Presence Of Time-varying Disturbances Research Articles

Adaptive fuzzy extended state observer for a class of nonlinear systems with output constraint

Abstract In this study, an adaptive fuzzy extended state observer (AFESO) for single-input–single-output nonlinear affine systems in the presence of external disturbances and output constraints is proposed. In this regard, an extended state observer (ESO) was employed to estimate the unmeasured states and external disturbances simultaneously. To improve the estimation accuracy, the observer gains were adjusted using an adaptation law. To obtain a more comprehensive mathematical analysis and an accurate model for the ESO and to increase the degree of freedom, a Takagi–Sugeno fuzzy system was employed. The proposed AFESO relaxes the limitations of the ESO and improves the system performance as compared with the classical methods in the presence of time-varying disturbances. Next, a command-filtered backstepping controller is designed based on the barrier Lyapunov function method, which guarantees fast convergence of the tracking error as well as satisfying the output constraints of the system. The stability analysis showed that both the estimation error of the AFESO and the tracking error of the controller are bounded, and the tracking error converges to a small neighborhood of the origin. A simulating example of a flexible-joint manipulator shows the effectiveness of the proposed method as compared with the recently proposed method in the literature.

Robust coverage control of multiple USVs with time-varying disturbances

This paper investigates the problem of optimal coverage control for multiple unmanned surface vehicles (USVs) in the presence of time-varying disturbances. To solve this problem, the disturbance vector observer is designed to approximate the unknown time-varying disturbances. It is demonstrated that the estimated disturbance vector converges to the actual disturbance vector within a finite time. To achieve the optimal coverage effect of the task region, the control idea of layer-by-layer design is borrowed, and the desired velocities of the USV are designed. By following the desired velocities, the USV network can achieve the optimal coverage effect of the task region. Based on the estimated disturbances, a robust coverage controller is designed to achieve the tracking of desired velocities by the USV within a finite time, ultimately achieving optimal coverage effect of the task region by the USV network. Finally, corresponding simulation results are provided to validate the effectiveness of the proposed approach.

A finite-time adaptive sliding mode control based on DOB for AUVs subject to matched and mismatched disturbances

This paper proposes an adaptive sliding mode control (SMC) based on disturbance observer (DOB) for trajectory tracking problem of autonomous underwater vehicles (AUVs). Due to sensitivity of the SMC to mismatched disturbances, this paper presents an adaptive SMC based on a new exponential reaching law. The controller uses a DOB to estimate both matched and mismatched time-varying disturbances. The stability of DOB in the presence of time-varying disturbances is proved via the Lyapunov stability theorem. To design the controller, sliding surfaces containing estimation of the matched and mismatched disturbances are defined. In order to increase the speed of reaching to the surfaces and avoid chattering, the gains of the proposed reaching law have been adapted based on the sliding surfaces. It has been proved that the proposed reaching law converges to the sliding surfaces in a finite time. The stability of the overall system with DOB and controller has also been proved using the Lyapunov technique. A simulation study has conducted to test how the proposed method controls the AUVs to track a desired trajectory when the vehicles are exposed to both matched and mismatched disturbances. The results demonstrate that the performance of the proposed controller is superior to the controllers previously reported in the literature.

Sliding mode controller design based on state estimation for underactuated AUVs in the presence of time-varying disturbances and uncertainties

Sliding mode controller design based on state estimation for underactuated AUVs in the presence of time-varying disturbances and uncertainties

On Active Disturbance Rejection Control in Presence of Measurement Noise

High-gain nature of extended state observer (ESO), which forms an integral part of active disturbance rejection control (ADRC) technique, results in the following limitations: 1) Sensitivity to high-frequency measurement noise which limits closed-loop performance in practical applications. 2) Escalation of observer gains up to a power <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{n+1}$</tex-math></inline-formula> of observer bandwidth, which complicates numerical implementation when system order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\boldsymbol{n})$</tex-math></inline-formula> or observer bandwidth is large. To overcome these limitations, a low-power higher order ESO is proposed in the present work for practical application of ADRC scheme in noisy environment. Moreover, a recently proposed cascade ESO (CESO), designed for noise suppression, is analyzed in the frequency-domain to reveal an underlying similarity with higher-order ESO, which is not reported in literature. Presented analysis justifies the performance improvement obtained over conventional ESO and provides a guideline for selecting the number of cascade levels based on the expected nature of disturbance. Case study performed on a dc–dc boost converter illustrates the practical advantages of proposed scheme over CESO in terms of improved immunity to high-frequency measurement noise, precise regulation in presence of time-varying disturbance, low observer gains that facilitate numerical implementation, and ease of tuning due to a single observer parameter.

Adaptive fault-tolerant control for an autonomous underwater vehicle

AbstractIn recent years, using autonomous underwater vehicles (AUVs) for submarine missions has increased substantially. One of the problems in controlling these nonlinear devices is the possibility of a fault in the system operators. Failure causes increased operating costs and reduced vehicle performance. Therefore, the use of fault tolerance control is essential to ensure the stability and ability of the device to continue its activity. The focus of this article is on the trajectory tracking control for an underactuated AUV with actuator faults using kinematics and dynamics modeling. An adaptive rule is used as an online estimation to compensate for malfunctions in robot performance. In this regard, the adaptive fault-tolerant control plan is proposed, so that the closed-loop system is stable, and all control objectives are achievable. At first, the dynamic model of AUV with actuator fault and disturbance is described. Next, the control algorithm is designed for trajectory tracking in the presence of time-varying disturbances and actuator faults. The proposed adaptive rules will overcome disturbances and actuator faults. Finally, to illustrate the effectiveness of the proposed method, the provided controller is compared with other common control methods.

Design of a Novel Integral Sliding Mode-Based Composite Nonlinear Feedback Controller for Electrostatic MEMS Micromirror

In this study, the precise tracking problem for electrostatic micromirror systems with disturbances and input saturation is investigated. Inspired by the composite nonlinear feedback (CNF)’s improvement of the transient performance and the sliding mode control’s enhancement of the robustness, a novel integral sliding mode with reaching law (ISMRL)-based composite nonlinear feedback (CNF) controller is proposed. Then, the stability of the closed-loop system is proved based on Lyapunov theorem. Finally, numerical simulations are investigated to evaluate the effectiveness of the proposed scheme. It is shown that the closed-loop system with the proposed scheme has precise positioning and improved transient performance in presence of time-varying disturbances.

Composite nonlinear feedback–based adaptive integral sliding mode control for a servo position control system subject to external disturbance

This paper presents a composite nonlinear feedback–based adaptive integral sliding mode controller with a reaching law (CNF-AISMRL) for fast and accurate control of a servo position control system subject to external disturbance. The proposed controller exploits the advantages of composite nonlinear feedback (CNF) and sliding mode control (SMC) schemes to improve the transient performance and increase the robustness of the closed-loop system. An integral sliding mode combined with a quick reaching law is designed to eliminate the effect of disturbances, which mitigates chattering and achieves finite-time convergence of the sliding mode. An adaptation tuning approach is utilized to deal with unknown but bounded system uncertainties and disturbances. When considering the model uncertainties and disturbances, the stability of the closed-loop system is verified based on the Lyapunov theorem. Numerical simulations are investigated to the effectiveness of the proposed scheme. The transient performance of load disk position to step signal with disturbances using CNF, composite nonlinear feedback based integral sliding mode control (CNF-ISM), and the proposed CNF-AISMRL schemes is given. The simulation results indicate that, without acquiring the knowledge of bounds on system disturbances, the proposed control scheme has superior performance in the presence of time-varying disturbances.

Disturbance-observer-based attitude control under input nonlinearity

A disturbance observer-based control scheme is proposed in this paper to deal with the attitude stabilization problems of spacecraft subjected to external disturbances, parameter uncertainties, and input nonlinearities. Particularly, the proposed approach addresses the dead-zone issue, a non-smooth nonlinearity affiliated with control input that significantly increases controller design difficulties. A novel nonlinear disturbance observer (NDO) is developed, which relaxes the strong assumption in conventional NDO design that disturbances should be constants or varying with slow rates. After that, a special integral sliding mode controller (ISMC) is combined with the NDO to achieve asymptotic convergence of system states. Simulations are performed in the presence of time-varying disturbances, parameter uncertainties, and dead-zone nonlinearity to justify the effectiveness of the proposed control scheme.

Disturbance Estimation-Based Robust Model Predictive Position Tracking Control for Magnetic Levitation System

This article presents an improved equivalent input disturbance observer-based model predictive control (IEIDO-based MPC) scheme for position tracking control of a magnetic levitation system. It overcomes the problem of the position tracking performance degradation for the magnetic levitation system in the presence of time-varying disturbances. To enhance the accuracy of estimation, an IEIDO is first proposed to estimate both the system states and the time-varying equivalent input disturbance. The estimations of IEIDO are then integrated into the MPC design for output position prediction. Afterward, an explicit analytical form of the optimal predictive controller is obtained to achieve the optimized tracking performance, as well as the fine robustness against lumped time-varying equivalent input disturbance. Rigorous stability analysis shows that the closed-loop system is stable. Simulation and experimental results demonstrate the effectiveness of the proposed method as compared with the conventional EID and Luenberger observer-based integral MPC approaches.

Robust particle filtering with enhanced outlier resilience and real-time disturbance compensation

This paper is concerned with the state estimation problem for nonlinear/non-Gaussian systems suffered from both time-varying disturbances (TVD) and measurement outliers. Conventional particle filtering (PF) approach can be used to track the non-Gaussian probability density functions, but its sampling efficiency is degraded in the presence TVD. To address this problem, we propose a disturbance observer based PF (DOBPF) method where the knowledge on the dynamics of TVD are fully exploited and real-time disturbance compensation is achieved. Furthermore, to enhance the resilience of our method against outliers, we adopt the skew-t distribution to characterize both skewness and heavy-tailedness of the measurement noise. On this basis, the variational Bayes approach is incorporated into the DOBPF under the marginalization PF framework to infer the noise statistics. Compared with conventional PF approaches, the proposed outlier-resilient DOBPF method exhibits improved resilience against measurement outliers and increased sampling efficiency in the presence of TVD. Simulation and experimental results confirm the effectiveness of the proposed algorithm.

Time-energy efficient guidance strategy for a realistic 3D interceptor: An adaptive robust time-delayed control approach with input saturation

To achieve successful interception of a target by a missile with efficient time-energy utilization and robustness against external disturbances, a consolidated guidance approach has been proposed in this manuscript. Time-energy efficiency has been accomplished by employing Sine-Cosine algorithm to generate a near-optimal reference trajectory for the pitch and yaw heading angles. Thereafter, an adaptive robust time delayed controller has been designed to track the reference trajectory thus providing robustness towards uncertainties. To incorporate realistic aspect in the interceptor scenario, input saturation has been considered for the lateral acceleration of the missile. Stability analysis has been performed using a suitable Lyapunov function which proves Uniformly Ultimately Bounded (UUB) stability of the system through the proposed control approach. The efficacy of the proposed methodology has been verified through simulations involving various engagement scenarios. The simulation results demonstrate the superior tracking performance of the proposed method in the presence of time-varying disturbances.

H∞ robust perimeter flow control in urban networks with partial information feedback

Perimeter control is an effective city-scale solution to tackle congestion problems in urban networks. To accommodate the unpredictable dynamics of congestion propagation, it is essential to incorporate real-time robustness against travel demand fluctuations into a pragmatic perimeter control strategy. This paper proposes robust perimeter control algorithms based on partial information feedback from the network. The network dynamics are modeled using the concept of the Macroscopic Fundamental Diagram (MFD), where a heterogeneously congested network is assumed to be partitioned into two homogeneously congested regions, and an outer region that acts as demand origin and destination. The desired operating condition of the network is obtained by solving an optimization program. Observer-based H∞ proportional (P) and proportional-integral (PI) controllers are designed based on Lyapunov theory, to robustly regulate the accumulation of each region and consequently to maximize the network outflow. The controller design algorithms further accommodate operational constraints by guarantying: (i) the boundedness of the perimeter control signals and (ii) a bounded offset between the perimeter control signals. Control parameters are designed off-line by solving a set of linear matrix inequalities (LMI), which can be solved efficiently. Comprehensive numerical studies conducted on the nonlinear model of the network highlight the effectiveness of the proposed robust control algorithms in improving the congestion in the presence of time-varying disturbance in travel demand.

Trajectory generation and tracking on SE(3) for an underactuated AUV with disturbances

This paper describes the trajectory tracking of an underactuated autonomous underwater vehicle (AUV) with three control inputs (surge, yaw and pitch moment) that operates in the presence of time-varying disturbances. The AUV kinematics are described in global coordinates as a Hamiltonian system on the Lie group SE(3) and the boundary-value problem arising from the geometric framing of Pontryagin’s Maximum Principle is applied to the vehicle kinematics. This 6-dimensional boundary value problem is solved using a numerical shooting method and a novel semi-analytical Lie group integrator. The integrator uses Rodrigue’s formula to express the exact solution of the solution curves, is symplectic and preserves energy and momentum. Inverse dynamics is applied to construct an inner-loop controller, which accounts for constraints on maximum torque and force via time reparametrization. This inner-loop control, which would drive the AUV along the reference trajectory in perfect conditions, is combined with a disturbance observer to construct an outer-loop controller, which ensures stability in the presence of bounded disturbances. Simulation results complete the work.

Intelligent Observer-Based Feedback Linearization for Autonomous Quadrotor Control

The presence of disturbances can cause instability to the quadrotor flight and can be dangerous especially when operating near obstacles or other aerial vehicles. In this paper, a hybrid controller called state feedback with intelligent disturbance observer-based control (SF-iDOBC) is developed for trajectory tracking of quadrotor in the presence of time-varying disturbances, e.g. wind. This is achieved by integrating artificial intelligence (AI) technique with disturbance observer-based feedback linearization to achieve a better disturbance rejection capability. Here, the observer estimates the disturbances acting on the quadrotor, while AI technique using the radial basis function neural network (RBFNN) compensates the disturbance estimation error. To improve the error compensation of RBFNN, the k-means clustering method is used to find the optimal centers of the Gaussian activation function. In addition, the weights of the RBFNN are tuned online using the derived adaptation law based on the Lyapunov method, which eliminates the offline training. In the simulation experiment conducted, a total of four input nodes and five hidden neurons are used to compensate for the error. The results obtained demonstrate the effectiveness and merits of the theoretical development.Â

Adaptive command-filtered fuzzy backstepping control for linear induction motor with unknown end effect

In this paper, the problem of the speed control is considered for linear induction motor with the end effects, uncertain system parameters, and external load disturbance. Firstly, the proposed controller is based on backstepping method, and the adaptive laws are designed.The fuzzy logic modeling approach is used to deal with the unknown nonlinear functions and uncertain parameters. Secondly, a constrained command filter is employed to overcome the problem of differential expansion and controller saturation in the backstepping method, and a filter’s compensating signal is used to mitigate the error caused by the constrained command filter. Thirdly, the projection operator introduced in the adaptive laws guarantees boundedness of the estimated functions and robustness of the designed controller in the presence of time-varying disturbances and uncertainties. Thus, the proposed control controller can ensure that all response signals in the closed-loop system are bounded. Finally, the effectiveness of the proposed controller is verified by simulation and comparison with command-filtered backstepping controller.

Velocity-Free Attitude Stabilization of a Nadir-Pointing Underactuated Rigid Spacecraft

This paper examines the velocity-free attitude stabilization of an underactuated nadir-pointing rigid spacecraft in a circular orbit in the presence of time-varying disturbances. A nonlinear observer is used to estimate the angular velocity of the spacecraft to complete an output feedback control law. A sliding-mode control strategy is proposed for this stabilization problem in conjunction with a nonlinear observer. The local ultimate boundedness of the closed-loop system is rigorously proven. Numerical examples demonstrate the performance of the controller in the presence of time-varying disturbances, nonzero orbital eccentricity, inertia matrix uncertainties, and measurement noise in a sampled data implementation. In particular, even though the theoretical ultimate boundedness guarantees are local, the numerical examples demonstrate ultimate boundedness with large initial attitude errors.

Predictor‐based output feedback control design for sampled systems with input delay subject to disturbance

In this study, a predictor-based output feedback control design is proposed for sampled systems with input delay subject to disturbance. An extended state observer (ESO) is first constructed to simultaneously estimate the system state and disturbance based on only the output measurement. Then a filtered predictor is constructed by using the estimated state and disturbance to compensate the input delay so as to improve the disturbance rejection performance. For the presence of a constant or asymptotically stable disturbance, a robust H infinity feedback control design based on state prediction and disturbance estimation is proposed to realise no steady-state output error, despite mismatched disturbance. When there exists a time-varying disturbance with deterministic dynamics, such as a sinusoidal type, the proposed predictor can achieve a small prediction error by properly tuning the filter, such that the existing observer-based feedback control methods for delay-free systems can be directly adopted to stabilise such a system with input delay. Moreover, the output error bounds in the presence of time-varying disturbance are quantitatively analysed for using the ESO-based predictor feedback and anti-disturbance predictor feedback, respectively. Two illustrative examples are given to demonstrate the effectiveness and merit of the proposed method.

Robust control for disturbed buck converters based on two GPI observers

The output voltage tracking problem of a disturbed buck converter is investigated in this paper via a GPI observer-based approach. Control performances of the converters are always influenced by undesirable effects of disturbances. These disturbances usually are of time-varying forms. Conventional backstepping schemes cannot achieve satisfactory performances in handling time-varying disturbances. By adding integral actions into the controller, only the slow-varying disturbances are asymptotically compensated in this way. In this paper, two GPI observers are constructed to estimate the lumped time-varying disturbances. By introducing the disturbance estimations into the design process, a composite GPI observer-based robust control scheme is developed. The proposed algorithm performs a promising disturbance rejection ability. Rigorous stability is guaranteed. Experimental results in the presence of time-varying disturbances are illustrated to show the feasibility of the proposed composite method.

A self-learning disturbance observer for nonlinear systems in feedback-error learning scheme

This paper represents a novel online self-learning disturbance observer (SLDO) by benefiting from the combination of a type-2 neuro-fuzzy structure (T2NFS), feedback-error learning scheme and sliding mode control (SMC) theory. The SLDO is developed within a framework of feedback-error learning scheme in which a conventional estimation law and a T2NFS work in parallel. In this scheme, the latter learns uncertainties and becomes the leading estimator whereas the former provides the learning error to the T2NFS for learning system dynamics. A learning algorithm established on SMC theory is derived for an interval type-2 fuzzy logic system. In addition to the stability of the learning algorithm, the stability of the SLDO and the stability of the overall system are proven in the presence of time-varying disturbances. Thanks to learning process by the T2NFS, the simulation results show that the SLDO is able to estimate time-varying disturbances precisely as distinct from the basic nonlinear disturbance observer (BNDO) so that the controller based on the SLDO ensures robust control performance for systems with time-varying uncertainties, and maintains nominal performance in the absence of uncertainties.