Discrete-time Disturbance Observer Research Articles

Discrete-time integral terminal sliding mode load following controller coupled with disturbance observer for a modular high-temperature gas-cooled reactor

With the appearance of digital computers and microprocessor technologies, the control systems used in nuclear reactors continue to transform from analog devices to digital ones in recent years. A heavy challenge is that applying the pre-existing intelligent load following control algorithms developed in the continuous-time domain to the current digital devices of the nuclear reactors may yield the so-called digital chattering effects, and even trigger system instability. To this end, this paper presents a discrete-time integral terminal sliding mode controller (DTITSMC) coupled with a discrete-time disturbance observer (DTDO) for the load following of a modular high-temperature gas-cooled reactor (MHTGR). The common continuous-time MHTGR model is first transformed into a discrete-time form with consideration of model uncertainties, exogenous disturbances, and discretization errors. Then, on the basis of this discrete-time MHTGR model, a DTDO that can estimate the lumped disturbances, composed of model uncertainties, exogenous disturbances, discretization errors, and unmeasured system states, is developed, subsequently being combined with the designed DTITSMC scheme in order to enhance the system robustness. The proposed DTITSMC scheme coupled with the DTDO is novel in that it can be directly implemented on the digital control system of the MHTGR, while at the same time providing an improved load following control performance, owing to the integration of the state-of-the-art sliding mode control techniques, backstepping control techniques, and the disturbance feedforward compensation supported by the disturbance observer techniques. Both the estimation error convergence of the DTDO and the overall system stability are theoretically proved by the Lyapunov stability theory in this paper. Finally, the feasibility and superiority of the proposed DTITSMC scheme coupled with the DTDO over the previous discrete-time linear sliding mode controller (DTLSMC) and discrete-time proportional–integral–derivative controller (DTPIDC) are further confirmed by simulation studies, where in the absence of lumped disturbances, the value of the accumulative absolute load error (AALE) produced by the proposed DTSMPPC scheme coupled with the DTDO is merely 0.0575% and 0.2675% to that of the previous DTLSMC and the optimized DTPIDC, respectively, while in the presence of lumped disturbances, the value of the AALE produced by the proposed DTSMPPC scheme coupled with the DTDO is merely 0.006% and 0.1952% to that of the previous DTLSMC and the optimized DTPIDC, respectively.

Distributed sliding mode consensus control for multiple discrete-Time Euler-Lagrange systems

This paper studies the consensus problem for multiple discrete-time Euler-Lagrange (DTEL) systems via distributed sliding mode control under a directed graph. Different from the existing work, we transform the DTEL system into a discrete-time second-order nonlinear system through the famous Euler’s first-order approximation method, and a local discrete-time disturbance observer (DTDO) is introduced to estimate both model uncertainties and external disturbances. In addition, a novel integral sliding surface is proposed to guarantee that the consensus error is asymptotically stable when agents move on the sliding surface. Based on such a sliding manifold combined with the proposed DTDO, a distributed sliding mode controller is constructed. Meanwhile, a sufficient condition is derived to ensure the existence of the quasi-sliding mode motion. Finally, numerical simulations of the two-link robot arm’s system are carried out to verify the effectiveness of the proposed control algorithm.

Discrete-time adaptive predictive sliding mode trajectory tracking control for dynamic positioning ship with input magnitude and rate saturations

This paper investigates the discrete-time adaptive predictive sliding mode trajectory tracking control problem based on a reference sliding mode trajectory for the dynamic positioning ship with model uncertainty, environmental disturbances and input magnitude and rate saturations. Initially, a two-step delay discrete-time disturbance observer is designed to estimate the model uncertainty and environmental disturbances, and the input constraints are processed by quadratic programming. Then, an adaptive expected heading is proposed to ensure faster trajectory tracking and more stable heading changes simultaneously. Furthermore, using a double closed-loop control strategy, a new discrete-time virtual velocity controller is designed in the outer loop based on Euler discretization to convert trajectory tracking into velocity tracking. In the inner loop, a discrete-time adaptive predictive sliding mode velocity controller is designed based on a new adaptive reference sliding mode trajectory and an integral terminal sliding mode surface with disturbance estimation error. The proposed strategy can adaptively adjust the sliding mode bandwidth and convergence speed, which not only ensures the system’s rapid convergence but also reduces the tracking error and weakens the chattering. Finally, the stability analysis proves that the closed-loop system is uniformly bounded stable. Comparative simulation results verify the effectiveness of the proposed control scheme.

An Adaptive Control Framework for the Autonomous Aerobatic Maneuvers of Fixed-Wing Unmanned Aerial Vehicle

This article proposes an adaptive flight framework that integrates a discrete-time incremental nonlinear dynamic inversion controller and a neural network (NN)-based observer for maneuvering flight. The framework is built on the feedback-inversion scheme in which the adaptive neural network augments a discrete-time disturbance observer in the loop. The effects of the modeling uncertainties and the exogenous perturbations are both taken into consideration and are alleviated by the observer. By utilizing the Lyapunov synthesis method, the updating rule of the NN’s weights is introduced, which guarantees the system’s stability with enhanced tracking performance. The efficiency of the proposed scheme is presented through numerical verification of a 6-DOF fixed-wing fighter performing several aggressive flight maneuvers. Extensive simulation results illustrate that this versatile controller is more practical for aerobatic flights compared with the discontinuous sliding mode (DSM) and the nonlinear dynamic inversion (NDI) methods. Given well-generated maneuver commands, the aircraft can accurately track the aggressive reference in the presence of modeling perturbations such as changes in aerodynamic coefficient, inertial parameters, and wind gusts.

Non-switching reference trajectory based discrete-time sliding mode path following control for dynamic positioning ship with time-varying disturbances

This paper investigates the discrete-time sliding mode (DSM) path following control problem for dynamic positioning ship (DPS) with time-varying disturbances and sideslip based on non-switching reference trajectory and discrete-time disturbance observer (DDO). Initially, a high-order DDO and a finite-time sideslip angle observer are designed to observe the time-varying disturbance and sideslip angle, respectively, to compensate for their effects on DPS. Then, the discrete-time integral sliding mode surface is designed by introducing the nonlinear integral with characteristics of small error amplification and large error saturation, which avoids the system instability due to integral saturation. Furthermore, a new DSM path following controller is designed based on the new reaching law composed of disturbance observation errors and non-switching reference trajectory. The conclusion that the position tracking error can asymptotically converge to zero is inferred. The proposed control scheme avoids the problem that the continuous-time control law is not suitable for the actual shipborne discrete-time controller and the system chattering caused by switching functions and simultaneously ensures the system’s anti-disturbance ability. Finally, comparative simulation results verify the effectiveness and superiority of the proposed control scheme.

Robust discrete‐time fractional‐order control for an unmanned aerial vehicle based on disturbance observer

AbstractIn this article, a robust discrete‐time fractional‐order tracking control scheme based on a discrete‐time disturbance observer (DTDO) is proposed for an unmanned aerial vehicle (UAV) system in the presence of unknown bounded variation disturbances. A DTDO is first constructed to estimate the unknown bounded disturbance. On the basis of the output of the DTDO and the discrete‐time fractional‐order theories, a robust discrete‐time fractional‐order control scheme is then designed by using the backstepping control technique for a discrete‐time UAV system with disturbances. The proposed control scheme is expected to guarantee the stability of the closed‐loop system with all system signals bounded. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed control scheme.

Optimized control strategy based on EPCH and DBMP algorithms for quadruple-tank liquid level system

According to the actual production requirements in process control, this paper proposes an optimized control strategy for the quadruple-tank liquid level system (QTLLS). Firstly, using the Bernoulli’s law and mass conservation principle, the dynamic mathematical model of QTLLS is established and linearized. Secondly, the state error port controlled Hamiltonian (EPCH) controller is designed by Hamiltonian system model construction which utilize the Hamiltonian principle, and a disturbance observer(DOB) is chosen to compensate disturbances impact. Thirdly, a deadbeat model predictive (DBMP) control algorithm with discrete-time disturbance observer (DTDOB) is proposed. Finally, in order to establish an optimized control strategy, an optimized function is proposed, which can give full play to the advantages of DBMP-OB algorithm with fast dynamic response and EPCH-OB algorithm with good steady-state performance. A wealth of results from simulation and experimental fully confirm the superiority of the proposed control strategies compare with proportional–integral–derivative (PID) control and sliding mode control (SMC). Moreover, the proposed optimized control strategy has been realized position control, tracking control and disturbance compensation control in this paper. It meets the needs of production and has great industrial application prospects.

Robust Discrete-Time Nonlinear Attitude Stabilization of a Quadrotor UAV Subject to Time-Varying Disturbances

A discrete-time improved input/output linearization controller based on a nonlinear disturbance observer is considered to secure the stability of a four-rotor unmanned aerial vehicle under constant and time-varying disturbances, as well as uncertain system parameters for its attitude behaviour. Due to the nature of the quadrotor system, it contains the most extreme high level of nonlinearities, system parameter uncertainties (perturbations), and it has to cope with external disturbances that change over time. In this context, an offset-less tracking for the quadrotor system is provided with the input/output linearization controller together with a discrete-time pre-controller. In addition, the robustness of the system is increased with a discrete-time nonlinear disturbance observer for time-varying disturbances affecting the system. The main contribution of this study is to provide highly nonlinearities cancellation to guarantee the aircraft attitude stability and to propose a robust control structure in discrete-time, considering all uncertainties. Various simulation studies have been carried out to illustrate the robustness and effectiveness of the proposed controller structure.

Immersion and invariance disturbance observer-based nonlinear discrete-time control for fully actuated mechanical systems

This paper addresses the attenuation problem of input disturbances in the control of fully actuated mechanical systems in the discrete-time setting. Firstly, a discrete-time disturbance estimator design with immersion and invariance (I&I) approach is presented for the n-degrees of freedom (DOF) fully actuated mechanical systems. Then, a discrete-time combined feedback linearising and backstepping control is established that this controller uses the estimated disturbance information. Global asymptotic stability of the estimator and local asymptotic stability of the entire closed-loop system in an arbitrarily large compact set are shown utilising the Lyapunov stability theory. In order to show the effectiveness of the proposed composite observer-based discrete-time control method, it is applied to the 3-DOF robotic manipulator. Performance of proposed direct discrete-time combined feedback linearising and backstepping controller with discrete-time I&I observer is compared with a direct discrete-time conventional second-order sliding mode controller with another discrete-time nonlinear disturbance observer via simulations. The superior performance of the proposed method is demonstrated with simulation results.

Disturbance Observer-Based Robust Formation-Containment of Discrete-Time Multiagent Systems with Exogenous Disturbances

This paper investigates robust formation-containment control of discrete-time multiagent systems (MASs) with exogenous disturbances. Based on the discrete-time disturbance observer method, both state feedback and output feedback control protocols are proposed. Formation-containment conditions are obtained and convergency analysis is given according to Lyapunov stability theory. And, the corresponding control gains are obtained by solving some discrete-time algebraic Riccati equations. Numerical simulations are presented to illustrate the theoretical findings.

Adaptive Neural Discrete-Time Fractional-Order Control for a UAV System With Prescribed Performance Using Disturbance Observer

In this paper, an adaptive neural discrete-time (ANDT) fractional-order tracking control scheme is proposed for an unmanned aerial vehicle system with prescribed performance in the presence of system uncertainties and unknown bounded disturbances based on a discrete-time disturbance observer (DTDO). The system uncertainties are handled using neural network (NN) approximation. To compensate for the adverse effects of unknown disturbances, an NN-based DTDO is designed. On the basis of the NN, the designed DTDO and the backstepping technology, an ANDT fractional-order control scheme with prescribed performance is developed. Then, the tracking errors are convergent under the proposed control scheme. Finally, the effectiveness of the proposed discrete-time control scheme is demonstrated by numerical simulation results.

Event-Triggered-Based Discrete-Time Neural Control for a Quadrotor UAV Using Disturbance Observer

An event-triggered-based (ETB) discrete-time neural control is studied for a quadrotor unmanned aerial vehicle (UAV) with external disturbances and input saturation by using the discrete-time disturbance observer (DTDO). First, the ETB mechanism of the neural network is given and the Sigmoid-type function is employed to tackle the problem of input saturation. Then, the DTDO is designed and the saturation function is utilized to ensure the boundedness of virtual control signal. Combining the discrete-time tracking differentiator and the backstepping technology, the stability of the closed-loop system is analyzed. Finally, the experiment results of the quadrotor UAV system are given to illustrate the feasibility of the proposed control scheme.

Robust predictive visual servoing control for an inertially stabilized platform with uncertain kinematics

In this paper, a disturbance observer (DOB) based predictive control approach is developed for the image-based visual servoing of an inertially stabilized platform (ISP). As the limitation in degrees of freedom of a two-axes ISP, it is hard to estimate the variable feature depth of the target at each control cycle when using an uncalibrated camera, which brings the challenge in the design of the visual servoing controller. To this end, a depth-independent kinematic matrix that only involves nominal parameters is obtained by employing the partitioned scheme in the system modeling. The uncertain kinematics arising from the unknown feature depth, angular velocity tracking errors, and uncalibrated intrinsic parameters is considered as the lumped uncertainty. A discrete-time DOB is then constructed to estimate the lumped uncertainty in real time. Instead of taking an integral action to eliminate tracking errors induced by the uncertain kinematics, the disturbance estimation is actively incorporated into the receding optimization process of the predictive controller. The stability of the closed-loop system is fully analyzed. Experiments on tracking a moving target are performed to validate promising qualities of the proposed approach.

Discrete-Time Angle Constraint Interception with Model-Assisted Target Maneuver Estimator

This paper investigates the problem of designing angle constraint guidance law against unknown maneuvering targets based on discrete-time sliding mode control theory. Invoking the fact that the future course of action of the target, an independent entity, cannot be predicted beforehand due to its complexity and unpredictability, a model-assisted discrete-time disturbance observer in cooperation with a singularity-free strategy is proposed first to estimate the target maneuver. Based on the reconstructed signal and a fast convergence time-varying sliding surface, a new chattering-mitigated super-twisting-like discrete-time impact angle constraint guidance law is then synthesized. Stability analysis shows that the closed-loop system trajectory can be forced to enter into a small region around the sliding surface. Simulations and comparisons with classical discrete-time sliding mode guidance law validate the effectiveness of the proposed guidance law.

Robust Model Predictive Speed Control of Induction Motors Using a Constrained Disturbance Observer

This paper proposes an offset-free speed control method for induction motors using a model predictive control and disturbance observer. The proposed method has cascade control loops i.e. inner-loop model predictive torque control and outer-loop robust speed control. The outer-loop robust speed controller is composed of a stabilizing MPC and a discrete-time disturbance observer. The disturbance observer estimates the effects of the parameter uncertainties and the load torque to yield an offset free speed tracking, while taking the torque limit of the motor into account. This speed controller generates the reference torque for the inner-loop torque controller. A loss-minimizing continuous control set model predictive torque controller(CCS-MPTC) considering the current and voltage constraints of the motor is used as the inner-loop torque controller. Experimental results show a significant performance improvement when the torque constraints are considered in the DOB design.

Robust predictive current control for IPMSM without rotor flux information based on a discrete‐time disturbance observer

This study proposes a novel robust predictive current control that is based on a discrete-time disturbance observer for an interior permanent magnet synchronous motor (IPMSM), does not require rotor flux information. To confirm the effects of the current control response on a parameter mismatch, the parameter sensitivity for the current prediction of a conventional deadbeat predictive current control (DPCC) is analysed. With the proposed method, disturbances owing to a parameter mismatch, rotor flux term, and unmodelled dynamics are estimated using a Luenberger observer in the discrete-time domain. The estimated disturbances are compensated with the predicted reference voltage model considering a digital delay. The stability of the proposed disturbance observer owing to a parameter mismatch of the stator resistance and d–q inductance is also analysed. The proposed method is robust against the stator resistance and an inductance variation, and an accurate predicted current control can be obtained without an offline or online estimation of the rotor flux. Compared with the conventional DPCC, the proposed method can eliminate a steady-state current and transient state error caused by disturbances of the system. Experimental results are presented to verify the proposed control scheme even with mismatched parameters of the IPMSM.

A Constant Switching Frequency Multiple-Vector-Based Model Predictive Current Control of Five-Phase PMSM With Nonsinusoidal Back EMF

Most of the existing finite-control-set model predictive current control (FCS-MPCC) schemes for multi-phase motor suffer from heavy computational burden, inevitable low-order harmonic currents, and variable switching frequencies. Some virtual voltage vector (V3)-based FCS-MPCC schemes can effectively suppress harmonic current by zeroing the harmonic subspace voltage on average during one sampling period. However, they fail when the motor has a nonsinusoidal back electromotive force. In order to solve the aforementioned issues, this paper proposes a constant switching frequency multiple-vector-based FCS-MPCC scheme. Unlike the traditional FCS-MPCC schemes, the proposed scheme selects optimal V3s and their duty ratios in two orthogonal subspaces. Thus, it can simultaneously track the references in both orthogonal subspaces. In this approach, the optimal V3s and their duty ratios are directly obtained from the principle of deadbeat current control without time-consuming enumeration-based state predictions and cost function calculations. In addition, the obtained optimal V3s and their duty ratios are adopted to rearrange the pulse sequence to obtain constant switching frequency and can be simply synthesized by carrier-based pulsewidth modulation. Furthermore, a discrete time disturbance observer is designed to improve the robustness of the proposed FCS-MPCC against parameter mismatch. Finally, comparative experiments with traditional MPCC schemes for five-phase surface-mounted permanent magnet synchronous machine are carried out to verify the effectiveness of the proposed scheme.

Adaptive Discrete-Time Flight Control Using Disturbance Observer and Neural Networks.

This paper studies the adaptive neural control (ANC)-based tracking problem for discrete-time nonlinear dynamics of an unmanned aerial vehicle subject to system uncertainties, bounded time-varying disturbances, and input saturation by using a discrete-time disturbance observer (DTDO). Based on the approximation approach of neural network, system uncertainties are tackled approximately. To restrain the negative effects of bounded disturbances, a nonlinear DTDO is designed. Then, a backstepping technique-based ANC strategy is proposed by utilizing a constructed auxiliary system and a discrete-time tracking differentiator. The boundness of all signals is proven in the closed-loop system under the discrete-time Lyapunov analysis. Finally, the feasibility of the proposed ANC technique is further specified based on numerical simulation results.

Disturbance observer-based discrete-time neural control for unmanned aerial vehicles with uncertainties and disturbances

In this paper, a disturbance observer-based discrete-time neural control problem is studied for unmanned aerial vehicle (UAV) in the presence of external disturbances and system uncertainties. To estimate the external disturbance, a nonlinear discrete-time disturbance observer (DTDO) is designed. Furthermore, the system uncertainties are approximated by employing neural network (NN). Then, a discrete-time neural tracking control scheme is proposed based on the designed DTDO, the discrete-time tracking differentiator and the backstepping technique. Under the discrete-time Lyapunov analysis, the boundness of all the closed-loop system signals are proven. Finally, numerical simulation results are shown to demonstrate the effectiveness of the proposed control scheme.

Combined Discrete-time Sliding Mode and Disturbance Observer for Current Control of Induction Motors

This paper proposes a composite control strategy which combines a discrete-time sliding mode controller with a disturbance observer aiming to decouple current control of vector oriented induction motor drives. The stator current control is carried out through an indirect field orientation in a dq reference frame rotating at synchronous speed. The cross-coupling variables of the induction motor stator currents at synchronous reference frame are modeled as disturbances, and these values are estimated using a discrete-time disturbance observer. The digital implementation delay was included in the plant model formulation, resulting in a control law suitable to direct implementation in microcontrollers and digital signal processors. Then, the nominal and decoupled part of the induction machine model is used for the design of the sliding mode controller, and the additional variables are modeled as disturbances. The cross-coupling variables are observed and used in the control law. The convergence analysis is presented in discrete-time domain. Simulation and experimental results are presented to validate the theoretical analysis, and they show the good performance of the proposed method.