wheeled Inverted PENdulum Type Assistant Robot. Compensating these disturbances and their effects results in the ability of the system to perform different tasks without changes in the control structure. This results in a unified controller for multiple tasks making the control system simple without sacrificing robustness. Estimation of these disturbances is performed using the extended state observer (ESO), which is a practical observer since it requires very little system information. To ensure proper application of the ESO, the analysis of the equilibrium states under disturbances was performed. The disturbance modeling and the effectiveness of the control are verified by results from disturbance and task tests. Finally, the bounded input bounded output behavior of the system with consideration to the disturbances is presented.     

基于无源性的全方位移动机器人自抗扰控制

针对全方位移动机器人轨迹跟踪控制中存在的外界干扰和系统参数不确定性问题,提出基于无源性的自抗扰控制方法.该方法通过扩张状态观测器对系统扰动进行估计,并在基于无源性的控制器中加入扰动补偿项以减小外界干扰和参数不确定性对系统的影响;进而,利用系统的无源特性和Lyapunov 理论证明在该控制器作用下闭环系统有界输入有界输出稳定.仿真结果表明,所提出的控制方法响应速度较快,控制精度较高,对系统外扰和模型参数不确定性具有较强的鲁棒性     

A new robust adaptive control algorithm for linear time-varying plants

Robustness is an important property of a control system. Robust adaptive control has been an active research area for more than a decade. Since it was shown that un-modelled dynamics or even a small bounded disturbance can cause most adaptive control algorithms to go unstable, various modifications of the adaptive control algorithms have been developed to counteract instability and improve robustness with respect to unmodelled dynamics and bounded disturbances. However, we know that most of the modified approaches to achieve robustness require knowledge of either the parameter of bounding function on the unmodelled dynamics, or the upper bound on the disturbances, or the bound on the norm of unknown matching controller/plant parameters, and such knowledge can hardly be obtained in practice. A new indirect adaptive control algorithm for linear time-varying plants is proposed to achieve robustness to a class of unmodelled dynamics, bounded disturbances and plant parameter time variations. A modified relative dead zone technique is used, so that knowledge of the parameters of the upper bounding function on the unmodelled dynamics and the disturbances is not required. The stability analysis and the robust performance of adoptively controlled time-varying systems are provided for the new scheme. A simulation example is given to show the effectiveness of the proposed algorithm.     

Indirect adaptive control for interconnected systems

An indirect adaptive controller for interconnected systems is introduced. Each subsystem is subject to bounded disturbances and to possibly unbounded interconnections with other subsystems. A variable dead zone is incorporated into a gradient estimation scheme to limit the effects of the interconnections and disturbances. An adaptive state feedback control law is described which stabilizes the interconnected system, forcing the input and output signals of each subsystem to remain bounded     

Stability and switching control design issues for a class of discrete time hybrid systems

For the class of systems considered, necessary and sufficient stabilizability conditions are unknown. However, by considering the same systems with unknown but bounded exogenous disturbances, we give finitely computable conditions, sufficient for stabilizability without disturbances, yet necessary for stabilizability with disturbances.