Tracking Differentiator Research Articles

Dynamic event-triggered fixed-time consensus control for coupled multi-permanent magnet synchronous motors stochastic system with prescribed performance

With the ubiquity of permanent magnet synchronous motors (PMSM), multi-PMSMs are increasingly being elastically coupled to achieve greater output power. The authors establish a general mathematical model of coupled multi-PMSMs system. The dynamic analysis of the coupled multi-PMSMs system is analyzed using coupled three-PMSMs system as an example, and a dynamic event-triggered fixed-time consensus controller with prescribed performance is constructed for coupled PMSMs stochastic system. In addition, Interval Type-3 Fuzzy System (IT3FS) is employed to estimate unknown functions, the computing cost is reduced by updating the weights based on only one adaptive law per PMSM. To enhance the efficiency of communication resource utilization, a dynamic event-triggered mechanism is introduced, where the triggering condition depends on a dynamic auxiliary variable. Moreover, fixed-time control technical is applied to guarantee the setting time and a novel fixed-time prescribed performance function (PPF) is constructed to constrain consensus errors. To cope with the “complexity explosion”, a fixed-time tracking differentiator (TD) is introduced and the corresponding filtered error compensation signals is designed. Finally, the authors demonstrate the system is fixed-time stabilized in probability by applying fixed-time stabilization Lyapunov stability criterion, and the simulation results of a coupled three-PMSMs stochastic system show that the presented algorithm is feasible.

The active disturbance rejection control method for small-scale turbojet engine

To enhance the disturbance resistance of the control system for a small-scale turbojet engine, research has been conducted on the active disturbance rejection control (ADRC) method. With gas generator speed N g as the control parameter, an ADRC control scheme was established. Tracking Differentiator (TD), Nonlinear State Error Feedback (NLSEF), and Extended State Observer (ESO) were analyzed in detail, and their parameters were designed. The ADRC method was compared with the Expert PID control method through simulation experiments. The results show that ADRC has a small overshoot and strong disturbance rejection capabilities, allowing for a faster recovery to a steady state when disturbances occur.

Research on linear/nonlinear active disturbance rejection switching control of PMSM speed servo system

An improved linear/nonlinear active disturbance rejection switching control strategy is proposed to enhance the dynamic response and disturbance suppression capabilities of the permanent magnet synchronous motor (PMSM) speed servo system. Firstly, facilitated by a tracking differentiator, rapid setpoint tracking is achieved without speed overshoot, effectively addressing the inherent conflict between fast system response and overshooting. Secondly, weight factors are introduced into the control law, and a novel switching criterion based on the step function is designed, enabling the system to smoothly transition between operating modes in the presence of disturbances with varying amplitudes. This facilitates accurate estimation and swift compensation for disturbances, thereby enhancing control precision and robustness. Additionally, a frequency domain analysis of the extended state observer is conducted, leading to the formulation of a parameter tuning scheme for the controller. Lastly, simulation tests validate the feasibility and effectiveness of this strategy as a PMSM speed controller. The system exhibits superior dynamic tracking and disturbance suppression performance over a wide speed range.

Distributed predefined-time estimator-based affine formation target-enclosing maneuver control for cooperative underactuated quadrotor UAVs with fault-tolerant capabilities

The paper presents a two-layer, disturbance-resistant, and fault-tolerant affine formation maneuver control scheme that accomplishes the surrounding of a dynamic target with multiple underactuated Quadrotor Unmanned Aerial Vehicles (QUAVs). This scheme mainly consists of predefined-time estimators and fixed-time tracking controllers, with a hybrid Laplacian matrix describing the communication among these QUAVs. At the first layer, we devise predefined time estimators for leading and following QUAVs, enabling accurate estimation of desired information. In the second layer, we initially devise a fixed-time hybrid observer to estimate unknown disturbances and actuator faults. Fixed-time translational tracking controllers are then proposed, and the intermediary control input from these controllers is used to extract the desired attitude and angular velocities for the fixed-time rotational tracking controllers. We employ an exact tracking differentiator to handle variables that are challenging to differentiate directly. The paper includes a demonstration of the control system stability through mathematical proof, as well as the presentation of simulation results and comparative simulations.

Double-loop control in air–ground cooperation for a switched-trajectory quadrotor under gust winds

In this paper, a double-loop tracking control strategy with finite-time convergence is investigated for a switched-trajectory quadrotor subjected to gust winds in air–ground cooperation. To handle the complexity of switched-trajectory tracking, an adaptive tracking differentiator is presented in an outer loop to arrange transition processes. Fast integral terminal sliding mode control is also used in the outer loop to improve convergence speed and tracking accuracy. The gust winds are estimated and compensated by a nonlinear extended state observer and a nonlinear controller with finite-time convergence in an inner loop, respectively. Convergency analyses are presented with the double-loop tracking control strategy for the switched-trajectory quadrotor. Comparison experiments with existing studies show superior performances of the proposed control method for the quadrotor in air–ground cooperation under gust winds.

UAV trajectory tracking under wind disturbance based on novel antidisturbance sliding mode control

With the widespread application of unmanned aerial vehicles, harsh environments require higher control performance. Numerous existing works offer solutions for handling external disturbances during flight; however, the timeliness of the disturbance compensation is rarely discussed. This study focuses on trajectory tracking under external wind disturbances, specifically under two types of interference: average wind and wind shear. After compensating for the disturbance, a novel antidisturbance sliding mode control is designed based on reference model, to realize accurate, robust, and chatterless trajectory tracking under wind disturbance. Firstly, we addressed the limitations of conventional extended state observers, nonderived forms, and inadequate use of information by introducing state compensation function observers to enhance estimation accuracy for states and disturbances that are challenging to measure directly. Moreover, the disturbance variation is estimated using tracking differentiator and then compensated in the controller to enhance antidisturbance sensitivity. In addition, the effectiveness and stability of the proposed observer and controller are analyzed. Finally, a two-step verification is presented, including simulation with input disturbances and actual flight under two wind field types; multiple industrial fans are used to generate the average wind and wind shear during the experiment. Two robust control methods, state-of-the-art active disturbance rejection control and sliding mode control, are also implemented for comparison, and the results indicate that more than 61.2% accuracy improvement over comparison methods is achieved in simulation and actual experiments.

An all-position type control strategy of the haptic interactive virtual training system based on cable-driven

The virtual microgravity training system based on cable drive usually uses a force-position hybrid control strategy which has following problems: the force control method is sensitive to load disturbances, variable stiffness characteristics of cables reduce the control accuracy of PID controllers, and the expected tension fluctuations are large. These will affect the control accuracy, and further affect the tactile sensation and training effectiveness of astronauts. For the above problems, an all-position type control strategy is proposed to improve the system control accuracy. This strategy uses a compliant control method. In this method, elastic elements are connected in cables, the conversion model of tension and displacement is established, and the tension control is realized by the displacement control which has characteristics of high control accuracy and strong resistance to load disturbance. The PID controller is replaced by the active disturbance rejection controller. In this controller, the tracking differentiator is used to reduce high frequency noises of the input signal, and the extended state observer is used to estimate and compensate the error caused by the change of the cable stiffness. A tension distribution method is designed to make expected cable tensions approach the average tension to reduce the tension fluctuation. The experimental results show that compared with the force-position hybrid control strategy, the all-position type control strategy reduces the tension error and speed error by about 51% and 33% respectively.

Event-based adaptive active disturbance rejection control for nonlinear large-scale systems with input delay

This paper explores the active disturbance rejection control (ADRC) issue for interconnected large-scale systems with unmeasured states, input delay and a total disturbance composed of unknown constrained external disturbances. An enhanced extended state observer is built via fuzzy logic systems to identify system uncertainties and states and keep restraining the total disturbance of uncertain systems. When the triggering condition is met, the tracking differentiator component of the ADRC is able to reduce the communication overhead by successfully applying the backstepping control approach and the dynamic event-triggered mechanism. Meanwhile, the integral compensation method eliminates the negative effect cased by the input delay. Furthermore, the developed decentralised fuzzy control scheme can ensure that all signals in the closed-loop systems are semiglobally uniformly ultimately bounded and Zeno behaviour does not occurs. Finally, an example is used to depict the validity of the control approach.

Adaptive tracking control for constrained nonlinear nonstrict-feedback switched stochastic systems with unknown control directions

This brief proposes a novel tracking control strategy to cope with the asymmetric state constraints for nonstrict-feedback and nonlinear switched stochastic systems with unknown control directions. Firstly, without requiring piecewise Barrier Lyapunov functions (BLFs), the asymmetric constraint restrictions are unfastened well in the recursive idea according to a series of new-style coordinate transformations. Then, a novel error compensation mechanism based on the state constraint conditions is incorporated into the tracking differentiator (TD) technology to tackle the “differential explosion” problem in the backstepping design, and a low-cost adaptive control strategy under single adaptive law is built to simplify the computation, meanwhile, the control objective is achieved. Followed by the rigorous theoretical proof, the applicability is presented by a practical example.

A novel strategy for a 7-DOF space manipulator transferring a captured target with collision avoidance

This paper presents a collision-free transferring strategy for space manipulator in the static environment. The entire trajectory is planned based on acceleration to improve the smoothness. Firstly, the improved bidirectional alternating search strategy and the variable-step search strategy are applied to A* algorithm to find a collision-free linear acceleration trajectory of the captured target in Cartesian space effectively and rapidly. Then, the collision between the accessories carried on the target and the space robot is avoided by adjusting the attitude of the target in the aforementioned trajectory. Tracking-differentiator (TD) is adopted to achieve the smooth transition between the adjacent expected attitudes of the target. In addition, considering the posture of the manipulator during the task, an acceleration potential field is established to guide the arm-angle within the safe range all the time. Finally, the performance of the trajectory planning strategy is verified by simulation.

Design of Backstepping Control Based on a Softsign Linear–Nonlinear Tracking Differentiator for an Electro-Optical Tracking System

To address the problems of a low tracking accuracy and slow error convergence in high-order single-input, single-output electro-optical tracking systems, a backstepping control method based on a Softsign linear–nonlinear tracking differentiator is proposed. First, a linear–nonlinear tracking differentiator is designed in conjunction with the Softsign excitation function, using its output as an approximate replacement for the conventional differentiation process. Then, this is combined with backstepping control to eliminate the “explosion of complexity” problem in conventional backstepping procedures due to repeated derivation of virtual control quantities. This reduces the workload of parameter tuning, takes into account the rapidity and stability of signal convergence, and improves the trajectory tracking performance. This method can ensure the boundedness of the system signal. The effectiveness and superiority of this control method are verified through simulations and experiments.

An Equivalent Linearized Discrete-Time Realization of Optimal Control Based Tracking Differentiator

The discrete-time optimal control (DTOC) based tracking differentiator (TD) was first proposed by Han, (named fHan-TD). As for a nonlinear differentiator, it is difficult to evaluate the stability of the system containing fHan-TD. The application of the fHan-TD is also constrained by complex computation. Hence, in this paper, a linearized TD was proposed for the fHan-TD based on the frequency-domain characteristics of fHan-TD and the Sanathanan-Koerner (S-K) iterative method. The linearized fHan-TD, abbreviated as linear-TD, shows the same frequency-domain characteristics as fHan-TD. The theoretical proof of the linear-TD is derived from the DTOC principle. Meanwhile, a sufficient but not necessary condition for the linearization is given. Both the analysis of frequency-domain characteristics and the principle of DTOC show that the conventional fHan-TD can be replaced by the proposed linear-TD with a simple structure and no loss in convergence time. A DSP28379D based testbed was used to verify the characteristics of linear-TD, thus validating the equivalence of fHan-TD and linear-TD. Moreover, experiment results demonstrate that the computational resources required for linear-TD are only 24.4% of fHan-TD. Finally, the effectiveness of the proposed method was verified through experiments on grid-forming (GFM) inverter.

Speed Fluctuation Suppression for Permanent Magnet Synchronous Motor Drives Using Dynamic Surface with Tracking Differentiator

Speed Fluctuation Suppression for Permanent Magnet Synchronous Motor Drives Using Dynamic Surface with Tracking Differentiator

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.

Position Identification Algorithm of PMSM Based on Improved Nonlinear Tracking Differentiator Method

Position Identification Algorithm of PMSM Based on Improved Nonlinear Tracking Differentiator Method

A Double-$r\ fhan$ algorithm for Tracking Different-iator of Active Disturbance Rejection Control

A Double-$r\ fhan$ algorithm for Tracking Different-iator of Active Disturbance Rejection Control

Frequency analysis of a discrete-time fast nonlinear tracking differentiator algorithm based on isochronic region method

<p>In fault detection, feedback control, and other fields, real-time differential estimation of a given signal in a complex noise environment is an important but challenging task. In this paper, a discrete-time fast nonlinear tracking differentiator (FNTD) based on hyperbolic tangent functions was proposed. To start, the differential signal acquisition problem was equated to the time-optimal control (TOC) law for constructing a double-integral system using a state feedback approach. Next, the FNTD algorithm based on the hyperbolic tangent function was presented by utilizing the isochronic region (IR) method in the discrete time domain. Then, the frequency-domain characteristics of the FNTD were analyzed and the rule for tuning the parameters was provided by the frequency scan test method. Finally, the simulation results demonstrated that the proposed FNTD had fast and accurate tracking performance, as well as excellent filtering and differential extraction capability compared with other differentiators.</p>

Tracking Differentiators for Both the Real Time Signals and the Time Delayed Signals

Tracking Differentiators for Both the Real Time Signals and the Time Delayed Signals

On the convergence of tracking differentiator with multiple stochastic disturbances

On the convergence of tracking differentiator with multiple stochastic disturbances

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.