Tracking Differentiator Research Articles

Robust Second‐Order Backstepping Design of Integrated Guidance and Control Based on a Fully Actuated System Approach

ABSTRACTThis article investigates the angle constraint issue in the integrated guidance and control (IGC) design. By using the high‐order fully actuated system (HOFAS) approach, a non‐linear robust controller is presented under the framework of the second‐order backstepping method. First, the IGC model is represented as a complete second‐order non‐linear system without any linearization assumption, where the modeling error, unmodeled non‐linearity, and external disturbance are unknown uncertainties. Combined with the dynamic model, the non‐linear system is transformed into a pseudo‐feedback system. An IGC model with fully actuated features is established, consisting of the guidance, dynamics, and attitude subsystems. Then, under the framework of the backstepping method, the non‐linear controller of each subsystem is designed based on the HOFAS approach and robust control law, and a tracking differentiator based on inverse hyperbolic sine function is used to obtain the precise differential signal of the virtual control command. The controller parameter matrix is solved according to the desired closed‐loop poles, while the closed‐loop system is transformed into a steady linear system with desired performance. The subsystem state convergence is proven by Lyapunov theory, and the stability of the whole system is analyzed. Finally, the simulation results of terminal angle constraint verify the effectiveness of the proposed robust IGC design.

Model-Free Speed Control for Pumping Kite Generator Systems Based on Nonlinear Hyperbolic Tangent Tracking Differentiator

This paper investigates the emerging field of grid-connected wind-powered pumping kite generator system (PKGS), focusing on the challenges associated with the generator/motor speed control. Conventional use of proportional–integral (PI) controllers faces difficulties in meeting requirements for dynamic response, tracking performance, stability, and disturbance rejection encountered in this technology, notably the periodical variation in the rotational speed reference in maximum power point tracking in generation phases and the dynamic response for the step reference in transient ones. To overcome these limitations, a model-free controller (MFC) approach is introduced, also known as intelligent PID controllers. Unlike traditional methods, MFC does not rely on a control model of the system and adapts to uncertainties and disturbances through online estimation based on the system’s input–output behavior. To further improve the control performances, a tracking differentiator based on a nonlinear hyperbolic tangent function is integrated in the MFC. The effectiveness of the proposed strategy is proved through simulations in MATLAB/Simulink. The results highlight the superior performances of the proposed MFC approach in terms of speed control accuracy, response time, and robustness.

Dynamic Analysis and Neural-Adaptive Prescribed-Time Control of the FO Memristive Magnetic-Field Electromechanical Transducer.

This article is concerned with dynamic analysis and neural-adaptive prescribed-time control of the magnetic-field electromechanical transducer incorporating a memristor. First, a fractional-order (FO) mathematical model is developed, which comprehensively characterizes fractional properties of various dielectrics and establishes the relationship between magnetic flux and electric charge. The dynamical analysis explores internal evolution and complexity performance concerning a single factor or double factors among the FO, system parameter, and memristor configuration by the Bifurcation diagram, sample entropy, and C0 complexity from multiple perspectives. Subsequently, a neural-adaptive prescribed-time control scheme is proposed to transform detrimental chaotic oscillations into orderly motions, achieve the pregiven tracking precision and accommodating both actuator fault and system uncertainty. The controller design consists of three key steps: 1) a deferred constraint function is imposed on the tracking error starting from anywhere to get assignable tracking precision within a specified time, ensuring collision avoidance; 2) a type-2 fuzzy wavelet neural network (FWNN) is utilized effectively to handle parameter perturbations and system uncertainties; and 3) a second-order FO tracking differentiator (TD) is utilized to address the "explosion of complexity" of traditional backstepping under actuator fault model. It is shown that the proposed scheme is able to ensure the boundness of all signals of the closed-loop system. Finally, extensive simulation experiments are conducted to validate the effectiveness and robustness of the rendered scheme.

Autonomous Landing of a Fixed‐Wing UAV With RTK GNSS and MEMS IMU

Autonomous landing system is an important part of unmanned aerial vehicle (UAV) autonomous flight. Large fixed‐wing UAVs often consume more onboard space and computing resources. With the improvement of system integration and the reduction of high‐performance global navigation satellite system (GNSS) costs, real‐time kinematic (RTK) GNSS has been widely used in small‐scale and low‐cost fixed‐wing UAVs. This article uses less onboard hardware and ground facility requirements to design an autonomous taking off and landing system suitable for general fixed‐wing UAVs. A modified gradient descent attitude estimator, based on microelectromechanical system (MEMS) inertial measurement unit (IMU) and RTK GNSS, and a guidance method based on a tracking differentiator for using in a high dynamic environment are proposed, and circular path following and vertical transient simulations are performed. The simulation results show that this method can improve attitude estimation accuracy, motion control accuracy, and altitudinal transient quality. Finally, the actual flight test verifies its feasibility in the actual environment. The flight test results prove that it is feasible to implement the autonomous landing process of fixed‐wing UAV with the proposed system and method.

Finite-Time Resource Allocation Algorithm for Networked Fractional Nonlinear Agents

This paper investigates finite-time resource allocation problems (RAPs) for uncertain nonlinear fractional-order multi-agent systems (FOMASs), considering global equality and local inequality constraints. Each agent is described by high-order dynamics with multiple-input multiple-output and only knows its local objective function. Due to the characteristics of dynamic systems, the outputs of agents are inconsistent with their inputs, making it challenging to satisfy the inequality constraints when solving RAPs. To address this complex optimization control problem, a novel hierarchical algorithm is proposed, consisting of a distributed estimator and a local controller. Specifically, the distributed estimator is established by adopting the ϵ-exact penalty function and the gradient descent method. This estimator enables the system states to reach the optimal solution of RAPs within a finite time. Furthermore, the local controller is presented based on the fractional-order tracking differentiator and adaptive neural control approach. Under this controller, the system states are slaved to track the optimal signals generated by the estimator within a finite time. In both the estimator and controller algorithms, the finite-time stability is uniformly guaranteed with the help of Lyapunov functions. Finally, the effectiveness of our algorithm is demonstrated through three simulation examples.

Generation of a BEST1 Pr-EGFP reporter human embryonic stem cell line via CRISPR/Cas9 editing.

The retinal pigment epithelium (RPE) cell, located between the neural retina and choriocapillaris, is vital for retinal maintenance and photoreceptor function. Human embryonic stem cells (hESCs) provide a limitless source of RPE cells for transplantation. Using CRISPR/Cas9, we inserted a fusion of the BEST1 promoter (an RPE-specific marker) and the EGFP gene into the AAVS1 locus to track differentiation in hESC-induced RPE (hESC-iRPE). The resulting gene-edited line, WAe009-A-2M, maintained a normal karyotype, expressed pluripotency markers, and demonstrated differentiation potential, making it invaluable for RPE development and therapeutic research.

Image motion compensation control method for the dynamic scan and stare imaging system

The main function of the dynamic scan and stare imaging system is to quickly and continuously search a large area and perform high-resolution imaging. To eliminate image motion during the scanning process, this paper proposes an image motion compensation control method with dual-channel control. First, an improved model-assisted active disturbance rejection control is proposed, in which an auxiliary model is integrated into the algorithm to improve the control accuracy and response speed of the rotation rate of the platform. Second, a fast steering mirror (FSM) is introduced into the control system to compensate for the scanning speed and multiple disturbances. By adopting the amplitude frequency characteristics of the tracking differentiator, a parallel tracking differentiator filter is designed to suppress the interference of gyroscope noise on the FSM. When the system is disturbed by multiple frequency disturbances, the residual error of the image motion compensation is less than the spatial angular resolution of one pixel through the dual-channel stable control of the platform and the FSM. In the scan imaging experiment results, the average value of the grayscale variance function for the compensated images is close to 90% that of the static reference images.

A Positioning and Tracking Performance–Enhanced Composite Control Algorithm for the Macro–Micro Precision Stage

In the macro–micro composite motion process, the macro stage achieves rapid motion in a large workspace, while the micro stage realizes precise positioning within a small displacement. The large-stroke and high-speed motion of the macro stage is influenced by nonlinear friction, overshooting, and vibrations, making it challenging to achieve rapid stabilization within the travel range of the micro stage, thereby impacting equipment operation efficiency. This paper proposes a composite controller structure designed to solve the fast point-to-point positioning of the macro stage driven by a linear motor and enhance the trajectory tracking performance of the stage. The proposed composite control algorithm (CCA) includes velocity feed-forward, gain-scheduled proportional integral differential (PID) control, and a plug-in repetitive control method. By employing a tracking differentiator, velocity feed-forward, and a gain-scheduled PID controller, the control algorithm can realize rapid stabilization and positioning for the macro stage. Through velocity feed-forward, gain-scheduled PID control, and a plug-in repetitive controller, the control algorithm can reduce the trajectory tracking error of the stage. Simulations and experimental studies of point response and sinusoidal trajectory tracking are carried out on a macro–micro stage to verify the effectiveness of the composite controller for the linear motor. The experimental results demonstrate that the proposed composite controller effectively reduces the macro stage’s settling time and overshoot, and improves the accuracy of sinusoidal trajectory tracking, which lays a foundation for submicron positioning accuracy in high-speed macro–micro motion stages.

Attitude tracking of rigid-liquid-flexible coupling spacecraft by active disturbance rejection control

Considering the complex attitude dynamics of Rigid-Liquid-Flexible Coupling Spacecraft, especially when the large amplitude sloshing of liquid exists in rapid attitude maneuver, the conventional control design method based on the linearized model is not suitable for the significant coupling and strong nonlinearity. By contrast, Active Disturbance Rejection Control is model-independent and easy to design and implement. In this paper, the three main components of Active Disturbance Rejection Control, Tracking Differentiator, Extended State Observer and Nonlinear State Error Feedback are comprehensively applied to the attitude tracking control of Rigid-Liquid-Flexible Coupling Spacecraft. Firstly, two cascaded Tracking Differentiators are used to arrange the transition process of the attitude command, which not only reduces overshoot and oscillation of the tracking process, but also obtains the angular acceleration information of attitude trajectory for feed-forward compensation. Secondly, the total disturbance caused by liquid sloshing and flexible vibration is observed by Extended State Observer and compensated synchronously. Finally, the Nonlinear State Error Feedback is used to further improve the transient behavior and steady-state quality of the control system. The simulation results show that the tracking accuracy of the attitude and angular velocity using the Active Disturbance Rejection Control are about 3–27 times and 6 to 115 times that of the PID control, respectively. The convergence time, overshooting are also significantly less than the PID control.

Positioning anti-sway control method for tower crane based on improved MFAC

A model-free adaptive control (MFAC) based on partial format is proposed for the complex modeling and uncertain model parameters of the tower crane (TC) in this paper. Firstly, considering the complexity of the TC nonlinear system, the data model of the TC is obtained through the partial format dynamic linearization method. Then, a model-free adaptive controller is designed for the TC, incorporating the change rate of the tracking error and its derivative into the objective function to address the inefficiency of traditional model-free controllers in controlling TCs. The convergence and stability of the proposed controller are also proved. To further improve the dynamic performance of the system, a tracking differentiator (TD) is introduced after the input signal. Finally, MATLAB simulation and experiments are conducted to verify that the proposed method can achieve precise trolley positioning while suppressing the load swing angle.

Nolinear tracking differentiator based practical prescribed time tracking control for perturbed wheeled mobile robot

Nolinear tracking differentiator based practical prescribed time tracking control for perturbed wheeled mobile robot

Four-stage cascaded adaptive sliding mode control for automatic carrier landing with airwake disturbances and uncertainties

ObjectiveThis paper addresses the carrier landing affected by airwake, parametric uncertainties, and carrier deck motion, its main target being the design of a novel sliding mode based automatic carrier landing system to obtain accurate tracking of the reference trajectory, robustness in terms of disturbances and uncertainties, as well as excellent touchdown accuracy. ApproachFor an aircraft nonlinear dynamics, written under a four-stage cascaded strict feedback form, the design of the novel landing control architecture involves the design of a guidance subsystem, robust sliding mode controllers (for the control of the heading angle, attitude angles, and angular rates), an approach power compensation system, adaptive control laws suppressing the uncertainties and disturbances, a Kalman filter for deck motion prediction, a block computing the reference trajectory, a tracking differentiator block for deck motion compensation, and first-order command filters. Main resultsThe software validation process proves the effectiveness of the sliding mode based control scheme and the suppression of the uncertainties and disturbances. Also, the comparison between the performances of the sliding mode control based carrier landing system and the ones associated to other automatic carrier landing systems shows the superiority of the sliding mode based control scheme, as well as its better touchdown accuracy and landing success rate. SignificanceThis study innovatively transforms the general carrier landing problem into a time-varying tracking control problem for cascaded strict feedback dynamics with disturbances and uncertainties. The new designed automatic carrier landing system is the first control architecture in the literature employing the sliding mode control augmented by adaptive control laws for carrier landing, subjected to airwake, deck motion, and uncertainties.

Tracking Differentiator-Based Identification Method for Temperature Predictive Control of Uncooled Heating Processes

The temperature control of uncooled heating processes presents challenges due to a substantial lag and the absence of active cooling mechanisms, which can lead to overshoot and oscillations. To address these issues, we propose an anti-disturbance identification method based on a tracking differentiator (TD) and an input-constrained temperature predictive control (ICTPC) strategy. Our approach specifically considers the impact of unknown disturbances on model identification within a second-order heating process. By employing a TD to differentiate the input and output signals, we effectively minimize the identification error caused by low-frequency disturbances, yielding a robust anti-disturbance identification technique. Following this, we establish input constraints to limit the amplitude and variation of the control input, ensuring a more controlled and predictable system response. Using the identified model, an ICTPC algorithm is designed to achieve stable temperature control in uncooled heating processes. Experimental results from a typical uncooled heating system demonstrate that our method not only significantly reduces overshoot but also effectively mitigates temperature fluctuations, leading to enhanced control performance and system stability. This study provides a practical solution for temperature control in systems without cooling capabilities, offering substantial improvements in the efficiency and quality of industrial production processes.

Active Disturbance Rejection Control of Hydraulic Quadruped Robots Rotary Joints for Improved Impact Resistance

Hydraulic actuated quadruped robots have bright application prospects and significant research values in unmanned area investigation, disaster rescue and other scenarios, due to the advantages of high payload and high power to weight ratio. Among these fields, inevitable collision of robots may occur when contact with unknown objects, step on empty objects, or collapse, all of which have an impact on the working hydraulic system. To overcome the unknown external disturbances, this paper proposes an active disturbance rejection control (ADRC) strategy of double vane hydraulic rotary actuators for the hip joints of the quadruped robots. Considering the order of the valve-controlled actuator model, a three-stage tracking differentiator, a four-stage extended state observer, and a state error feedback controller are designed relatively, and the extended state observer is adopted to observe and compensate the uncertainty of external load torque of the system. The effectiveness of the ADRC method is verified in simulation environment and a single joint experimental platform. Moreover, the impact experiments of the limb leg unit are carried out after introducing the proposed ADRC strategy into hip joint, the limb leg unit of quadruped robots presents better impact resistance ability.

A novel FOTD-FRSET for optimization TFF analysis under impulsive noise

Impulsive noise is characterized by large amplitude and short duration, causing significant interference to the non-stationary signal representation and characteristic extraction. In response to the inadequacy of existing time-frequency analysis (TFA) methods in accurately representing the signal under impulsive noise, a novel time-fractional-frequency (TFF) analysis method based on FOTD-FRSET is proposed in this paper. This method effectively suppresses impulsive noise through fractional order tracking differentiator (FOTD), and then establishes the non-stationary signal TFF distribution by fractional synchroextraction transform (FRSET). Experimental results demonstrate that FOTD-FRSET can construct high-resolution TFF spectrum under impulsive noise, with superior energy concentration and ridge extraction over some existing methods. Furthermore, a noise correction algorithm is utilized to address the signal representation and characteristic extraction in the presence of non-standard symmetric α-stable distribution impulsive noise, enhancing the practicality of the proposed method for measured noise. Ultimately, the developed FOTD-FRSET method is effectively employed for linear frequency modulation (LFM) signal parameter estimation, and shows superior performance in the estimation accuracy, noise robustness, and practicality compared with existing methods.

An efficient tracking differentiator based active disturbance rejection control for flight environment simulation system

The flight environment simulation system plays a crucial role in aeroengine testing, replicating real mission pressure and temperature conditions. However, existing systems face challenges in handling strong measurement noises and total disturbances during transient tests, leading to inaccurate simulations and potential actuator damage. To address these gaps, an enhanced tracking differentiator based active disturbance rejection control scheme is proposed and implemented. Our method introduces two key innovations: a discrete-time optimal control law that dynamically adjusts control inputs based on state transition and sampling times, and a phase-advancing method that mitigates filtering phase delays by incorporating derivative signals to predict input trends. These components are integrated into a novel tracking differentiator, enhancing the estimation capability of the extended state observer in active disturbance rejection control. Frequency-domain analysis demonstrates the proposed tracking differentiator's superior filtering performance and phase quality. Simulations of intake environment pressure during aeroengine transient tests reveal that, compared to traditional tracking differentiator-based active disturbance rejection control, the proposed approach significantly reduces both control signal oscillations and setpoint deviations by 75.44% and 53.9%, respectively. These improvements effectively address environment simulation deviations and unnecessary actuator wear, thereby enhancing the accuracy and reliability of aeroengine testing.

Broad learning system based on attention mechanism and tracking differentiator

Broad learning system based on attention mechanism and tracking differentiator

A Real-Valued Kalman Estimation Method for Harmonic Signal Analysis in Biomedical Applications

This work presents a methodology for obtaining the harmonic estimation of biomedical signals such as electrocardiogram, cardiorespiratory and blood pressure signals. The proposed methodology is achieved using polynomial approximation and the Kalman filter. As advantage, the technique includes instant estimations of signal harmonics and its derivatives using a real-valued model. Furthermore, a comparison of the results is conducted with the Savitzky-Gola, nonlinear tracking differentiator methods, extended state observer and digital differentiator base on Taylor series. The results suggest that the proposed method has the potential to enhance the quality of signal measurements, especially in the presence of noise.

Adaptive event-triggered finite-time prescribed performance control of PMSM stochastic system considering time-varying delays

This paper investigates the finite-time prescribed performance tracking control problem of permanent magnet synchronous motor (PMSM) considering stochastic disturbances and time-varying delays under event-triggered mechanism. A quintuple polynomial finite-time prescribed performance function (FPPF) is introduced to ensure the transient and steady-state performance of the system output, and a nonlinear transformation function is employed to convert the constrained error into an unconstrained one. The Lyapunov-Krasovskii function is constructed to address time delays. And the system uncertainties are approximated by the radial basis function neural networks (RBFNN). For the “explosion of complexity” caused by backstepping method, a tracking differentiator (TD) is employed. By combining finite time control, command filtering backstepping control, and event-triggered mechanism, the effect of the filter errors is decreased, and the update frequency of the control signals are reduced. It is shown that the proposed controller can guarantee finite time convergence bounded of all signals in the closed-loop system, and the tracking error can converge in finite time. Finally, simulation results are presented to illustrate the effectiveness of the proposed controller.

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