Unknown Exogenous Disturbances Research Articles

Disturbance observer-based event-triggered impulsive control for nonlinear systems with unknown external disturbances

Input-to-state practical stability (ISpS) of a kind of nonlinear systems suffering from unknown exogenous disturbances is explored in this article, where a disturbance observer is established to estimate the information of the exogenous disturbances. To achieve ISpS of the system, the impulsive controller as well as state-feedback controller are both considered to regulate the discrete and continuous dynamics of the system, respectively. Especially, a novel disturbance observer-based event-triggered mechanism is devised to decide the release of impulsive control signal. Furthermore, several adequate conditions are given for excluding the occurrence of Zeno phenomenon. To confirm the feasibility of the proposed results, two numerical instances and their corresponding simulation results are presented.

A dual scale spatio‐temporal control for complex distributed parameter systems

AbstractIt is very difficult to control the distributed parameter system (DPS) for consistent spatial performance. In this paper, a dual scale spatio‐temporal control is designed for the DPS to achieve a consistent performance across the entire workspace under unknown exogenous disturbances. First, the generalized “spatial observer” should be designed under spectral decomposition/synthesis, to act as the nominal model of the DPS, through which the spatial mismatch between the model and the process could be estimated. Then a distributed disturbance compensator can be constructed to suppress all the undesirable spatial disturbance through the inner loop, and the compensated system will become closer to the nominal model and easier to control. Third, a dual controller will be designed in the outer loop for the final consistent spatial performance. Since the spatial performance is mainly affected by the dominant dynamics on the slow scale, a convex optimization algorithm can be effectively established in terms of nonlinear matrix inequalities for the dual controller. In this way, the nonlinear optimization problem is solved by converting it into the problem of a linear matrix inequalities with constraints. Besides, the spatio‐temporal state variable of the controlled plant is demonstrated to converge in Hilbert space. The feasibility and effectiveness of the proposed control method are verified by temperature control of a catalytic rod, a benchmark in chemical reactors.

Leader-following consensus tracking control for fractional-order multi-motor systems via disturbance-observer

Abstract The leader-following consensus tracking control of fractional-order (FO) multi-motor systems (FOMMSs) in the presence of exogenous disturbances is investigated. It is widely recognized that FO models are better than integer-order (IO) ones for representing systems with memory effects. Therefore, studying the consensus tracking control of FOMMSs is essential. In this paper, a consensus tracking protocol is developed using a disturbance-observer and state feedback to deal with unknown exogenous disturbances. The closed-loop system stability is analyzed via Lyapunov and graph theory. Novel sufficient conditions for the stabilization of each motor are derived in the form of linear matrix inequalities. Simulation results illustrate the validity and efficacy of the proposed consensus protocol, namely its strong synchronization ability and robustness.

Robust synchronization of four-dimensional chaotic finance systems with unknown parametric uncertainties

ABSTRACT The inherent randomness in economic factors causes complex and irregular behaviour that affects financial system stability and economic growth. Such chaotic behaviour can make it difficult to synchronize financial systems. The chaotic finance system synchronization precision maintains financial stability and economic growth. In this paper, the controller design procedure assumes that the financial system is exposed to unknown bounded exogenous disturbances and model uncertainties. This research proposes a novel direct adaptive control strategy that achieves robust synchronization of two identical four-dimensional finance chaotic (FDFC) systems. The proposed controller establishes a faster, smoother synchronization error vector convergence to zero. The controller design procedure does not eliminate the closed-loop's nonlinear terms and is independent of the financial system parameters. These controller's attributes accomplish the closed-loop robust performance. Further, this controller uses real-time estimates of unknown model uncertainties and bounds to compensate for unknown exogenous disturbances. Computer simulation results and proofs of theoretical analysis based on the Lyapunov stability theory confirm that the proposed control technique compels the error vector trajectories to the origin in a short transient time with less active oscillations for all signals. The paper includes comparative computer simulations for verifying the theoretical findings.

An adaptive robust path-tracking control algorithm of multi-articulated and redundantly actuated virtual track train

Multi-articulated and redundantly actuated virtual track trains (VTTs) are inevitably exposed to unknown exogenous disturbances and various operating conditions. To address the complex over-actuated tracking-control problem, this study proposes a decoupling control scheme for an all-wheel independent drive and all-wheel active steering VTT composed of multiple modules, wherein the adaptive robust path-tracking and longitudinal speed control algorithms of the VTT are decoupled. An appropriate control-oriented nonlinear dynamic model for VTT path-tracking control is formulated using Lagrange’s equations. To compensate for the model uncertainties and environmental disturbances without priors and parameter estimations, a robust control algorithm using radial basis function neural network and sliding mode is proposed. The asymptotic stability of the algorithm is proved, and its adaptation law is derived using the Lyapunov theory. Moreover, a novel traction/braking control algorithm based on the wheel speed distribution model and double closed-loop control algorithm is suggested. Using a multi-body dynamic model of the VTT with seven modules, simulations are performed to evaluate the effectiveness and superiority of the proposed path-tracking algorithm. The obtained results indicate that the proposed algorithm could realise the expectable performance of the VTT path tracking and longitudinal speed control. Moreover, the proposed control algorithm has good scalability for multi-articulated and redundantly actuated VTT.

Design of equivalent‐input‐disturbance estimator based modified repetitive control with adaptive periodic event‐triggered for time‐varying delay nonlinear systems

AbstractThis article addresses the problems of the disturbance rejection and the periodic signal tracking for a class of time‐varying delay nonlinear systems subjected to unknown exogenous disturbances. To approximate the nonlinearity of the system, a Takagi‐Sugeno (T‐S) fuzzy model has been used. The proposed modified repetitive controller (MRC) scheme based on the equivalent‐input‐disturbance (EID) estimator improves the performance of periodic and aperiodic unknown disturbances rejection effectively and achieves good tracking performance for periodic references. Furthermore, an adaptive periodic event triggered mechanism based fuzzy state observer (APETM‐FSO) has been utilized to reduce data transmission, energy consumption, and computational burden, save the resources of communication. With the help of a designed adaptive event triggering condition, the APETM can detect the event occurrence, which is described by exceeding the error signal to a predetermined threshold. Only when the event occurs, the current data are transmitted otherwise, data can be kept unchanged using a zero‐order hold. Hence, The MRC, EID, and APETM‐FSO based on a time‐varying delay T‐S fuzzy model construct the overall system. Then, to achieve the asymptotic stability of the overall system subjected to unknown disturbances, sufficient conditions based on the Lyapunov–Krasovskii functional stability theory and linear matrix inequalities (LMIs) are derived. In addition, the FSO and fuzzy state feedback controller gains are designed using the matrix decomposition and LMI approaches. Simulation results with comparative study are presented to demonstrate the effectiveness and feasibility of the proposed scheme.

Synchronization Of Two-Rotor Vibration Units Using Neural Network-Based PID Controller

In the paper, the problem of controlled synchronization of Two-rotor Vibration Units is considered. A new bidirectional control law combined with Neural Network based PID controller is proposed for multisynchronization of rotors. Besides, an algorithm for design of Neural Network based PID Controller of Two rotor Vibration Units is developed. The robustness of the proposed controller under the effect of unknown exogenous disturbances is illustrated.

Disturbance Rejection and Predictive Control for Systems With Input and Output Delays

Disturbance rejection and time-delay compensation are important for control systems in practice. This article presents an observer-and-predictor-based method to reject an unknown exogenous disturbance for an input-delay system in which only delayed output is available. First, the equivalent-input-disturbance method is employed to reconstruct the system state and to estimate the disturbance. A prediction of the disturbance is calculated to reduce the effect of a phase lag caused by the delays. A new predictive scheme is designed for feedback control. Next, the system is divided into two subsystems for analysis and design: one for reference tracking and the other for disturbance rejection. Sufficient conditions are derived to guarantee the system’s stability. An analysis of the method reveals that the disturbance rejection can be viewed as a patch to the predictor-based feedback control. Finally, two case studies are used to show the validity and superiority of the method.

Attenuated-chattering adaptive second order variable structure controller for mismatched uncertain systems

In this paper, an attenuated-chattering adaptive second order variable structure controller (ACASOVSC) is proposed for mismatched uncertain systems using a Moore-Penrose inverse method. The key achievements of this study include three tasks: 1) influence of the chattering in control input is diminished, 2) finite-time convergence of system states is guaranteed, and 3) external disturbance is generally assumed to be unknown in advance. Firstly, a switching manifold which comprises only output information is defined. Secondly, a reduced-order variable structure estimator (ROVSE) with lower dimension is designed to reduce the computation burden and enhance the robustness. Thirdly, an adaptive approach is used to guess the upper bound of the unknown exogenous disturbance. Next, an ACASOVSC is investigated for attenuating the chattering phenomenon and stabilizing the system. Then, a novel linear matrix inequality (LMI) constraint by the Lyapunov technique is given such that the plant is entirely invariant to matched uncertainties and asymptotically stable. Finally, a mathematical illustration is simulated, which exhibits the usefulness and the feasible application of the proposed method.

Periodic event-triggered modified repetitive control with equivalent-input-disturbance estimator based on T-S fuzzy model for nonlinear systems

In this paper, the periodic signal tracking and the disturbance rejection problems are considered for a class of time-varying delay nonlinear systems with unknown exogenous disturbances under limited communication resources. The Takagi–Sugeno (T-S) fuzzy model is used to approximate the nonlinear system. The developed scheme achieves periodic reference tracking and improves the performance of periodic and aperiodic unknown disturbances rejection effectiveley. This can be operated by incorporating the equivalent-input-disturbance (EID) estimator with the modified repetitive controller (MRC) scheme. Moreover, a fuzzy periodic event-triggered feedback observer (FPETFO) is proposed for the purpose of reducing the computational burden, energy consumption and saving communication resources. The periodic event-triggered technique is designed to observe the occurrence of an event which is described by an error signal. When this error signal exceeds a prescribed threshold, the event occurs and the current data are transmitted; otherwise, there is a zero-order hold to keep data unchanged. The overall system consists of MRC, EID and FPETFO based on a T-S fuzzy model. Then, some sufficient conditions are derived to gurantee the asymptotic stability of the overall system subjected to unknown disturbances using the Lyapunov–Krasovskii functional (LKF) stability theory and linear matrix inequalities (LMIs). The fuzzy state feedback controller and observer gains are designed using the LMI and matrix decomposition approaches. Simulation results illustrate the effectiveness and feasibility of the proposed scheme with comparative study.

Improved radial basis function artificial neural network and exact-time extended state observer based non-singular rapid terminal sliding-mode control of quadrotor system

PurposeThe purpose of this paper is to design a hybrid robust tracking controller based on an improved radial basis function artificial neural network (IRBFANN) and a novel extended-state observer for a quadrotor system with various model and parametric uncertainties and external disturbances to enhance the resiliency of the control system.Design/methodology/approachAn IRBFANN is introduced as an adaptive compensator tool for model and parametric uncertainties in the control algorithm of non-singular rapid terminal sliding-mode control (NRTSMC). An exact-time extended state observer (ETESO) augmented with NRTSMC is designed to estimate the unknown exogenous disturbances and ensure fast states convergence while overcoming the singularity issue. The novelty of this work lies in the online updating of weight parameters of the RBFANN algorithm by using a new idea of incorporating an exponential sliding-mode effect, which makes a remarkable effort to make the control protocol adaptive to uncertain model parameters. A comparison of the proposed scheme with other conventional schemes shows its much better performance in the presence of parametric uncertainties and exogenous disturbances.FindingsThe investigated control strategy presents a robust adaptive law based on IRBFANN with a fast convergence rate and improved estimation accuracy via a novel ETESO.Practical implicationsTo enhance the safety level and ensure stable flight operations by the quadrotor in the presence of high-order complex disturbances and uncertain environments, it is imperative to devise a robust control law.Originality/valueA new idea of incorporating an exponential sliding-mode effect instead of conventional approaches in the algorithm of the RBFANN is used, which makes the control law resistant to model and parametric uncertainties. The ETESO provides rapid and accurate disturbance estimation results and updates the control law to overcome the performance degradation caused by the disturbances. Simulation results depict the effectiveness of the proposed control strategy.

Accelerating self-optimization control of refrigerant cycles with Bayesian optimization and adaptive moment estimation

This paper presents a model-free self-optimization control algorithm for modulating multiple inputs simultaneously to minimize the power consumption of a vapor compression system (VCS). We propose the use of Bayesian Optimization (BO) to warm-start a state-of-the-art extremum seeking control (ESC) algorithm and then accelerate the ESC on-line with Adam, a well-studied adaptive moment-based optimization method used to solve high-dimensional non-convex optimization problems such as training deep neural networks. BO initializes the ESC at conditions favorable for rapid convergence while concurrently learning a surrogate map of VCS power consumption as a function of the inputs. In addition, the warm-start increases the likelihood of attaining a global optimum for locally convex, but globally non-convex, objective functions by identifying regions where the global optimum most likely resides. The proposed algorithm is evaluated using a Modelica model of an air conditioning system with variable compressor speed, an electronic expansion valve and two variable speed fans. We demonstrate the acceleration of this algorithm in simulations of an occupied space with a realistic heat pump model with realistic ambient temperature profiles, variation in heat-load, and different actuation rates. We also show that, in spite of the presence of unknown exogenous disturbances, the proposed algorithm computes better set-points, faster than the ESC. We also observe that the proposed method improves transient performance compared to the state-of-the-art. • Learn calibration cost functions instead of dynamical models for setpoint optimization. • Energy model learned analytic model of underlying system dynamics. • Accelerate convergence of extremum-seeking algorithms via Bayesian optimization. • Optimize many setpoints at various operating modes without re-estimating gradient. • Case study with high-fidelity Modelica heat pump model in realistic environment.

Bipartite containment for linear multi‐agent systems subject to unknown exogenous disturbances

AbstractThis study concentrates on the bipartite containment of multi‐agent systems (MASs) in signed communication topology with antagonistic interactions. Different from the subsistent related works, disturbances generated from exogenous systems are considered, and an observer‐based approach is developed to estimate them. Two distributed disturbance‐observer‐based controllers are accordingly designed via full state‐feedback control and dynamic output‐feedback control. By utilizing stability theories and other mathematical analyses, sufficient criteria are established to reach asymptotic bipartite containment control. Finally, simulations are used to certify the effectiveness and correctness of theoretical results.

Modified repetitive periodic event-triggered control with equivalent-input-disturbance for linear systems subject to unknown disturbance

ABSTRACT This paper studies the disturbance rejection and the periodic signal tracking problems for linear systems with unknown exogenous disturbances under limited communication resources. The developed scheme achieves periodic reference tracking and improves the performance of periodic and aperiodic unknown disturbances rejection by incorporating the equivalent-input-disturbance (EID) estimator with the modified repetitive controller (MRC). Furthermore, a periodic event-triggered feedback observer (PETFO) is proposed to reduce the computational burden and energy consumption, and saving communication resources. The PETFO observes the occurrence of a predetermined event or not, where the current data are transmitted only when the event occurs otherwise, there is a zero-order hold keeps the data unchanged. The stability of the overall systems is guaranteed using the Lyapunov Krasovskii functional theory and linear matrix inequalities (LMIs). The observer and the controller gains are designed using the LMI and matrix decomposition approaches. Simulation results illustrate the effectiveness and feasibility of the proposed scheme.

Robust Tracking Control of a Quadrotor Unmanned Aerial Vehicle-Suspended Payload System

In this article, the control problem for the underactuated dynamic system, which consists of a quadrotor unmanned aerial vehicle and a suspended payload is investigated under the effects of unknown exogenous disturbances. A novel nonlinear controller based on the robust integral of the sign of the error is developed to deal with the position trajectory tracking control and the antiswing control of the suspended payload with the presence of unknown air turbulence. The Lyapunov-based stability analysis is employed to prove the asymptotic stability of the closed-loop system. The real-time experimental results are presented to verify the performance of the proposed control design.

Observer‐based model reference control of Takagi–Sugeno–Lipschitz systems affected by disturbances using quadratic boundedness

AbstractIn this paper, a model reference control strategy is proposed in order to perform trajectory tracking in Takagi–Sugeno–Lipschitz (TSL) systems. Since the state vector is assumed not to be completely available for measurement, a proportional observer is added to the control scheme in order to apply an estimate‐feedback control action instead of a state‐feedback one. The overall design of both the controller and the observer gains are performed using a Lyapunov‐based quadratic boundedness specification, in order to improve the robustness against unknown exogenous disturbances. It is shown that the conditions that ensure convergence within ellipsoidal regions of the tracking and estimation errors can be expressed in the form of a linear matrix inequality (LMI) formulation. The effectiveness of the developed control strategy is demonstrated by means of simulation results.

Disturbance rejection and performance analysis for nonlinear systems based on nonlinear equivalent-input-disturbance approach

This paper presents a nonlinear equivalent-input-disturbance (NEID) approach to rejecting an unknown exogenous disturbance in a nonlinear system. An NEID compensator has two parts: a conventional equivalent-input-disturbance estimator and a nonlinear state feedback term. This design ensures that only the exogenous disturbance is rejected and the useful nonlinearity of the system is retained. Unlike other active disturbance-rejection methods, a Lipschitz condition is not necessary to guarantee the convergence of the observation error. Analysis of control performance provides upper bounds for the evaluation of disturbance rejection and the degree of nonlinearity retention. Numerical examples show the validity and superiority of this method.

Nonlinear Disturbance Observer Based Sliding Mode Control of Quadrotor Helicopter

This paper develops tracking control of quadrotor unmanned air vehicle in the presence of parametric uncertainties and mismatched exogenous disturbances. First, a traditional sliding mode control (SMC) law is synthesized for a nominal model without parametric uncertainties and disturbances to achieve nominal control performance. Then to compensate the system uncertainties existing in the actual system, gain-scheduling based SMC law is synthesized. However, the gained scheduled SMC does not provide better control performance in the presence of unknown exogenous disturbances existing in actual system. To end this, a novel nonlinear disturbance observer is integrated with gain scheduled SMC to counteract the exogenous disturbances and attain the performance of reference nominal model. The proposed nonlinear disturbance observer SMC method exhibits the following two salient characteristics: first, the design gains should be greater than the bound of disturbance estimation error rather than that of disturbances, second; in the absence of uncertainties the nominal control performance of sliding mode control strategy is retained. The stability analysis of the proposed control strategy is validated using Lyapunov theorem. Finally, numerical simulation results are exhibited to illustrate the efficacy of the proposed control strategy.

Sliding-Mode Disturbance Observer-Based Control for Fractional-Order System with Unknown Disturbances

This paper concentrates on the disturbances estimation and attenuation problem of a general class of the fractional-order systems. For this purpose, this paper proposes a fractional sliding-mode disturbance observer (FSMDO)-based control scheme, which is capable of mitigating the unknown disturbances asymptotically. Meanwhile, by incorporating a novel fractional sliding-mode controller into the proposed control scheme, the asymptotical convergence of trajectory tracking errors is guaranteed. The developed control scheme owns three attractive highlights: (1) it is suitable for the general fractional-order systems, including nonlinear systems and incommensurate systems; (2) the proposed FSMDO can estimate the unknown exogenous disturbances and system uncertainties timely and precisely; (3) nominal performance can be retained by compensating the observed disturbances in a feedforward manner, and thus, the robustness of the system can be strengthened. Illustrative examples are provided to show the availability and superiority of the presented FSMDO control method in terms of robust control. As compared with the conventional methods, the dynamic control performance of the closed-loop system can be improved.

Nonlinear Robust Fault-Tolerant Control of the Tilt Trirotor UAV Under Rear Servo's Stuck Fault: Theory and Experiments

This paper presents a fault-tolerant control strategy to deal with the rear servo's stuck fault together with unknown exogenous disturbances of a trirotor unmanned aerial vehicle. A supertwisting-based observer is utilized to estimate the rear servo's stuck fault which is unknown, and a robust integral of the signum of the error based fault-tolerant controller is designed to compensate for the observation errors and exogenous disturbances. To avoid the singularity associated with orientation representations, the unit quaternion is utilized to formulate the attitude controller. The composite stability is analyzed via the Lyapunov-based methodology. Real-time experiments are implemented on a self-built hardware-in-loop-simulation trirotor testbed and the contrast experimental results with the sliding-mode-based fault-tolerant controller show that the proposed control scheme has achieved better control performance under the rear servo's stuck fault.