A disturbance reduction scheme for linear small delay systems with modeling uncertainties

A disturbance reduction scheme for linear delay systems with modeling uncertainties is presented in this paper. The linear systems in this study are assumed to be nominally stable, minimum phase and relative degree one systems. The control structure is based on Astrom's modified Smith predictor with a disturbance reduction scheme and an artificial neural network (ANN). Unlike other disturbance rejection methods, the proposed scheme does not require information about unknown disturbance frequencies. The ANN is used to approximate a product of an inverse of a time delay and a nonnegative gain and to augment the robustness of the proposed approach against modeling uncertainties including a time-varying delay. Connective weights of the ANN are trained on-line using a back-propagation algorithm according to a disturbance estimation error function. Simulation results show the effectiveness of the presented disturbance reduction scheme for linear delay systems with modeling uncertainties, subjected to both periodic and non-periodic unknown load disturbances.     

Modified Smith predictor scheme for periodic disturbance reduction in linear delay systems

This paper presents a disturbance reduction scheme for linear systems with time delays. The linear systems in the study are assumed to be nominally stable, minimum phase, and relative degree one systems. The proposed scheme is a combination of Astrom’s modified Smith predictor with a disturbance reduction controller and a grey predictor. Unlike conventional disturbance rejection methods, the scheme proposed in this study does not require the estimation of disturbance frequencies. The grey prediction method is used to approximate the inverse of the time delay and to enhance the robustness of the disturbance reduction scheme against errors in the estimated delay time. The simulation results demonstrate the successful performance of the proposed disturbance reduction method for controlling a linear system with time delays, subjected to both step and periodic disturbances.     

Robust control of uncertain nonlinear systems with state delays based on an uncertainty and disturbance estimator

In this article, one linear and one nonlinear robust control strategies are proposed for uncertain nonlinear continuous‐time systems with disturbances and state delays. The approaches are based on the uncertainty and disturbance estimator (UDE) introduced in 2004. In the case of a linear controller, the terms containing the nonlinear functions and time delays are treated as additional disturbances to the system. In the case of a nonlinear controller, both known and unknown delay scenarios are considered. In the case of an unknown time delay, the terms containing the delay are treated as additional disturbances to the system. The algorithms provide excellent tracking and disturbance rejection performance. Simulations are given to show the effectiveness of the strategies, first via a simple example and second via an application to a continuous stirred tank reactor system. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive disturbance observer‐based control for stochastic systems with multiple heterogeneous disturbances

Antidisturbance control problem is discussed for stochastic systems with multiple heterogeneous disturbances, which include the white noise and the disturbance with unknown frequencies and amplitudes. An adaptive disturbance observer is designed to estimate the disturbance with unknown frequencies and amplitudes, based on which, an adaptive disturbance observer‐based control scheme is proposed by combining adaptive technique and linear matrix inequality method. It is proved that the closed‐loop system is asymptotically bounded in mean square when multiple heterogeneous disturbances exist simultaneously and that the equilibrium is globally asymptotically stable in probability as additive disturbance disappears. Finally, two simulation examples, including a wind turbine system, are given to show the effectiveness of the proposed scheme.     

Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation

This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L₂ gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

Improved disturbance rejection for predictor-based control of MIMO linear systems with input delay

In this paper, we are concerned with the predictor-based control of multi-input multi-output (MIMO) linear systems with input delay and disturbances. By taking the future values of disturbances into consideration, a new improved predictive scheme is proposed. Compared with the existing predictive schemes, our proposed predictive scheme can achieve a finite-time exact state prediction for some smooth disturbances including the constant disturbances, and a better disturbance attenuation can also be achieved for a large class of other time-varying disturbances. The attenuation of mismatched disturbances for second-order linear systems with input delay is also investigated by using our proposed predictor-based controller.     

Finite‐Time Fault‐Tolerant Control for a Class of Non‐Affine Nonlinear System Using Sliding Mode Disturbance Observer

This study investigates a finite‐time fault‐tolerant control scheme for a class of non‐affine nonlinear system with actuator faults and unknown disturbances. A global approximation method is applied to non‐affine nonlinear system to convert it into an affine‐like expression with accuracy. An adaptive terminal sliding mode disturbance observer is proposed to estimate unknown compound disturbances in finite time, including external disturbances and system uncertainties, which enhances system robustness. Controllers based on finite‐time Lyapunov theory are designed to force tracking errors to zero in finite time. Simulation results demonstrate the effectiveness of proposed method.     

Disturbance‐prediction–based control of input time delay systems for rejection of unknown frequency disturbances

In this paper, a novel disturbance rejection approach is presented for a class of input time‐delay systems subject to sinusoidal disturbances with unknown frequency. In particular, an auxiliary observer is proposed to represent the periodic disturbance in a parametric uncertainty form, where the unknown factor related to disturbance frequency can be estimated. Furthermore, the correlation between the future disturbance and the auxiliary observer output is analyzed, such that the future disturbances can be predicted and rejected through the input channel. Based on the aforementioned observer and predictor structure, the overall control architecture can be established as a framework of disturbance‐prediction–based control for systems with input time delays, where the conditions on the asymptotic stability of the closed‐loop systems are also derived. Finally, numerical examples are provided to illustrate the effectiveness of the proposed control approach.     

Robust adaptive tracking control for a class of mechanical systems with unknown disturbances under actuator saturation

A robust adaptive tracking control scheme is presented for a class of multiple‐input and multiple‐output mechanical systems with unknown disturbances under actuator saturation. The unknown disturbances are expressed as the outputs of a linear exogenous system with unknown coefficient matrices. An adaptive disturbance observer is constructed for the online disturbance estimation. An actuator saturation compensator is introduced to attenuate the adverse effects of actuator saturation. The adaptive backstepping method is then applied to design the robust adaptive tracking control law. It is proved that the designed control law makes the system outputs track the desired trajectories and guarantees the global uniform ultimate stability of the closed‐loop control system. Simulations on a two‐link robotic manipulator verify the effectiveness of the proposed control scheme.     

具有输入饱和的近空间飞行器鲁棒控制

针对近空间飞行器这一类存在外部扰动,输入饱和和参数不确定的多输入多输出线性系统,提出了一种基于干扰观测器的抗饱和鲁棒控制方案.将干扰观测器与抗饱和控制技术相结合,从而消除系统存在的未知外部扰动、输入饱和和不确定性对系统控制的影响.首先,设计干扰观测器对线性外部系统产生的未知扰动进行估计.然后根据干扰观测器输出,通过超前抗饱和方法设计抗饱和补偿器,并将其加入到鲁棒控制器的设计中,保证闭环系统存在输入饱和、未知外部扰动和参数不确定情况下的稳定性.为便于设计,干扰观测器、抗饱和补偿器和控制器设计矩阵均通过求解线性矩阵不等式得到.最后,将提出的鲁棒抗饱和控制方法应用于近空间飞行器,仿真结果验证了该控制方案的有效性.     

Adaptive finite‐time stabilization of nonlinearly parameterized systems subject to mismatching disturbances

This paper gives a first try to the finite‐time control for nonlinear systems with unknown parametric uncertainty and external disturbances. The serious uncertainties generated by unknown parameters are compensated by skillfully using an adaptive control technique. Exact knowledge of the upper bounds of the disturbances is removed by employing a disturbance observer–based control method. Then, based on the disturbance observer–based control, backstepping technique, finite‐time adaptive control, and Lyapunov stability theory, a composite adaptive state‐feedback controller is strictly designed and analyzed, which guarantees the closed‐loop system to be practically finite‐time stable. Finally, both the practical and numerical examples are presented and compared to demonstrate the effectiveness of the proposed scheme.     

Composite disturbance‐observer‐based control and H ∞ control for nonlinear time‐delay systems

A novel type of control scheme combined the distance‐observer‐based control (DOBC) with H_∞ control is proposed for a class of nonlinear time‐delay systems subject to disturbances. The disturbances are supposed to include two parts. One in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other is supposed to have the bounded H₂ norm. The disturbance observers based on regional pole placement and D‐stability theory are presented, which can be designed separately from the controller design. By integrating disturbance‐observer‐based control with H_∞ control laws, the disturbances can be rejected and attenuated, simultaneously, the desired dynamic performances can be guaranteed for nonlinear time‐delay systems with unknown nonlinear dynamics. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Adaptive decentralized fault‐tolerant tracking control for large‐scale nonlinear systems with input quantization

In this paper, an adaptive decentralized tracking control scheme is designed for large‐scale nonlinear systems with input quantization, actuator faults, and external disturbance. The nonlinearities, time‐varying actuator faults, and disturbance are assumed to exist unknown upper and lower bounds. Then, an adaptive decentralized fault‐tolerant tracking control method is designed without using backstepping technique and neural networks. In the proposed control scheme, adaptive mechanisms are used to compensate the effects of unknown nonlinearities, input quantization, actuator faults, and disturbance. The designed adaptive control strategy can guarantee that all the signals of each subsystem are bounded and the tracking errors of all subsystems converge asymptotically to zero. Finally, simulation results are provided to illustrate the effectiveness of the designed approach.     

Adaptive neural network control of bilateral teleoperation with unsymmetrical stochastic delays and unmodeled dynamics

In this paper, adaptive NN control is proposed for bilateral teleoperation system with dynamic uncertainties, unknown external disturbances, and unsymmetrical stochastic delays in communication channel to achieve transparency and robust stability. Compared with previous passivity‐based teleoperation framework, the communication delays are unsymmetrical and stochastic. By partial feedback linearization using nominal dynamics, the nonlinear dynamics of the teleoperation system are transformed into two subsystems: local master/slave dynamics control and time‐delay motion tracking. By integrating Markov jump systems and adaptive parameters updating, adaptive NN control strategy is developed. The stability of the closed‐loop system and the boundedness of tracking errors are proved using Lyapunov–Krasovskii functional synthesis under specific linear matrix inequalities conditions. The proposed adaptive NN control is robust against motion disturbances, parametric uncertainties, and unsymmetrical stochastic delay, which effectiveness is validated by extensive simulation studies. Copyright © 2013 John Wiley & Sons, Ltd.     

Feedback passification of switched stochastic time‐delay systems with multiple disturbances via DOBC

This paper is concerned with the problem of feedback passification for switched stochastic time‐delay systems with multiple disturbances subject to mode‐dependent average dwell‐time switching. The multiple disturbances are composed of two parts: one is given through an exogenous system and the other is described in the form of norm‐bounded vector. A disturbance observer is constructed to estimate an exogenous disturbance. Then, a state feedback controller that includes the estimation value is designed to guarantee the passivity of the closed‐loop system. The observer and controller gains are developed via linear matrix inequalities. The effectiveness of the proposed method is verified through a numerical example and an application example to PWM‐driven boost converter.     

Observer‐based tracking control for switched stochastic systems based on a hybrid 2‐D model

This paper is concerned with the observer‐based output tracking problem for a class of linear switched stochastic systems with time delay and disturbance by using repetitive control approach. More precisely, a two‐dimensional hybrid model is incorporated to obtain and optimize the repetitive controller. In particular, the repetitive controller is used to improve the tracking performance through its continuous learning actions. In addition, an equivalent‐input‐disturbance estimator is incorporated into the repetitive control design approach to reduce the effect of the external disturbances. The main aim of the control design is to track the periodic reference signal with the measured output of the system under consideration even in the presence of an unknown bounded disturbance. By constructing a suitable Lyapunov‐Krasovskii functional and using average dwell time approach and Jensen inequality, sufficient conditions are obtained in terms of linear matrix inequalities to guarantee the mean‐square exponential stability of the considered system. Eventually, a numerical example is provided to demonstrate the effectiveness of the developed method.     

An Efficient Finite Difference Method for The Time‐Delay Optimal Control Problems With Time‐Varying Delay

In this paper, an efficient finite difference method is presented for the solution of time‐delay optimal control problems with time‐varying delay in the state. By using the Pontryagin's maximum principle, the original time‐delay optimal control problem is first transformed into a system of coupled two‐point boundary value problems involving both delay and advance terms. Then the derived system is converted into a system of linear algebraic equations by using a second‐order finite difference formula and a Hermite interpolation polynomial for the first‐order derivatives and delay terms, respectively. The convergence analysis of the proposed approach is provided. The new scheme is also successful for the optimal control of time‐delay systems affected by external persistent disturbances. Numerical examples are included to demonstrate the validity and applicability of the new technique. Some comparative results are included to illustrate the effectiveness of the proposed method.     

Approximation-based disturbance observer approach for adaptive tracking of uncertain pure-feedback nonlinear systems with unmatched disturbances

This paper presents an approximation-based nonlinear disturbance observer (NDO) methodology for adaptive tracking of uncertain pure-feedback nonlinear systems with unmatched external disturbances. Compared with existing control results using NDO for nonlinear systems in lower-triangular form, the major contribution of this study is to develop an NDO-based control framework in the presence of non-affine nonlinearities and disturbances unmatched in the control input. An approximation-based NDO scheme is designed to attenuate the effect of compounded disturbance terms consisting of external disturbances, approximation errors and control coefficient nonlinearities. The function approximation technique using neural networks is employed to estimate the unknown nonlinearities derived from the recursive design procedure. Based on the designed NDO scheme, an adaptive dynamic surface control system is constructed to ensure that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to a neighbourhood of the origin. Simulation examples including a mechanical system are provided to show the effectiveness of the proposed theoretical result.     

基于线性自抗扰的开关磁阻电机调速控制研究

开关磁阻电机调速系统是复杂的非线性时变系统,负载扰动大,变量之间耦合严重,针对上述系统的性能特点提出采用线性自抗扰控制策略对系统进行控制的方法。首先为克服负载扰动变化,电机磁链呈非线性以及电流、位置等参数耦合的内外部干扰问题,设计扩张状态观测器对系统内扰和外扰进行准确估计并实时补偿。然后设计PD（比例-微分）控制器抑制系统给定与扩张状态观测器反馈的观测对象状态变量之间的跟踪误差。最后在仿真平台上对设计的控制系统进行试验并与传统PID控制方案进行对比,结果显示,对于给定的阶跃信号线性自抗扰控制器只需0.09s即可达到稳态且无超调,而PID控制器需要3s才能实现稳定跟踪。因此相比于传统PID控制,线性自抗扰控制器拥有更优的动静态性能,并且系统在外部负载扰动和内部模型参数变化的情况下也有良好的控制效果,表现出了很好的鲁棒特性。     

Aero‐Engine DCS Fault‐Tolerant Control with Markov Time Delay Based On Augmented Adaptive Sliding Mode Observer

With a focus on aero‐engine distributed control systems (DCSs) with Markov time delay, unknown input disturbance, and sensor and actuator simultaneous faults, a combined fault tolerant algorithm based on the adaptive sliding mode observer is studied. First, an uncertain augmented model of distributed control system is established under the condition of simultaneous sensor and actuator faults, which also considers the influence of the output disturbances. Second, an augmented adaptive sliding mode observer is designed and the linear matrix inequality (LMI) form stability condition of the combined closed‐loop system is deduced. Third, a robust sliding mode fault tolerant controller is designed based on fault estimation of the sliding mode observer, where the theory of predictive control is adopted to suppress the influence of random time delay on system stability. Simulation results indicate that the proposed sliding mode fault tolerant controller can be very effective despite the existence of faults and output disturbances, and is suitable for the simultaneous sensor and actuator faults condition.