Anti-disturbance control theory for systems with multiple disturbances: A survey

The problem of anti-disturbance control has been an eternal topic along with the development of the control theory. However, most methodologies can only deal with systems subject to a single equivalent disturbance which was merged by various types of uncertainties. In this paper, a review on anti-disturbance control is presented for systems with multiple disturbances. First, the classical control methods are briefly reviewed for disturbance attenuation or rejection problems. Then, recent advances in disturbance observer based control (DOBC) theory are introduced and especially, the composite hierarchical anti-disturbance control (CHADC) is firstly addressed. A comparison of different approaches is briefly carried out. Finally, focuses in the field on the current research are also addressed with emphasis on the practical application of the techniques.     

Generalized Discrete-time nonlinear disturbance observer based fuzzy model predictive control for boiler–turbine systems

The boiler–turbine system (BTS) is usually subject to the tight input constraint, the strong nonlinearity and the complex disturbance, which makes the control a challenging task To this end, a disturbance observer based fuzzy model predictive control (DOBFMPC) scheme is proposed for the BTS in this paper. The generalized discrete-time nonlinear disturbance observer (GDNDO) is first developed to estimate the higher-order disturbance by systematically extending the conventional nonlinear disturbance observer. The GDNDO exhibits a series structure of the internal states, and can precisely estimate the disturbance if its order is equal to or greater than that of the disturbance In addition, a baseline fuzzy model predictive control (FMPC) law is synthesized on the fuzzy model. With FMPC, the asymptotic stability is guaranteed, and meanwhile the input constraints are satisfied by both the free control variables and the future control inputs in the form of the state feedback law. At last, the disturbance estimate and the FMPC are applied to constitute the DOBFMPC law. With the proper design of the disturbance compensation gain, the disturbance influence is removed from the output channels by the composite DOBFMPC law at the steady state. Simulations for a 300 MW subcritical BTS well demonstrate the effectiveness of the proposed control scheme.     

A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances

This paper investigates the stabilization and disturbance rejection for a class of fractional-order nonlinear dynamical systems with mismatched disturbances. To fulfill this purpose a new fractional-order sliding mode control (FOSMC) based on a nonlinear disturbance observer is proposed. In order to design the suitable fractional-order sliding mode controller, a proper switching surface is introduced. Afterward, by using the sliding mode theory and Lyapunov stability theory, a robust fractional-order control law via a nonlinear disturbance observer is proposed to assure the existence of the sliding motion in finite time. The proposed fractional-order sliding mode controller exposes better control performance, ensures fast and robust stability of the closed-loop system, eliminates the disturbances and diminishes the chattering problem. Finally, the effectiveness of the proposed fractional-order controller is depicted via numerical simulation results of practical example and is compared with some other controllers.     

Robust passive control for a class of uncertain neutral systems based on sliding mode observer

The passivity-based sliding mode control (SMC) problem for a class of uncertain neutral systems with unmeasured states is investigated. Firstly, a particular non-fragile state observer is designed to generate the estimations of the system states, based upon which a novel integral-type sliding surface function is established for the control process. Secondly, a new sufficient condition for robust asymptotic stability and passivity of the resultant sliding mode dynamics (SMDs) is obtained in terms of linear matrix inequalities (LMIs). Thirdly, the finite-time reachability of the predesigned sliding surface is ensured by resorting to a novel adaptive SMC law. Finally, the validity and superiority of the scheme are justified via several examples.     

Composite disturbance rejection control based on generalized extended state observer

Traditional extended state observer (ESO) design method does not focus on analysis of system reconstruction strategy. The prior information of the controlled system cannot be used for ESO implementation to improve the control accuracy. In this paper, composite disturbance rejection control strategy is proposed based on generalized ESO. First, the disturbance rejection performance of traditional ESO is analyzed to show the essence of the reconstruction strategy. Then, the system is reconstructed based on the equivalent disturbance model. The generalized ESO is proposed based on the reconstructed model, while convergence of the proposed ESO is analyzed along with the outer loop feedback controller. Simulation results on a second order mechanical system show that the proposed generalized ESO can deal with the external disturbance with known model successfully. Experiment of attitude tracking task on an aircraft is also carried out to show the effectiveness of the proposed method.     

Disturbance observer based fault estimation and dynamic output feedback fault tolerant control for fuzzy systems with local nonlinear models

This paper addresses the problems of fault estimation (FE) and fault tolerant control (FTC) for fuzzy systems with local nonlinear models, external disturbances, sensor and actuator faults, simultaneously. Disturbance observer (DO) and FE observer are designed, simultaneously. Compared with the existing results, the proposed observer is with a wider application range. Using the estimation information, a novel fuzzy dynamic output feedback fault tolerant controller (DOFFTC) is designed. The controller can be used for the fuzzy systems with unmeasurable local nonlinear models, mismatched input disturbances, and measurement output affecting by sensor faults and disturbances. At last, the simulation shows the effectiveness of the proposed methods.     

Fixed-time disturbance observer based fixed-time back-stepping control for an air-breathing hypersonic vehicle

This paper proposes a fixed-time backstepping control scheme based on fixed-time disturbance observer for flexible air-breathing hypersonic vehicles. The backstepping control is combined with the fixed-time control technique to achieve fixed-time convergence. A fixed-time super-twisting disturbance observer, which is convergent independently of initial conditions, is employed to estimate and compensate the uncertainties and flexible effects in tracking process. A nonlinear first-order filter is adopted to avoid the “explosion of complexity” problem that arises in traditional backstepping, and to guarantee overall fixed-time stability. The closed-loop system is proven to be semi-globally uniformly ultimately fixed-time bounded via Lyapunov analysis. Simulation results are given to demonstrate the effectiveness of the proposed scheme.     

Modified reduced order observer based linear active disturbance rejection control for TITO systems

This paper proposes an observer based control approach for two input and two output (TITO) plant affected by the lumped disturbance which includes the undesirable effect of cross couplings, parametric uncertainties, and external disturbances. A modified reduced order extended state observer (ESO) based active disturbance rejection control (ADRC) is designed to estimate the lumped disturbance actively as an extended state and compensate its effect by adding it to the control. The decoupled mechanism has been used to determine the controller parameters, while the proposed control technique is applied to the TITO coupled plant without using decoupler to show its efficacy. Simulation results show that the proposed design is efficiently able to nullify the interactions within the loops in the multivariable process with better transient performance as compared to the existing proportional-integral-derivative (PID) control methods. An experimental application of two tanks multivariable level control system is investigated to present the validity of proposed scheme.     

Performance analysis of active disturbance rejection tracking control for a class of uncertain LTI systems

The paper considers the tracking problem for a class of uncertain linear time invariant (LTI) systems with both uncertain parameters and external disturbances. The active disturbance rejection tracking controller is designed and the resulting closed-loop system׳s characteristics are comprehensively studied. In the time-domain, it is proven that the output of closed-loop system can approach its ideal trajectory in the transient process against different kinds of uncertainties by tuning the bandwidth of extended state observer (ESO). In the frequency-domain, different kinds of parameters׳ influences on the phase margin and the crossover frequency of the resulting control system are illuminated. Finally, the effectiveness and robustness of the controller are verified through the actuator position control system with uncertain parameters and load disturbances in the simulations.     

Adaptive sliding mode disturbance rejection control with prescribed performance for robotic manipulators

This study proposes an adaptive sliding mode disturbance rejection control with prescribed performance for robotic manipulators. A transformation with respect to tracking error using certain performance functions is used to ensure the transient and steady-state performances of the trajectory tracking control for robotic manipulators. Using the transformed error, a nonsingular terminal sliding mode surface is proposed. A continuous terminal sliding mode control (SMC) is presented to stabilize the system. To compensate for the uncertainty and external disturbance, a novel sliding mode disturbance observer is proposed. Considering the unknown boundary of the derivative of a lumped disturbance, an adaptive law based on the idea of equivalent control is designed. Combining the adaptive law, continuous nonsingular terminal SMC, and sliding mode disturbance observer, the adaptive sliding mode disturbance rejection control with prescribed performance is developed. Simulations are carried out to demonstrate the effectiveness of the proposed approach.     

Robust control of uncertain feedback linearizable systems based on adaptive disturbance estimation

In this paper, an adaptive disturbance estimation-based control of a class of uncertain feedback linearizable systems with the presence of, both, external perturbations as well as non-modeled dynamics is considered. The aim of the control design was to solve the tracking trajectory problem for a class of output-based linearizable uncertain systems. An adaptive scheme is proposed for developing a state estimator of the uncertain dynamics. The estimation of both, the states and the uncertain dynamics is attained despite the limited knowledge of the plant and the information contained in the output signal. The uncertain section in the linearized system was approximated by a class of time-dependent combination of the system states. The observer implemented a parametric identifier to obtain the time varying parameters associated to the estimation of the uncertain section. This method ensured the adequate estimation process of the uncertainties/perturbations, measured in terms of the mean square error. Simultaneously, an adaptive gain associated to the observer adjusts its trajectories to provide the ultimate boundedness of the estimation error. Once the states of the uncertain system are obtained, a feedback controller rejects actively the perturbations that affect the system by a compensation scheme. Two numerical examples were developed to show the observer-based control performance.     

Anti-disturbance dynamic surface control scheme for a class of uncertain nonlinear systems with asymmetric dead-zone nonlinearity

This study proposes anti-disturbance dynamic surface control scheme for nonlinear strict-feedback systems subjected simultaneously to unknown asymmetric dead-zone nonlinearity, unmatched external disturbance and uncertain nonlinear dynamics. Radial basis function-neural network (RBF-NN) is invoked to approximate the uncertain dynamics of the system, and the dead-zone nonlinearity is represented as a time-varying system with a bounded disturbance. The nonlinear disturbance observer (NDO) is proposed to estimate the unmatched external disturbance which further will be used to compensate the effect of the disturbance. Then, by integrating RBF-NN, NDO and dynamic surface control (DSC) approaches, the proposed anti-disturbance control scheme is designed. Stability analysis of the closed-loop system shows that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error can be made arbitrarily small by proper selection of the design parameters. In comparison with the existing methods, the proposed scheme deals with the unmatched external disturbance, uncertain dynamics and unknown asymmetric dead-zone nonlinearity, simultaneously; it avoids the "explosion of complexity" problem and develops the simple control law without singularity concern. Furthermore, some imposed assumptions to the dead-zone input and disturbances are relaxed. Simulation and comparison results verify the effectiveness of the proposed approach.     

Observer based fault tolerant control for a class of Two-PMSMs systems

In this paper, an observer-based state-feedback fault-tolerant controller is proposed for two coupling permanent magnet synchronous motors (PMSMs) system. The controller compensates the actuator faults and allows the system states to track the reference states corresponding to the output of the original two-PMSMs system. To design such a controller, the information of system actuator faults are required. Then, a robust adaptive observer is designed to estimate the system actuator faults firstly. Next, by setting the reference outputs the equilibrium control inputs and reference speeds are computed based on the mathematic model of the two-PMSMs system. Meanwhile, the variation dynamic model is derived. Additionally, the robust stability of the closed-looped system with fault-tolerant controller is analyzed via the Lyapunov theory and interval matrix. Sufficient stability conditions and the gain matrix of the fault-tolerant controller are obtained by solving the linear matrix inequalities (LMIs). Finally, simulation results are presented to illustrate the effectiveness of the proposed observer and fault tolerant control (FTC) scheme.     

Reduced-order observer based fault estimation and fault-tolerant control for switched stochastic systems with actuator and sensor faults

This paper addresses the problems of fault estimation and fault-tolerant control for a class of switched stochastic systems with sensor and actuator faults. A reduced-order fault estimation observer is designed to estimate the system states, actuator and sensor faults, simultaneously. In the observer design process, intermediate variables are introduced such that the differential information of the measurement output is not included in the designed observer. Compared with the existing results, the dimension of the proposed observer is reduced, and the sensor fault can be completely unknown and unbounded. An observer based fault-tolerant controller is designed to stabilize the switched stochastic systems. Under arbitrary switching signal, the designed observer and controller can ensure that both the estimation error system and the closed-loop system are mean-square exponentially stable with disturbance attenuation performance. At last, both a numerical example and a switched electrical circuit example verify the proposed method.     

Gain-scheduled predictive extended state observer for time-varying delays systems with mismatched disturbances

In this paper, a novel control scheme for systems with input and output time-varying delays is provided in discrete-time domain. The control strategy combines predictor-like techniques with a delay-dependent gain-scheduled extended state observer. The main goal is twofold: (i) to minimize the negative effect of time-varying delays in the closed-loop performance and, (ii) to actively compensate the effect of mismatched disturbances in the controlled output. Moreover, a sufficient condition based on Linear Matrix Inequalities (LMI) is provided to obtain the maximum delay interval that ensures the stability of the closed-loop system. Finally, the achieved benefits of the proposal are shown by simulation in open-loop unstable plants, and experimentally validated in a test-bed quadrotor platform.     

On performance analysis of ADRC for a class of MIMO lower-triangular nonlinear uncertain systems

This paper designs the active disturbance rejection control (ADRC) to achieve desired performance for a class of MIMO lower-triangular nonlinear systems with large uncertainties under un-matched condition. We develop the ADRC with a set of extended state observers, and prove that the closed-loop system can achieve satisfied dynamic performance. The theoretical results illustrate the relationship between the bound of the concerned error and the bandwidth of extend state observers.     

基于降维观测器的系统最优容错控制

针对含有传感器故障的线性连续系统,利用Riccati矩阵方程设计了故障情况下的动态最优容错控制律,并设计了能同时检测出系统状态和故障状态的增广的降维故障检测器,从而实现了系统的故障检测和容错控制并能满足二次型性能指标.仿真实例验证了这种方法简单有效.     

An enhanced tracking control of marine surface vessels based on adaptive integral sliding mode control and disturbance observer

In this paper, a new control methodology is developed to enhance the tracking performance of fully actuated surface vessels based on an integrating between an adaptive integral sliding mode control (AISMC) and a disturbance observer (DO). First, an integral sliding mode control (ISMC), in which the backstepping control technique is used as the nominal controller, is designed for the system. The major features, i.e., benefits and drawbacks, of the ISMC are discussed thoroughly. Then, to enhance the tracking performance of the system, an adaptive technique and a new disturbance observer based on sliding mode technique are developed and integrated into the ISMC. The stability of the closed-loop system is proved based on Lyapunov criteria. Computer simulation is performed to illustrate the tracking performance of the proposed controller and compare with the existing controllers for the tracking control of a surface vessel. The simulation results demonstrate the superior performance of the proposed strategy.     

采用滑模观测器的机械臂故障检测与控制优化

针对复合干扰影响下机械臂的故障检测和控制精度问题,提出了一种基于滑模观测器的故障检测和控制优化方法。首先建立了带有电机故障、模型误差和机械摩擦等复合干扰的机械臂系统故障模型,然后设计了滑模观测器来实现在复合干扰下对电机故障的准确检测,最后引入滑模观测器对电机故障程度进行估计,并设计了反步容错控制方法,从而实现了对机械臂系统的精确控制。仿真结果表明,基于滑模观测器的故障检测和控制优化方法能够快速、准确检测和估计电机故障,确保机械臂系统准确跟踪指令信号,角度跟踪误差范围仅为-0.2°～0.2°,能够准确估计出复合干扰的大小,估计误差范围仅为-0.1～0.1 (°)/s²,大大改善了对机械臂的控制效果。