Composite adaptive disturbance observer based control and back-stepping method for nonlinear system with multiple mismatched disturbances

A novel control scheme combining disturbance observer technique and back-stepping method is proposed for a class of nonlinear system with multiple mismatched disturbances. The uncertain multiple mismatched disturbances contain not only single harmonic or constant disturbances but also another unexpected nonlinear signal presented as a nonlinear function. The composite adaptive disturbance observers are designed to estimate the disturbances with partial known information. By integrating disturbance observer based control with back-stepping method, a composite controller is designed. Here, the disturbance estimations are introduced into the design of virtual control laws in each step to compensate the mismatched disturbances. Rigorous stability analysis for the closed-loop system is established by direct Lyapunov function method. It is shown that the system output asymptotically converges to zero in spite of existing multiple mismatched disturbances. Finally, a simulation example is applied to demonstrate the effectiveness of the proposed method.     

Disturbance rejection for nonlinear systems with mismatched disturbances based on disturbance observer

A disturbance rejection approach based on disturbance observer is proposed for a class of nonlinear systems subject to mismatched disturbances. The mismatched disturbances are described by exogenous systems and satisfy partially-known information, which enter the system in the different channels with the control input. The disturbance observer is designed to estimate the mismatched disturbances, which can be introduced separately from the controller design. By integrating disturbance observer with back-stepping method, the disturbance observer plus back-stepping (DOPBS) controller can be constructed to reject the mismatched disturbances. And the asymptotically stability for the closed-loop system can be achieved. Finally, simulation examples are given to demonstrate the feasibility and effectiveness of the proposed scheme compared with existing methods.     

An event-triggered based robust control for electro-hydraulic servo machines with active disturbances rejection

From an interdisciplinary perspective, the event-triggered scheme, the state observer, and the nonlinear disturbance observer are introduced in a robust tracking control to study the networked electro-hydraulic servo system control problems with digital communication challenge, sensor installation restricted problem, matched modeling uncertainties, and mismatched disturbances. Control packets are likely to be delayed or even lost in the networked control system when the communication medium is shared by multiple nodes and the available communication bandwidth is limited. Therefore, it is necessary to save communication resources. To improve the control performance and the efficiency of the network resource utilization, the event-triggered scheme is introduced. Specifically, the practical application of the event-triggered scheme in an actual electro-hydraulic servo system is a breakthrough in this paper. In addition, to obtain the real-time states of the unmeasurable system and compensate for both matched disturbances and external disturbances simultaneously, the state observer and the nonlinear disturbance observer are collaboratively designed. Finally, to evaluate the control performance of the designed controller, the related comparative experiments are carried out in an actual system. The results show that theoretical analysis and experimentation are cross verified.     

Disturbance observer-based robust missile autopilot design with full-state constraints via adaptive dynamic programming

This paper aims to develop a robust optimal control method for longitudinal dynamics of missile systems with full-state constraints suffering from mismatched disturbances by using adaptive dynamic programming (ADP) technique. First, the constrained states are mapped by smooth functions, thus, the considered systems become nonlinear systems without state constraints subject to unknown approximation error. In order to estimate the unknown disturbances, a nonlinear disturbance observer (NDO) is designed. Based on the output of disturbance observer, an integral sliding mode controller (ISMC) is derived to counteract the effects of disturbances and unknown approximation error, thus ensuring the stability of nonlinear systems. Subsequently, the ADP technique is utilized to learn an adaptive optimal controller for the nominal systems, in which a critic network is constructed with a novel weight update law. By utilizing the Lyapunov's method, the stability of the closed-loop system and the convergence of the estimation weight for critic network are guaranteed. Finally, the feasibility and effectiveness of the proposed controller are demonstrated by using longitudinal dynamics of a missile.     

Observer-based terminal sliding mode control of non-affine nonlinear systems: Finite-time approach

This paper studies the problem of observer based fast nonsingular terminal sliding mode control schemes for nonlinear non-affine systems with actuator faults, unknown states, and external disturbances. A hyperbolic tangent function based extended state observer is considered to estimate unknown states, which enhances robustness by estimating external disturbance. Then, Taylor series expansion is employed for the non-affine nonlinear system with actuator faults, which transforms it to an affine form system to simplify disturbance observer and controller design. A finite time disturbance observer is designed to address unknown compound disturbances, which includes external disturbances and system uncertainties. A fast nonsingular terminal sliding mode with exponential function sliding mode is proposed to address output tracking. Simulation results show the proposed scheme is effective.     

Anti-disturbance control based on disturbance observer for nonlinear systems with bounded disturbances

A composite anti-disturbance control problem for a class of nonlinear systems is studied in this paper. There are two types of disturbances in the systems, one is the matched disturbance with bounded variation rate, the other is the unmatched time-varying disturbances. A nonlinear disturbance observer is designed to estimate the matched disturbances, which can be presented separately from the controller design. By integrating DOBC with back-stepping method, a composite DOBC and back-stepping controller is proposed, and the disturbance estimations are introduced into the design of virtual control laws to compensate the unmatched disturbances. In addition, it is proved that all the states in the closed-loop system are uniformly ultimate bounded (UUB). Finally, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed method.     

Multivariable uniform finite-time output feedback reentry attitude control for RLV with mismatched disturbance

A continuous multivariable uniform finite-time output feedback reentry attitude control scheme is developed for Reusable Launch Vehicle (RLV) with both matched and mismatched disturbances. A novel finite-time controller is derived using the bi-limit homogeneous technique, which ensures that the attitude tracking can be achieved in a uniformly bounded convergence time from any initial states. A multivariable uniform finite-time observer is designed based on an arbitrary order robust sliding mode differentiator to estimate the unknown states and the external disturbances, simultaneously. Then, an output feedback control scheme is established through the combination of the developed controller and the observer. A rigorous proof of the uniform finite-time stability of the closed-loop system is presented using Lyapunov and homogeneous techniques. Finally, numerical simulation is provided to demonstrate the efficiency of the proposed scheme.     

Approximate decoupling and output tracking for MIMO nonlinear systems with mismatched uncertainties via ADRC approach

In this paper, we consider output tracking for a class of MIMO nonlinear systems which are composed of coupled subsystems with vast mismatched uncertainties. First, all uncertainties influencing the performance of controlled outputs, which include internal unmodelled dynamics, external disturbances, and uncertain nonlinear interactions between subsystems, are refined into the total disturbance in the control channels of subsystems. The total disturbance is shown to be sufficiently reflected in the measured output of each subsystem so that it can be estimated in real time by an extended state observer (ESO) in terms of the measured outputs. Second, we decouple approximately the MIMO systems by cancelling the total disturbance based on ESO estimation so that each subsystem becomes approximately independent linear time invariant one without uncertainty and interaction with other subsystems. Finally, we design an ESO based output feedback for each subsystem separately to ensure that the closed-loop state is bounded, and the closed-loop output of each subsystem tracks practically a given reference signal. This is completely in comply with the spirit of active disturbance rejection control (ADRC). Some numerical simulations are presented to demonstrate the effectiveness of the proposed output feedback control scheme.     

Scale-based cluster formation for multi-agent systems with mismatched disturbances

This paper studies scale-based cluster formation problem of multi-agent system (MASs) under mismatched disturbances. A distributed sliding mode control with a disturbance observer is proposed to solve the aforementioned problem in the leaderless and leader-follower cases. The proposed control strategy provides satisfactory robust performance under mismatched disturbances and is thus more applicable to complicated formation control tasks. Finally, simulation results are provided to justify the validity of the proposed method.     

Continuous output feedback sliding mode control for underactuated flexible-joint robot

The tracking control based on output feedback for a category of flexible-joint robot (FJR) systems is investigated in this brief. Control performance of the systems is inevitably bearing the brunt of various unknown time-varying disturbances, which can be categorized to be matched and mismatched and generally cover internal parameter uncertainties, couplings, unmodelled dynamics, and external load or changing operating environments. To cope with these disturbances, the mismatched disturbances are first transferred to the matched ones by a flatness method, which eliminates the computational cost of estimating mismatched disturbances. Then, a generalized proportional integral observer (GPIO) is constructed to estimate the unavailable states and disturbances. By integrating the estimated disturbance and states provided by the GPIO, a novel dynamic sliding surface is constructed. Finally, a continuous sliding mode control (CSMC)-based output feedback control framework is further designed. The presented control strategy only requires link position information and is continuous, which can effectively reduce the chattering driven by the high-frequency switching item in the traditional SMC method. Asymptotic convergence of output tracking error is guaranteed by theoretical analysis under some mild conditions. Comparative tests on a two-link FJR verify the claimed control performance.     

Distributed observer-based consensus tracking for nonlinear MASs with nonuniform input delays and disturbances

In this paper, we investigate the consensus tracking problem of nonlinear MASs with nonuniform time-varying input delays and external disturbances. For each follower, the composited disturbance observer and the state observer are employed to estimate bounded composited disturbances and unmeasured states, and a distributed observer based on output-feedback is proposed to approximate the leader’s states approachably. Sequentially, the consensus tracking control is converted into a stability control problem for the nonlinear MASs with nonuniform time-varying input delays. Subsequently, a distributed controller based on the truncated prediction approach is presented, which only depends on the boundary value of time-varying input delays. The distributed controller can render each follower synchronically stable via the Lyapunov stability theory. Finally, a group of single-link manipulators is used as an example to verify the effectiveness of the theoretical results.     

Composite fault-tolerant control with disturbance observer for stochastic systems with multiple disturbances

In this paper, a composite fault tolerant control (CFTC) with disturbance observer scheme is considered for a class of stochastic systems with faults and multiple disturbances. The disturbances are divided into two parts. One represents the stochastic disturbance with partial known information which is formulated by an exogenous system. The other is independent Wiener process. A stochastic disturbance observer is designed to estimate exogenous disturbance. To make the first type of disturbance can be rejected and the fault can be diagnosed, a composite fault diagnosis observer with disturbance observer is constructed. Furthermore, a composite fault-tolerant controller is proposed to compensate disturbances and faults. Finally, simulation examples are given to demonstrate the feasibility and effectiveness of the proposed scheme.     

Consensus disturbance rejection for Lipschitz nonlinear multi-agent systems with input delay: A DOBC approach

In this paper, a new predictor-based consensus disturbance rejection method is proposed for high-order multi-agent systems with Lipschitz nonlinearity and input delay. First, a distributed disturbance observer for consensus control is developed for each agent to estimate the disturbance under the delay constraint. Based on the conventional predictor feedback approach, a non-ideal predictor based control scheme is constructed for each agent by utilizing the estimate of the disturbance and the prediction of the relative state information. Then, rigorous analysis is carried out to ensure that the extra terms associated with disturbances and nonlinear functions are properly considered. Sufficient conditions for the consensus of the multi-agent systems with disturbance rejection are derived based on the analysis in the framework of Lyapunov–Krasovskii functionals. A simulation example is included to demonstrate the performance of the proposed control scheme.     

Output feedback tracking control for polynomial nonlinear systems with measurement noises and mismatched disturbances

In this paper, the output feedback tracking control problem is investigated for polynomial nonlinear systems (PNSs) with measurement noises and mismatched disturbances. First, in order to suppress measurement noises, a polynomial observer is introduced to simultaneously estimate states and mismatched disturbances. Next, based on the idea of backstepping control, a novel output feedback controller is designed for PNSs to compensate mismatched disturbances. Command filters are employed to avoid the repeated derivatives of virtual control and measurement noises in the recursive controller design. Then, a sufficient condition in terms of the parameter-dependent linear matrix inequality (PDLMI) is derived to guarantee the boundedness of tracking errors and estimation errors. By utilizing the sum of squares (SOS) decomposition technique, the PDLMI is solved to obtain desired controller parameters. Finally, an example of dynamic point-the-bit rotary steerable drilling tool system is performed to demonstrate the effectiveness and feasibility of the proposed strategy.     

Cascade ADRC with neural network-based ESO for hypersonic vehicle

In this paper, active disturbance rejection control (ADRC) based on a neural network has been investigated for the attitude control of the hypersonic vehicle (HV) with uncertain disturbances, which are regarded as a strongly time-varying, nonlinear, and coupled system. The structure of nonlinear state error feedback (NLSEF) with an Extended State Observer (NLSEF+ESO) utilized in ADRC is considered to have good disturbance resistance ability in engineering applications with less dependence on the mathematical model of the system. However, the strong coupling of the HV makes it complicated to separately design ADRC for each channel. In addition, the bandwidth and parameters of the ESO can seriously affect the performance of the ADRC, while jitter occurs when they are not well matched. A cascade active-rejection control scheme is designed by introducing the Radial Basis Function (RBF) Neural Network to substitute the ESO in ADRC, which mitigates the shortcoming of ADRC in addressing the control problems of the MIMO system with coupling disturbances. The NNESO can adapt well to disturbance characteristics through online training and fitting and can effectively reduce the jitter of the control. The stability of the NNESO is proved by Lyapunov stability theory, and the numerical simulations are presented to demonstrate the effectiveness of our theoretical results. In summary, the proposed NNESO-based cascade ADRC is an effective method for solving the problem of HV control with better disturbance resistance.     

Observer based switching ILC for consensus of nonlinear nonaffine multi-agent systems

This study considers the main challenges of presenting an iterative observer under a data-driven framework for nonlinear nonaffine multi-agent systems (MASs) that can estimate nonrepetitive uncertainties of initial states and disturbances by using the information from previous iterations. Consequently, an observer-based iterative learning control is proposed for the accurate consensus tracking. First, the dynamic effect of nonrepetitive initial states is transformed as a total disturbance of the linear data model which is developed to describe I/O iteration-dynamic relationship of nonlinear nonaffine MASs. Second, the measurement noises are considered as the main uncertainty of system output. Then, we present an iterative disturbance observer to estimate the total uncertainty caused by the nonrepetitive initial shifts and measurement noises together. Next, we further propose an observer-based switching iterative learning control (OBSILC) using the iterative disturbance observer to compensate the total uncertainty and an iterative parameter estimator to estimate unknown gradient parameters. The proposed OBSILC consists of two learning control algorithms and the only difference between the two is that an iteration-decrement factor is introduced in one of them to further reduce the effect of the total uncertainty. These two algorithms are switched to each other according to a preset error threshold. Theoretical results are demonstrated by the simulation study. The proposed OBSILC can reduce the influence of nonrepetitive initial values and measurement noises in the iterative learning control for MASs by only using I/O data.     

Asymptotic adaptive tracking control and application to mechatronic systems

This article develops an asymptotic tracking control strategy for uncertain nonlinear systems subject to additive disturbances and parametric uncertainties. To fulfill this work, an adaptive-gain disturbance observer (AGDO) is first designed to estimate additive disturbances and compensate them in a feedforward way, which eliminates the impact of additive disturbances on tracking performance. Meanwhile, an updated observer gain law driven by observer estimation errors is adopted in AGDO, which reduces the conservatism of observer gain selection and is beneficial to practical implementation. Also, the parametric uncertainties existing in systems are addressed via an integrated parametric adaptive law, which further decreases the learning burden of AGDO. Based on the parametric adaption technique and the proposed AGDO approach, a composite controller is employed. The stability analysis uncovers the system asymptotic tracking performance can be attained even when facing time-variant additive disturbances and parametric uncertainties. In the end, comparative experimental results of an actual mechatronic system driven by a dc motor uncover the validity of the developed approach.     

Adaptive disturbance attenuation for a class of uncertain nonlinear systems: A double-gain nonlinear observer method

This paper is concerned with the problem of adaptive disturbance attenuation for a class of nonlinear systems. The traditional adaptive methods are almost impossible to compensate the time-varying unknown disturbance by designing parameter adaptive laws without a priori knowledge about the bounds of external disturbances. To solve the problem, a new strategy is proposed by constructing an augmented system where the external disturbance is considered as another component of the augmented state vector. Based on this, a double-gain nonlinear observer is employed to estimate the state of the augmented nonlinear system. Further, an output feedback control strategy is designed, and it is proved that the proposed strategy ensures that all the signals are bounded and the tracking error exponentially converges to an adjustable compact set. Finally, an example is performed to demonstrate the validity of the proposed scheme.     

Robust control of unmanned helicopters with high-order mismatched disturbances via disturbance-compensation-gain construction approach

In this paper, a novel robust control strategy based on disturbance-compensation-gain (DCG) construction approach is proposed for small-scale unmanned helicopters in the presence of high-order mismatched disturbances. The overall control structure consists of two hierarchical layers. The inner-loop controller is to guarantee the stability of the unmanned helicopters subject to high-order mismatched disturbances. With the estimation of the disturbances and their successive derivatives via finite-time disturbance observer (FTDO), by properly designing some disturbance compensation gains, a novel robust controller is developed to remove the high-order mismatched disturbances from the output channels. The outer-loop controller is to produce flight commands for inner-loop system, as well as to track the reference trajectory, which is carried out with the dynamic inversion technique. The simulation results demonstrate that the unmanned helicopters are capable to perform flight missions autonomously with the proposed control strategy.