Linear Tracking Differentiator Research Articles

On the convergence of the linear tracking differentiator for signals with KH-integrable derivatives

On the convergence of the linear tracking differentiator for signals with KH-integrable derivatives

Distributed Estimator-Based Containment Control for Multi-AUV Systems Subject to Input Saturation and Unknown Disturbance

This article addresses the containment control issue for multi-AUV systems with the intervention of both external disturbance and input saturation. Firstly, a distributed estimator is established for the sake of acquiring precise estimation information of the desired position and its derivative for each follower AUV in the system. Next, on the basis of the proposed distributed estimator, a virtual control law is designed for each follower AUV. Then, due to the difficulty in obtaining accurate information about the derivative of the virtual control law, a linear tracking differentiator is introduced. Additionally, a disturbance observer is employed to tackle the composite disturbance, which mainly contains the internal model uncertainties and external bounded disturbances. Meanwhile, the issue of input saturation is handled by constructing the auxiliary system. Furthermore, a containment control law is designed with the assistance of the introduced linear tracking differentiator, the established disturbance observer, and the constructed auxiliary system. Additionally, the Lyapunov stability theory is applied to analyze the stability of the multi-AUV system. Finally, simulation results are given to confirm the feasibility of the proposed containment control scheme.

Linear Active Disturbance Rejection Lateral Controller for Unmanned All-Terrain Vehicle

Abstract: To address the disturbance of model uncertainty, a linear active disturbance rejection controller (LADRC) was designed for robust lateral control of unmanned all-terrain vehicle. In terms of relative motion of target node and current state, first-order lateral tracking model is established. According to the developed model, linear tracking differentiator (LTD), linear extended state observer (LESO) and linear state error feedback (LSEF) are designed in turn. LESO could observe the uncertainty of system and LSEF could compensate the uncertainty to make system robust. In order to verify the effectiveness, two typical scenarios, circle and double lane tracking, were designed for test. And the uncertainties of wheelbase and steering ratio were considered. Results illustrate that the designed LADRC can stably control the unmanned all-terrain vehicle tracking reference trajectory under both scenarios and has the advantages of small tracking error and small overshoot compared with the conventional pure tracking methods.

On convergence of nonlinear tracking differentiator based on finite-time stable system subject to stochastic noise

In this paper, we consider convergence for a nonlinear tracking differentiator constructed from a finite-time stable system, where the input signal is corrupted by bounded stochastic noise. The existence of global weak solutions is firstly proved. It is shown that the nonlinear tracking differentiator tracks the input signal in the almost surely practical sense. With the same tuning parameter, the convergence accuracy is shown to be higher than that of the linear tracking differentiator. Some numerical simulations are performed to validate the effectiveness of the proposed differentiator.

Fast luffing control of flexible boom of mobile elevated work platform with uncertain control input gain

In this paper, the dynamic model between input electric signal of hydraulic valve and boom luffing angle is established, and luffing control of flexible boom of mobile elevated work platform (MEWP) is studied. The control input gain for the luffing motion of the MEWP is extremely difficult to solve and varies with boom length, work platform load, and luffing angle. For the variable control input gain, all low-order state quantities, rigid-flexible coupling quantity, and control input are included as the “total disturbance” to be observed. Based on the third-order linear tracking differentiator and the first-order ordinary differential linear equation, an active disturbance rejection controller without control input gain is proposed. With the bandwidth-based parameter settings, the controller only needs to adjust two parameters. As a comparison, this paper analyzes in detail the proposed controllers, the fixed input gain active disturbance rejection controller and the PID controller in terms of tracking error, overshoot, setting time, tracking stability, and robustness.

A Variable Parameter Linear Tracking Differentiator and Its Application in Large Ground-based Telescopes

This paper is concerned with the characteristics of a tracking differentiator (TD) in arranging transition process for the physical system. In order to overcome disadvantages of linear TD (LTD) in practice, a novel variable parameter linear tracking differentiator (VLTD) is proposed. By designing the speediness factor as a function of the tracking error, the VLTD can track a large range of set values with reasonable speed and acceleration. Analysis shows that VLTD can converge to its set value under certain conditions. Meanwhile, the speed and acceleration bounds are added to the VLTD, which guarantees that the proposed transition signal really plays a transitional role. The numerical simulation results emphasize necessity for adding speed and acceleration bounds to the VLTD. By comparing VLTD with the nonlinear TD (NLTD) in the simulations and experiments, VLTD can achieve almost the same performance as the NLTD while it is easier to be implemented.

Swarm Control for Connectivity-Preserving and Collision-Avoiding Unmanned Surface Vehicles Subject to Multiple Constraints

This paper investigates swarm control for unmanned surface vessels subject to multiple constraints. These constraints can be summarized as model parameter uncertainty, the unavailability of velocity measurements, time-varying environmental disturbances, input saturation and output constraints. Firstly, to recover unmeasured velocity information, to identify unknown vehicle dynamics and to estimate time-varying environmental disturbances, a neural adaptive state observer is designed for each vessel. Secondly, to avoid complex calculations, a second-order linear tracking differentiator is employed to generate a smooth reference signal and to extract the time derivative of the kinematic control law. Thirdly, to solve the input saturation, an auxiliary dynamic system is introduced. Fourthly, the barrier Lyapunov function is used to achieve connectivity preservation, collision avoidance and swarm control. Meanwhile, by using the estimated velocities of vessels, an output feedback controller is designed. The stability of the closed-loop system is proved. The simulation results show the effectiveness of the proposed swarm control strategy.

Variable parameter linear tracking differentiator and its application in altazimuth large area telescope

ä¸ºäº†å¯¹å ·æœ‰é€Ÿåº¦å’ŒåŠ é€Ÿåº¦é™åˆ¶çš„ç‰©ç†ä¿¡å·å®‰æŽ’åˆç†çš„è¿‡æ¸¡è¿‡ç¨‹ï¼Œæå‡ºäº†ä¸€ç§å¸¦æœ‰é€Ÿåº¦å’ŒåŠ é€Ÿåº¦é¥±å’Œé™åˆ¶çš„å˜å‚æ•°çº¿æ€§è·Ÿè¸ªå¾®åˆ†å™¨ã€‚å°†è·Ÿè¸ªå¾®åˆ†å™¨çš„å¿«é€Ÿå› å­è®¾è®¡ä¸ºè·Ÿè¸ªè¯¯å·®å‡å‡½æ•°çš„å½¢å¼ï¼Œå³ä½¿åœ¨åˆå§‹è·Ÿè¸ªè¯¯å·®éžå¸¸å¤§çš„æ—¶å€™ä¹Ÿä¸ä¼šäº§ç”Ÿéžå¸¸å¤§çš„åŠ é€Ÿåº¦ï¼ŒåŒæ—¶ç»“åˆé€Ÿåº¦å’ŒåŠ é€Ÿåº¦é¥±å’Œçš„é™åˆ¶ï¼Œä½¿ç”¨åŒä¸€ç»„å‚æ•°å°±å¯ä»¥å¯¹å¤§èŒƒå›´çš„é˜¶è·ƒä¿¡å·ç»™å‡ºä¸Žç‰©ç†ç³»ç»Ÿåé¦ˆèƒ½åŠ›ç›¸åŒ¹é çš„è¿‡æ¸¡è¿‡ç¨‹ä¿¡å·ã€‚ä»¿çœŸè®¡ç®—è¡¨æ˜Žï¼Œæ‰€è®¾è®¡çš„è·Ÿè¸ªå¾®åˆ†å™¨çš„è·Ÿè¸ªæ•ˆæžœä¸Žç»å ¸çš„éžçº¿æ€§è·Ÿè¸ªå¾®åˆ†å™¨å‡ ä¹Žç›¸åŒï¼Œè®¡ç®—å¤æ‚åº¦å´æ˜Žæ˜¾é™ä½Žã€‚å°†æ‰€è®¾è®¡çš„è·Ÿè¸ªå¾®åˆ†å™¨åº”ç”¨äºŽåœ°å¹³å¼å¤§è§†åœºæœ›è¿œé•œçš„å¿«é€Ÿè°ƒè½¬å®šä½ä¸­ï¼Œä¸Žå·¥ç¨‹ä¸­å¸¸ç”¨çš„ä½ç½®åˆ†æ®µæ–¹å¼è¿›è¡Œå¯¹æ¯”ï¼Œå“åº”æ—¶é—´ç¼©çŸ­äº†å¤§çº¦15%~37%，有效提高了望远镜的搜索效率。变参数跟踪微分器不但能够起到过渡作用，还能最大限度地激发物理系统的反馈能力。该方法参数设置简单，易于工程中的调试和实现。

Event-triggered distributed coordinated control of networked autonomous surface vehicles subject to fully unknown kinetics via concurrent-learning-based neural predictor

This paper is concerned with distributed coordinated control of networked autonomous surface vehicles (ASVs) guided by multiple parameterized paths. The model of each ASV is subject to fully unknown kinetics, including environment disturbances, model uncertainties, and unknown input coefficients. A coordinated control method is presented for multiple ASVs to achieve a containment formation based on event-triggered mechanisms. Specifically, an event-triggered kinematic control law is firstly developed based on aperiodic communication. The desired path during the triggering interval is predicted by the last event-triggered velocity. Then, an event-triggered kinetic control law is developed, a third-order linear tracking differentiator is introduced to take the derivative of the kinematic control law, and the control input is updated only if the predefined event is triggered. A concurrent-learning-based neural predictor is constructed by using historical data such that model uncertainties and unknown input coefficients are identified simultaneously. Next, an event-triggered path update law is constructed by using a path-maneuvering design and the aperiodic information received from the network. The proposed method ensures the input-to-state stability of the resulting closed-loop system. Finally, simulation results are provided to demonstrate the effectiveness of the proposed distributed coordinated control for networked ASVs by using event-triggered mechanisms and concurrent-learning-based neural predictors.

On disturbance rejection control for nonlinear three‐revolute prismatic spherical ball and plate systems

AbstractThe three‐revolute prismatic spherical ball and plate system (BP) is a typical complex nonlinear uncertain system involving axial coupling, friction, and other nonlinear factors. It is difficult to identify the model for each factor and isolate its effect from other factors. In addition to such challenge, the measurement noise, which is beyond the capability of many traditional closed‐loop control methods, exists in the system. For this reason, an active disturbance‐rejection control scheme combining linear tracking differentiator is presented to tackle the problems in the BP system. The simulation and real system test are conducted in response to point‐to‐point trajectories, circular and rectangular loci. The results demonstrate that fast response with small steady error can be achieved by the proposed control method.GTOC:The paper provide an active disturbance‐rejection control scheme combining linear tracking differentiator for the BP system control, The simulation and real system test demonstrate that fast response with small steady error can be achieved by the proposed control method.

Event-triggered control for containment maneuvering of second-order MIMO multi-agent systems with unmatched uncertainties and disturbances

This paper is concerned with distributed containment maneuvering of second-order Multi-Input Multi-Output (MIMO) multi-agent systems with non-periodic communication and actuation. The agent is subject to unmatched nonlinear dynamics and external disturbances. Event-triggered containment maneuvering control methods is developed based on a modular design. Specifically, an estimator module is constructed based on neural networks and the non-periodic obtained follower information through event-triggered communication. Next, a controller module is designed by using the identified information from the estimator module and a third-order linear tracking differentiator. An event-triggered mechanism is introduced for updating the actuator. Then, a path update law is designed based on the non-periodic leader information through event-triggered communication. The closed-loop system cascaded by the estimation subsystem and control subsystem is proved to be input-to-state stable, and Zeno behavior is excluded in the control process. The proposed method is capable of reducing the consumption of communication and actuation. A simulation example is provided to substantiate the effectiveness of the proposed event-triggered control method for distributed containment maneuvering of second-order MIMO multi-agent systems.

Event-triggered ISS-modular neural network control for containment maneuvering of nonlinear strict-feedback multi-agent systems

The paper is concerned with containment maneuvering of nonlinear multi-input multi-output (MIMO) strict-feedback multi-agent systems under the distributed directed communication. Followers are driven into a convex hull spanned by all virtual leaders guided by desired parameterized paths. Multi-agent systems are driven to achieve the desired behavior. A containment maneuvering controller is developed based on an event-triggered modular-ISS neural network control method to decouple estimation and control. Specifically, in the estimation loop, an RBF-network-based predictor module is constructed to design the adaptation law, where an RBF network is employed to identify the uncertain nonlinear dynamics. An event-triggered communication mechanism is introduced to decrease the burden of followers communication. In the control loop, a control module is constructed by using the output of predictor module and a third-order linear tracking differentiator. An event-triggered actuation mechanism is introduced to reduce the actuator burden of followers. A path update law is constructed to achieve coordination among leaders. An event-triggered communication scheme is introduced for leaders to decrease the communication burden of leaders. The input-to-state stability of the total cascade system is demonstrated by using the cascade stability theorem. Simulation results are provided to substantiate the efficacy of the proposed containment maneuvering controller for nonlinear MIMO strict-feedback multi-agent systems.

Distributed containment maneuvering of uncertain under-actuated unmanned surface vehicles guided by multiple virtual leaders with a formation

Abstract This paper is concerned with the distributed containment maneuvering for a fleet of under-actuated unmanned surface vehicles (USVs) guided by multiple virtual leaders moving along multiple parameterized paths with a formation. Each USV is subject to model uncertainties and ocean disturbances caused by wind, waves and ocean currents. Distributed containment maneuvering controllers are constructed for under-actuated USVs based on an auxiliary variable approach, an extended state observer, a linear tracking differentiator, and a path maneuvering design. The proposed controllers drive the vehicle fleet to converge to a convex combination of multiple virtual leaders regardless of the model uncertainties and ocean disturbances. The input-to-state stability of the closed-loop system is analyzed via Lyapunov theory and the containment maneuvering errors converge to a small neighborhood of the origin. Simulation results show that the feasibility and efficacy of the proposed distributed containment maneuvering controllers for the under-actuated USVs.

Containment Maneuvering of Marine Surface Vehicles With Multiple Parameterized Paths via Spatial-Temporal Decoupling

The containment maneuvering of marine surface vehicles has two objectives. The first one is to force the marine vehicles to follow a convex hull spanned by multiple parameterized paths. The second one is to meet the requirement of a desired dynamic behavior along multiple paths during containment. A modular design approach to the containment maneuvering of marine surface vehicles is presented. At first, an estimator module using a recurrent neural network is proposed to estimate the unknown kinetics induced by model uncertainty, unmodeled dynamics, and environmental disturbances. Next, a controller module is developed based on a distributed path maneuvering design and a linear tracking differentiator. Finally, two path update laws based on a maneuvering error feedback and a filtering update scheme, respectively, are constructed. The estimator-controller pair forms a cascade system, which is proved to be input-to-state stable. The developed controller has a desirable spatial-temporal decoupling property, and geometric and dynamic objectives can be achieved separately. Results of comparative studies are provided to substantiate the efficacy of the proposed method.

Neural adaptive steering of an unmanned surface vehicle with measurement noises

This paper presents an autopilot design for a robotic unmanned surface vehicle in the presence of unknown yaw dynamics and measurement noises. A robust adaptive steering law is developed with the aid of a predictor, neural networks, and a modified dynamic surface control technique. Specifically, a predictor together with a low-frequency learning-based neural updating law is developed to identify the unknown yaw dynamics, as well as to reconstruct the states corrupted by measurement noises. Besides, to avoid the noise amplification effect of first-order filter, a linear tracking differentiator is incorporated into the dynamic surface control design approach to produce a noise-tolerant estimate of virtual control derivative. The stability of the closed-loop autopilot system is established by Lyapunov analysis. A salient feature of the developed controller is that it can achieve the desired performance in the presence of model uncertainty and measurement noises, simultaneously. Both simulation and experiment results are given to validate the efficacy of the proposed method.

Adaptive trajectory tracking control design with command filtered compensation for a quadrotor

The design of a flight controller capable of not only stabilizing attitude but also tracking a trajectory accurately for a quadrotor aircraft in presence of parametric uncertainties and external disturbances is more challenging than that in the absence of uncertainties. In this paper we propose an adaptive trajectory tracking control algorithm, based on the relationship between attitude and linear acceleration, using online adaptive approximator to estimate unknown aerodynamic parameters and external disturbance upper bounds, and a linear tracking-differentiator to eliminate the timescale separation assumption between attitude and linear dynamics in control system design. The stability of the closed-loop control system is proven subsequently. Finally, the validity and the improvement of this proposed algorithm relative to the previous work are demonstrated through numerical simulations of tracking a circular trajectory under several conditions, including basic parametric uncertainty, exogenous wind disturbance and control input oscillation eliminating via a hyperbolic tangent function instead of a sign function.

Acceleration estimation method and sliding mode control design for car-following distance control

Vehicle following for traffic safety has been an active area of research. Car-following distance control is key for vehicle following mode in autonomous cruise system. Sliding mode control has been applied in vehicle longitudinal distance control. But most of them ignore or simplify acceleration information and reduce control performance. The purpose of this paper is to design sliding mode control method considering relative acceleration parameter to control car-following distance for autonomous cruise control (ACC). Meanwhile, tracking-differentiator is designed to estimate acceleration information as the control parameter and enhances the control system performance. Theoretical analysis and computer simulation prove that the designed linear tracking-differentiator can effectively estimate the relative acceleration and sliding mode control method considering relative acceleration parameter can also effectively control headway distance.

Trajectory tracking control design with command-filtered compensation for a quadrotor

The design of a flight control system capable of not only stabilising attitude but also tracking a trajectory accurately for an under-actuated quadrotor aircraft is quite challenging. This study constructs the relationship between the attitude and linear acceleration of a small quadrotor unmanned aircraft and proposes a trajectory tracking control design algorithm, based on the relationship, using a new command-filtered backstepping technique to stabilise the attitude and a linear tracking differentiator to eliminate the classical inner/outer-loop structure. Finally, the validity and the effectiveness of this algorithm are demonstrated by various numerical simulations under different conditions.

Linear tracking-differentiator and application to online estimation of the frequency of a sinusoidal signal with random noise perturbation

A simple linear tracking-differentiator is proposed and the convergence proved for any differentiable signal with random perturbation to be tracked. This enables us to design a relatively simple globally convergent online estimator of the frequency of a sinusoidal signal under small random perturbation. The polynomial convergent rate is obtained.