Tracking Differentiator Research Articles

Fixed‐time fault‐tolerance attitude tracking control for spacecraft without unwinding

In this paper, the attitude tracking control problem is investigated for rigid spacecraft subjected to external disturbance, inertia uncertainties, and actuator faults. The rotation matrix is used to model the spacecraft attitude control system which can get rid of the unwinding problem. A nonlinear observer is developed to achieve a high accuracy estimation for the lumped disturbance in fixedtime without the awareness of the boundary of disturbance. To restrain measurement noise, a tracking differentiator is used in the observer to construct signals instead of using the polluted measurement values. Based on the estimation provided by the disturbance observer, a fixed-time attitude tracking controller is proposed by backstepping technique to stabilize attitude tracking errors in fixed time regardless of initial values. The singularity problem in traditional fixed-time controllers based on signal function is eliminated with the help of the arctangent function in the proposed controller. The feature of the designed fixed-time attitude controller is that it can suppress actuator faults, measurement noises and has no unwinding problem. Theoretical analysis based on Lyapunov theory and numerical simulations are presented to illustrate the robustness and effectiveness of the proposed control strategy.

New Sliding Mode Control Based on Tracking Differentiator and RBF Neural Network

In order to solve the problem that the control system of permanent magnet synchronous motor (PMSM) is difficult to meet the high control accuracy due to the influence of non-repeated disturbances such as external disturbance, system parameter variation, and friction force during operation, a novel sliding mode control (NSMC) method based on tracking differentiator (TD) and radial basis (RBF) neural network was proposed. Firstly, a new sliding mode reaching law is proposed by adding the state variables to the traditional exponential reaching law, which can effectively reduce the chattering of the system. Then, the speediest tracking differentiator is designed to estimate the given speed signal and its differential signal, to realize the novel sliding mode variable structure algorithm. Finally, the RBF neural network is used to compensate for the uncertainty and external interference of the system; the robustness of the system is further improved by adaptive weight updating. The simulation results show that, by comparing with the traditional exponential approach law, the overshoot of 22 r/min is reduced by the control method based on the new hybrid reaching law, the speed decrease amplitude is reduced by 77.1% under load disturbance, and the speed recovery time is shortened by 0.059 s. After the optimization of the new sliding mode control method based on tracking differentiator and RBF neural network, the overshoot of 86 r/min is further reduced, the speed decrease amplitude of load disturbance is reduced again by 48.5%, and the speed recovery time is shortened again by 0.073 s.

Distributed fixed-time time-varying formation-containment control for networked underactuated quadrotor UAVs with unknown disturbances

This paper focuses on the fixed-time time-varying formation-containment (TVFC) control problem for multiple underactuated quadrotor unmanned aerial vehicles (QUAVs) with unknown disturbances. A two-layer control framework comprising reference trajectory generators and trajectory tracking controllers is proposed. Under undirected communication topology, the first layer includes two fixed-time distributed reference trajectory generators for leaders and followers. The generated trajectories can be in accordance with the TVFC control requirements. In the second layer, two fixed-time tracking controllers are proposed, and a fixed-time disturbance observer (FTDO) is developed to ensure the robustness and timeliness of the control system. Meanwhile, the intermediary control input developed in the translational controller can be used to obtain the desired attitude by the attitude extraction algorithm. To handle the derivative calculations of variables in the rotational controller, an exact tracking differentiator is adopted, and the closed-loop stability of the control system is proved mathematically. In the end, the proposed control methods are verified through simulations and two comparison simulations are presented to show the superiority.

Attitude Control Method of Unmanned Helicopter Based on Asymmetric Tracking Differentiator and Fal-Extended State Observer

In order to meet the constraints of velocity and acceleration of displacement and attitude motion of an unmanned helicopter during an automatic carrier landing mission, an asymmetric tracking differentiator, which could set the speed and acceleration limits in two directions of tracked signal motion respectively, was derived based on the tracking differentiator in the active disturbance rejection control method. Based on the proposed asymmetric tracking differentiator, a fal-extended state observer based on the fal function was added to construct the attitude and angular velocity controller which is programmable during the transition process of unmanned helicopters. The mathematical simulation and result analysis show that the newly proposed attitude estimation algorithm effectively compensates for the deficiencies of the existing methods, improves the anti-jamming capability and the accuracy of attitude estimation in the maneuvering process, achieving the expected design purposes.

A hierarchical disturbance rejection depth tracking control of underactuated AUV with experimental verification

This paper presents a hierarchical disturbance rejection depth tracking control scheme for the underactuated autonomous underwater vehicle (AUV) with comparative experimental results. The proposed hierarchical control scheme is constructed by two layers in the kinematics and dynamics. First, the line-of-sight (LOS) guidance is adopted to transform the depth tracking problem of the underactuated AUV into the pitch tracking in the kinematics layer, and then the adaptive line-of-sight guidance (ALOS) is proposed to estimate online and compensate for the angle of attack neglected in the traditional LOS guidance or in the presence of disturbance. Second, in order to further enhance the capability of disturbance rejection, active disturbance rejection control (ADRC) is adopted to track the desired pitch angle in the dynamics layer. In addition, a modified velocity saturation tracking differentiator (VSTD) by considering the motion characteristics of the AUV is introduced to enable the easy tuning of the control parameters and the adaptability to varying conditions in practice. Finally, a small size underactuated AUV prototype named as ARMs-AUV 1.0 is used to implement the control algorithms. Comparative experimental results are illustrated to demonstrate the effectiveness and the remarkable performance of the proposed depth tracking control scheme.

On novel trajectory tracking control of quadrotor UAV: A finite-time guaranteed performance approach

In this work, aiming at the trajectory tracking control of the quadrotor UAV subject to external disturbances and model uncertainties, a finite-time approach with preassigned performance guaranteed is proposed. First, the control system is decoupled into translational and rotational subsystems. Then, in both two subsystems, the performance bounds constructed by the newly established appointed-time performance functions are devised for guaranteeing the tracking performance, and the controllers are designed via applying the dynamic surface control technique with integral barrier Lyapunov functions involved. Moreover, finite-time tracking differentiators and finite-time multivariable disturbance observers are exploited to estimate the target signals and the lumped disturbances, respectively. Finally, two examples of simulation are carried out to validate the effectiveness and superiority of the proposed control method.

Adaptive cooperative control for air‐ground systems with actuator saturation under disturbances

SummaryIn this article, an adaptive cooperative control strategy is proposed for an air‐ground system with actuator saturation. The air‐ground system with actuator saturation includes a ground vehicle with road bumps and a quadrotor with gust winds. The adaptive cooperative control strategy is composed of four tracking differentiators, four adaptive extended state observers and two adaptive integral SMC laws. Based on Silverman canonical transformation and pole placement, the adaptive extended state observers are designed to estimate disturbances from the road bumps and gust winds. The adaptive integral SMC laws are proposed to achieve cooperation between the ground vehicle and the quadrotor in the air‐ground system with actuator saturation. Simulation results are provided to show effectiveness of the adaptive cooperative control strategy by a ground vehicle and a quadrotor.

Dual-Time-Scale Sliding Mode Control for Surface-Mounted Permanent Magnet Synchronous Motors

The permanent magnet synchronous motors (PMSMs) as the completely symmetrical three-phase machines, which are usually driven by symmetrical voltage signals. Unfortunately, a PMSM system usually suffers from the different lumped disturbances, such as internal parametric perturbations and external load torques, the speed regulation problem should be addressed within the different operation situations. Characterizing by the current variation speed of the motor winding is much faster than that of the mechanical dynamic velocity, a dual-time-scale sliding mode control (SMC) method for the surface-mounted PMSMs is proposed in this paper. Firstly, the mathematical model of PMSMs is established in the two-phase synchronous rotating orthogonal reference coordinate system, and the slow and fast variation subsystems are obtained based on the quasi-steady-state theory. Secondly, a tracking differentiator (TD)-based and exponential reaching law-based sliding mode controllers are individually designed within dual-time-scale, respectively. As a result, the eventual SMC strategy is presented, and the stability of control system is analyzed by applying the Lyapunov stability theory. The main contribution of this study is to present an alternative control framework for the PMSMs servo system, where the dual-time-scale characteristic is involved, and thus a non-cascade control structure that different from the traditional drive strategy is proposed in the motor community. Finally, the model of whole system is built and carried out on the simulation platform. Research results demonstrate that the presented servo control system can accurately track the reference angle velocity signal, while the strong robustness and fast response performance are guaranteed in the presence of external disturbances. In addition, the three-phase current transient response values are completely symmetrical with the rapid adjustment characteristic.

Finite-Time Extended State Observer-Based Fixed-Time Attitude Control for Hypersonic Vehicles

A finite-time extended, state-observer-based, fixed-time backstepping control algorithm was designed for hypersonic flight vehicles. To enhance the robustness of the controller, two novel finite-time extended state observers were introduced to compensate for the negative effects of lumped disturbances such as uncertainties and external disturbances. Two hyperbolic sine tracking differentiators were used to approximate the derivatives of the virtual control signals and guidance commands, thereby alleviating the computational burden associated with traditional backstepping control. Furthermore, a fixed-time backstepping attitude controller was used to guarantee that the tracking errors converged to a small neighbor of the origin in fixed time. According to the simulation results, the proposed controller outperformed a fixed-time sliding mode disturbance, observer-based, finite-time backstepping controller in terms of the tracking precision and convergence rate. Moreover, the proposed controller was noted to be robust in simulations involving lumped disturbances.

An Improved Dynamic Surface Sliding Mode Method for Autonomous Cooperative Formation Control of Underactuated USVS with Complex Marine Environment Disturbances

Abstract In this paper, a novel dynamic surface sliding mode control (DSSMC) method, combined with a lateral velocity tracking differentiator (LVTD), is proposed for the cooperative formation control of underactuated unmanned surface vehicles (USVs) exposed to complex marine environment disturbances. Firstly, in view of the kinematic and dynamic models of USVs and the design idea of a virtual control law in a backstepping approach, the trajectory tracking control problem of USVs’ cooperative formation is transformed into a stabilisation problem of the virtual control law of longitudinal and lateral velocities. Then, aiming at the problem of differential explosion caused by repeated derivation in the process of backstepping design, the first-order low-pass filter about the virtual longitudinal velocity and intermediate state quantity of position is constructed to replace differential calculations during the design of the control law, respectively. In order to reduce the steady-state error when stabilising the virtual lateral velocity control law, the integral term is introduced into the design of the sliding mode surface with a lateral velocity error, and then the second-order sliding mode surface with an integral is structured. In addition, due to the problem of controller oscillation and the role of the tracking differentiator (TD) in active disturbance rejection control (ADRC), the LVTD is designed to smooth the state quantity of lateral velocity. Subsequently, based on the dynamic model of USV under complex marine environment disturbances, the nonlinear disturbance observer is designed to observe the disturbances and compensate the control law. Finally, the whole cooperative formation system is proved to be uniformly and ultimately bounded, according to the Lyapunov stability theory, and the stability and validity of the method is also verified by the simulation results.

Input-and-Measurement Event-Triggered Output-Feedback Chattering Reduction Control for MEMS Gyroscopes

This article presents an input-and-measurement event-triggered output-feedback chattering reduction control for microelectromechanical system (MEMS) gyroscopes. To realize online estimation with decreased communication burden along sensor-to-control channel, a switching threshold-based sampler is embedded to achieve an intermittent measurement-based extended state observer (IMESO) capable of synchronously observing unavailable velocity states and disturbances, meanwhile, a mathematical presentation reflecting the interaction between design parameters and upper boundary of estimation errors is deduced to make argument tuning easy. Next, an event-triggered output-feedback control rule is developed in the controller-to-actuator channel to obtain a discrete control signal with less occupation on communication resources without inducing Zeno phenomena. Besides, to enforce system profiles evolve within the predefined performance boundaries with reduced chattering, a tracking differentiator (TD)-based prescribed performance control (TDPPC) is proposed, where the time differentiation of the preselected envelopes can be managed with smooth transient, and a balance between system performance and sampling cost can be ensured. Finally, a sigmoid function-based TD (STD), rather than dynamic surface control, is utilized to overcome the complexity explosion. Comparison simulations are performed to show the superiorities and effectiveness of the established controller.

Adaptive Neural-Network-Based Nonsingular Fast Terminal Sliding Mode Control for a Quadrotor with Dynamic Uncertainty

This paper proposes an adaptive neural-network-based nonsingular fast terminal sliding mode (NN-NFTSMC) approach to address the trajectory tracking control problem of a quadrotor in the presence of model uncertainties and external disturbances. First, the dynamic model of the quadrotor with uncertainty is derived. Then, a control scheme using nonsingular fast terminal sliding mode control (NFTSMC) is proposed to guarantee the finite-time convergence of the quadrotor to its desired trajectory. NFTSMC is firstly formulated for the case that the upper bound of the lumped uncertainty is known in advance. Under this framework, a disturbance observer by using the hyperbolic tangent nonlinear tracking differentiator (TANH-NTD) is designed to estimate the external interference, and a neural network (NN) approximator is used to develop an online estimate of the model uncertainty. Subsequently, adaptive algorithms are designed to compensate the approximation error and update the NN weight matrix. An NN-NFTSMC algorithm is formulated to provide the system with robustness to the model uncertainty and external disturbance. Moreover, Lyapunov-based approach is employed to prove the global stability of the closed-loop system and the finite-time convergence of the trajectory tracking errors. The results of a comparative simulation study with other recent methods illustrate the proposed control method reduces the chattering effectively and has remarkable performance.

An Improved Extended State Observer-Based Composite Nonlinear Control for Permanent Magnet Synchronous Motor Speed Regulation Systems

This paper addresses the problems of an improved extended state observer (ESO)-based composite nonlinear control for the permanent magnet synchronous motor (PMSM) speed regulation systems, which is primarily constituted by a linear ESO-based feedforward compensation and nonlinear proportional feedback (NPF) control law. Firstly, by taking the parametric perturbations and external disturbances into account, a novel linear ESO is designed and analyzed to estimate the lumped disturbance, such that the system anti-disturbance performance is preserved. Meanwhile, the estimation of system state is also performed. Then, an optimal control synthesis function-based tracking differentiator (TD) is developed to arrange the transition dynamic for the reference velocity value, while its high quality differential signal is facilitated. Furthermore, an adaptive proportional control law is proposed, resulting in the eventual composite nonlinear strategy by incorporating the estimate values into the designed NPF controller. Finally, a PMSM servo system is studied to demonstrate the advantages and effectiveness of the proposed approaches.

Distributed active disturbance rejection formation containment control for multiple autonomous underwater vehicles with prescribed performance

In this paper, a distributed formation containment control (FCC) issue is studied for multiple autonomous underwater vehicles (MAUVs) system with prescribed performance based on the active disturbance rejection control (ADRC) method in three-dimensional space. The unknown nonlinearities and external disturbances of the MAUVs system are approximated in real time by means of extended state observers (ESOs). Furthermore, tracking differentiators (TDs) are introduced for the sake of refraining from the explosion of complexity induced by the derivatives of the virtual control variables of autonomous underwater vehicles. Applying funnel variables, our designed control strategy ensures the formation tracking errors and containment errors to keep within the specified ranges, hence enhancing the control performance of the MAUVs system. Then, a FCC-ADRC scheme for MAUVs system is proposed. Compared with the traditional FCC scheme, the proposed FCC-ADRC scheme not only does not depend on the specific system configuration, but also can deal with any bounded disturbances, thus obtaining a more general, effective and robust disturbance rejection FCC strategies. Additionally, the stability of MAUVs system is verified through Lyapunov stability analysis. At last, the error curves and time-varying formation containment trajectories obtained by simulation confirm the feasibility and effectiveness of our method.

Flexible joint parameters identification method based on improved tracking differentiator and adaptive differential evolution.

The assembly error of flexible joints and the change in joint stiffness during movement make the actual value of joint parameters inconsistent with the given value, which affects the joint control accuracy. In order to suppress the influence of parameters error, a parameters identification method for flexible joint combined offline identification and online compensation is proposed. First, the offline identification model of inertia, mass, and damping and the online identification model of joint stiffness are established, respectively. Then, a hybrid tracking differentiator based on an improved Sigmoid function is designed to track the differential signals of joint motion parameters, and the Lyapunov function is designed to prove its convergence. The adaptive differential evolution is used as the identification algorithm, and the improved adaptive crossover, mutation factor, and Metropolis acceptance criterion are designed to improve the convergence speed. Finally, a feedforward control structure based on identification is designed to compensate for the model deviation. Simulation and experimental results show that the improved differentiator can effectively improve the tracking speed and derivation accuracy of the signals. Compared with other algorithms, the proposed identification method has a faster convergence speed and higher identification accuracy, and feedforward compensation control can effectively correct model parameters and improve control accuracy.

A Dual-Position Loop LLADRC Control Method Based on Harmonic Gear Drive

High-resolution imaging has become a development trend and is widely used in military and civil fields. As the carrying equipment of imaging system, the speed stability of tracking turntable is the basis of high-resolution and stable imaging. At present, in the aerospace field, there are high requirements for peak power dissipation and holding torque, so flexible joints such as harmonic gear drive are mostly used to realize the function. The characteristics of flexible load have a great impact on the characteristics of motion control, which is easy to cause mechanical resonance, lead to system instability, and have a great impact on speed stability and position tracking accuracy. Therefore, it is necessary to study the servo system of flexible load. In order to solve the problems of high-precision position control and speed stability at low speed of flexible turntable with uncertain load, on the one hand, we comprehensively consider the advantages and disadvantages of semi-closed-loop and full closed-loop control and design a dual-position loop feedback control system combined with the analysis of dynamic equation to realize speed stability and high-precision position control. On the other hand, according to the requirements of the speed stability at low speed of the turntable, the tracking differentiator (TD) is designed innovatively through the language three-point interpolation subdivision and five-point pre-deduction calculation method. Finally, a dual-position loop LLADRC (language linear active disturbances rejection controller) control method based on harmonic gear drive is studied. By comparing the semi-closed loop, dual-position loop, dual-position loop LADRC (linear active disturbances rejection controller, ADRC), and dual-position loop LLADRC methods through simulation analysis, it can be shown that the double position LLADRC control method is obviously superior to other schemes in terms of rapidity, speed stability at low speed, and position tracking accuracy. The theoretical research is verified by experimental test. When the given speed is 0.1 ° / s , taking the pitch axis as an example, the pitch speed error is 0.0039 ° / s (3σ). When the maximum speed of the given curve is 20 ° / s and the maximum acceleration is 16 ° / s , the position tracking error is 0.0025° (3σ). This control method solves the problems of system instability and low-speed stability in high-precision control of turntable system based on harmonic gear drive and provides a method for high-precision control of high-resolution imaging turntable.

Mathematical Modeling and Control of COVID-19 Using Super Twisting Sliding Mode and Nonlinear Techniques.

Since the outbreak of the COVID-19 epidemic, several control strategies have been proposed. The rapid spread of COVID-19 globally, allied with the fact that COVID-19 is a serious threat to people's health and life, motivated many researchers around the world to investigate new methods and techniques to control its spread and offer treatment. Currently, the most effective approach to containing SARS-CoV-2 (COVID-19) and minimizing its impact on education and the economy remains a vaccination control strategy, however. In this paper, a modified version of the susceptible, exposed, infectious, and recovered (SEIR) model using vaccination control with a novel construct of active disturbance rejection control (ADRC) is thus used to generate a proper vaccination control scheme by rejecting those disturbances that might possibly affect the system. For the COVID-19 system, which has a unit relative degree, a new structure for the ADRC has been introduced by embedding the tracking differentiator (TD) in the control unit to obtain an error signal and its derivative. Two further novel nonlinear controllers, the nonlinear PID and a super twisting sliding mode (STC-SM) were also used with the TD to develop a new version of the nonlinear state error feedback (NLSEF), while a new nonlinear extended state observer (NLESO) was introduced to estimate the system state and total disturbance. The final simulation results show that the proposed methods achieve excellent performance compared to conventional active disturbance rejection controls.

Three-dimensional integrated guidance and control with input saturation and impact angle constraints

Considering the problem of a skid-to-turn (STT) interceptor attacking maneuvering targets in the three-dimensional space, a new integrated guidance and control (IGC) law with the constraints of impact angles and input saturation is developed. To achieve the finite-time convergence and satisfactory input characteristics, a time-varying sliding mode control (TVSMC) method is presented based on a time base generator function. To this end, the IGC scheme is developed based on the TVSMC and the back-stepping. At each step, the derivative of the virtual signal is approximated by a tracking differentiator. Meanwhile, an auxiliary compensation system is designed to reduce the adverse effect raised from the saturation error. Moreover, the modeling uncertainties and disturbances are attenuated effectively by using fractional power extended state observers to estimate them. The closed-loop system states are proved to be uniformly ultimately bounded and the controlled states are proved to converge into small neighborhoods of the origin at the interception time. Finally, the performance of the presented IGC law is verified through numerical simulations.

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.

A relative degree one modified active disturbance rejection control for four-tank level control system

Abstract This paper deals with the disturbance rejection, parameter uncertainty cancelation, and the closed-loop stabilization of the water level of the four-tank nonlinear system. For the four-tank system with relative degree one, a new structure of the active disturbance rejection control (ADRC) has been presented by incorporating a tracking differentiator (TD) in the control unit to obtain the derivate of the tracking error. Thus, the nonlinear-PD control together with the TD serves as a new nonlinear state error feedback. Moreover, a sliding mode extended state observer is presented in the feedback loop to estimate the system's state and the total disturbance. The proposed scheme has been compared with several control schemes including linear and nonlinear versions of ADRC techniques. Finally, the simulation results show that the proposed scheme achieves excellent results in terms of disturbance elimination and output tracking as compared to other conventional schemes. It was able to control the water levels in the two lower tanks to their desired value and exhibits excellent performance in terms of Integral Time Absolute Error (ITAE) and Objective Performance Index (OPI).