Tracking Differentiator Research Articles

Adaptive neural network observer‐based filtered backstepping control for nonlinear systems with fuzzy dead‐zone and uncertainty

SummaryThis study proposes a high gain observer‐based filtered backstepping control scheme for nonlinear systems with unknown dynamics and dead‐zone constraint. Majority of the previously papers describe dead‐zone by the conventional certain models, assume that all state variables are available and invoke the backstepping or conventional dynamic surface control (CDSC) approaches for controller design. This work describes the dead‐zone by the fuzzy model, invokes radial basis function neural network (RBFNN) to model the unknown functions and proposes a RBFNN‐based high gain observer to estimate unmeasurable states. To avoid the complexity explosion in the backstepping approach and eliminate the sensitivity to the time‐constant of the first‐order filters in the CDSC, a nonlinear tracking differentiator (NTD) with finite time convergence property is used instead of the first‐order filters in the CDSC to obtain derivative of the virtual inputs. Moreover, the error compensation mechanism and auxiliary signal are proposed to eliminate the influence of the filtering error and input nonlinearity, respectively. Despite the fuzzy dead‐zone, the proposed scheme makes the closed‐loop signals uniformly ultimately bounded. In comparison with the existing results, (i) some assumptions like certain model of dead‐zone and full state measurement are removed, (ii) “explosion of complexity” and sensitivity to the time constant of the first‐order filters are eliminated, (iii) effect of the filtering error and input nonlinearity are compensated, (iv) number of adjustable parameters and online computational burden are decreased effectively. Simulation results on the two well‐known examples verify the effectiveness and applicability of the proposed new design technique.

Neuroadaptive Optimal Fixed-Time Synchronization and its Circuit Realization for Unidirectionally Coupled FO Self-Sustained Electromechanical Seismograph Systems.

This article investigates the neuroadaptive optimal fixed-time synchronization and its circuit realization along with dynamical analysis for unidirectionally coupled fractional-order (FO) self-sustained electromechanical seismograph systems under subharmonic and superharmonic oscillations. The synchronization model of the coupled FO seismograph system is established based on drive and response seismic detectors. The dynamical analysis reveals this coupled system generating transient chaos and homoclinic/heteroclinic oscillations. The test results of the constructed equivalent analog circuit further testify its complex nonlinear dynamics. Then, a neuroadaptive optimal fixed-time synchronization controller integrated with the FO hyperbolic tangent tracking differentiator (HTTD), interval type-2 fuzzy neural network (IT2FNN) with transformation, and prescribed performance function (PPF) together with the constraint condition is developed in the backstepping recursive design. Furthermore, it is proved that all signals of this closed-loop system are bounded, and the tracking errors fall into a trap of the prescribed constraint along with the minimized cost function. Extensive studies confirm the effectiveness of the proposed scheme.

Learning-based design optimization of second-order tracking differentiator with application to missile guidance law

Tracking differentiator is widely used to estimate the differential signal of noisy systems with unknown structures. However, there still lacks an efficient approach to tracking differentiator design and optimization, partly due to the nonlinearity by nature, and the high dimension of design parameters. Thus, this paper proposes a learning-based design optimization method. First, neural networks are trained to approximate the multivariate influence on tracking differentiator performance. The resultant learning-based surrogate model is then used to optimize the parameters of tracking differentiator by differential evolution algorithm. The proposed method is applied to Sigmoid-type tracking differentiator and further compared to the unscented Kalman filter with various input signals. The estimation error of the optimized tracking differentiator is reduced by 65.70% compared to that of the benchmark method. The second-order tracking differentiator is integrated into an angular acceleration-based guidance law. Simulation results of tracking moving targets show that the miss distance and control resource are separately lowered by at least 35.70% and 74.12% as opposed to the crude guidance law.

Modified Tracking Differentiator for Enhancing the Performance of Exoskeleton Knee System Based on Active Disturbance Rejection Control

Exoskeleton robots help users with mechanical forces by recognizing their intentions, and they require a lot of energy efficiency, a lot of load capacity, and a good fit. A basic one degree of freedom (DOF) construction was devised in this work, which was mostly used in the knees of exoskeleton robots. The exoskeleton is a small robotic device used for knee injury training. It is a nonlinear mathematical model with many mechanical factors that might vary and produce uncertainty, as well as external disturbances that can be utilized to monitor control. The transitioning process is frequently organized using tracking differentiator TD to resolve the conflict between system speed and overshoot. An active disturbance rejection control (ADRC) with a modified tracking differentiator is described to tackle these challenges, enhance control accuracy, and reduce settling time for exoskeleton modified trajectory differentiator (MTD).Simulation tests showed that (MTD) reduced the tracking error by 36%, when compared with the improved TD1 and 37.5% for Hans TD2 at uncertainty case . Despite the presence of several model uncertainties, the suggested training knee exoskeleton robot system using the MTD-ADRC was able to achieve the necessary target value. Control design and analysis can be done with Matlab and Simulink. Index Terms— Exoskeleton system, ADRC, MTD, nonlinear calculus, robustness

Motion Control of Autonomous Underwater Helicopter Based on Linear Active Disturbance Rejection Control with Tracking Differentiator

As a new disk-shaped autonomous underwater vehicle (AUV), the autonomous underwater helicopter (AUH) is devoted to subsea operations, usually diving into the seabed and docking with a subsea docking system. Due to the motion control’s performance, the AUH’s stability and steady-state accuracy are affected remarkably while docking. Moreover, considering the difficulties of hydrodynamic modeling of AUHs, the classical model-based control method is unsuitable for AUHs. Moreover, there is a large gap between the hydrodynamic simulation results and real situations. Hence, based on the data-driven principle, the linear active disturbance rejection control with a tracking differentiator (LADRC-TD) algorithm is employed for AUH depths and heading control. As the simulation experiments prove, LADRC and LADRC-TD have better anti-interference performance when compared with PID. According to the pool experiments, overshoots of the LADRC-TD are 20 cm and 3° for the depth control and heading control, respectively, which are superior to PID and LADRC. Meanwhile, the steady-state accuracy of the LADRC-TD is ±21 cm and ±2.5° for the depth and heading control, respectively, which is inferior to PID and the same as LADRC.

Robust Liquid Level Control of Quadruple Tank System: A Nonlinear Model-Free Approach

In this paper, two new versions of modified active disturbance rejection control (MADRC) are proposed to stabilize a nonlinear quadruple tank system and control the water levels of the lower two tanks in the presence of exogenous disturbances, parameter uncertainties, and parallel varying input set-points. The first proposed scheme is configured from the combination of a modified tracking differentiator (TD), modified super twisting sliding mode (STC-SM), and modified nonlinear extended state observer (NLESO), while the second proposed scheme is obtained by aggregating another modified TD, a modified nonlinear state error feedback (MNLSEF), and a fal-function-based ESO. The MADRC schemes with a nonlinear quadruple tank system are investigated by running simulations in the MATLAB/SIMULINK environment and several comparison experiments are conducted to validate the effectiveness of the proposed control schemes. Furthermore, the genetic algorithm (GA) is used as a tuning algorithm to parametrize the proposed MADRC schemes with the integral time absolute error (ITAE), integral square of the control signal (ISU), and integral absolute of the control signal (IAU) as an output performance index (OPI). Finally, the simulation results show the robustness of the proposed schemes with a noticeable reduction in the OPI.

Design Decoupling Controller based on Feedforward and Improved PID for Tension System

It is difficult to precisely control the substrate tension due to the tension system of roll-to-roll coating machine with strong coupling and time-varying parameters. Therefore, a feedforward improved proportional integral derivative (PID) parameters self-tuning decoupling controller of tension system is proposed in this paper. According to the components and working principle of the coating machine, the nonlinear coupling mechanism model of the global tension system is established, and the model is linearized by using the Taylor series. Based on the linear model, a feedforward improved PID parameters self-tuning decoupling controller is designed for tension system. Through the feedforward control compensates the modeled tension and speed interference, a tracking differentiator (TD) is used to improve the performance of PID, and the online self-tuning of PID parameters can be realized by an Radial Basis Function (RBF) identification network. The simulation results show that the proposed decoupling control strategy of tension system can well suppress the coupling interference between the units, and realize the real-time tuning of PID parameters.

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.

Output-Feedback Flexible Performance-Based Safe Formation for Underactuated Unmanned Surface Vehicles

This article studies a cooperative time-varying formation of underactuated unmanned surface vehicles (USVs) with position-heading measurements, following the philosophies of (i) balance operation between performance constraints and safety requirements including collision avoidance and connectivity maintenance, and (ii) concise finite-time control design based on the integrated finite-time extended state observer (IFTESO) to facilitate the practical implementation. At first, to accomplish the guidance design of networked vehicles in the complex ocean environment and guarantee the performance of cooperative tracking errors, a flexible performance-based control scheme is investigated by feeding the potential effects of safety requirements into the modification signals of the user-specified performance functions. Then, without the application of cumbersome nonlinear tracking differentiators and backstepping techniques, a output-feedback IFTESO-based method provides a concise solution with a convenient design by taking advantage of homogeneous system theories, which further reduces the traditional computation consumption. Finally, the performance of the proposed scheme is validated by numerical simulations.

Adptive Heading Control of Underactuated Unmanned Surface Vehicle Based on Improved Backpropagation Neural Network

Abstract Aiming at the challenges to the accurate and stable heading control of underactuated unmanned surface vehicles arising from the nonlinear interference caused by the overlay and the interaction of multi interference, and also the uncertainties of model parameters, a heading control algorithm for an underactuated unmanned surface vehicle based on an improved backpropagation neural network is proposed. Based on applying optimization theory to realize that the underactuated unmanned surface vehicle tracks the desired yaw angle and maintains it, the improved momentum of weight is combined with an improved tracking differentiator to improve the robustness of the system and the dynamic property of the control. A hyperbolic tangent function is used to establish the nonlinear mappings an approximate method is adopted to summarize the general mathematical expressions, and the gradient descent method is applied to ensure the convergence. The simulation results show that the proposed algorithm has the advantages of strong robustness, strong anti-interference and high control accuracy. Compared with two commonly used heading control algorithms, the accuracy of the heading control in the complex environment of the proposed algorithm is improved by more than 50%.

Disturbance observer–based neural adaptive fault-tolerant control for flexible air-breathing hypersonic vehicles with multiple model uncertainties

One of the critical problems for flexible vehicles is how to simultaneously address the multiple uncertainty compensation and flexible vibration suppression. This paper focuses on the smooth adaptive fault-tolerant control design problem of a two-layer framework for flexible air-breathing hypersonic vehicles subject to contingent actuator failures and multiple model uncertainties. The first layer provides a disturbance observer–based neural adaptive fault-tolerant controller overcoming actuator failures and multiple model uncertainties. The second layer relies on the tracking differentiator and filter combined with the controller seamlessly, generating smooth reference information, which is highly desirable for flexible vibration suppression. Then, the analysis by the Lyapunov theory strictly proves the uniform ultimately boundedness of all the control and filter state variables. Finally, the simulation results demonstrate the dominant tracking control performance of the proposed control method.

Control method for permanent magnet synchronous motor based on fractional active disturbance rejection

To improve the response speed and anti-interference ability of a permanent magnet synchronous motor (PMSM), a PMSM control method based on fractional-order active disturbance rejection control (FOADRC) is proposed in this study. First, a fractional-order tracking differentiator (FOTD) and fractional-order extended state observer (FOESO) are designed using the fractional calculus. According to the response speed of the FOTD and the observation effect of the FOESO, a new fastest function and new nonlinear function are designed. Second, a fractional-order active disturbance rejection (FOADR) controller is built based on the new FOTD, new FOESO, and nonlinear feedback control law, and its stability is proven. Finally, the superiority and effectiveness of the proposed strategy are verified through a simulation and experiments.

A fast transient tracking differentiator for high-precision motion systems

High-quality velocity signal plays an important role in fast and precise motion systems, but most commercially available motion systems are not commonly equipped with velocity sensors; hence, full access to the system states is impossible. A fast transient tracking differentiator is proposed in this article for obtaining the noise-less time derivative from a noisy measurement. The fast transient tracking differentiator is conceived within the framework of tracking differentiator methodology and is accomplished by integrating a power-like function with a smooth hyperbolic sine function. Tracking differentiator theory and Lyapunov direct method are employed to show the global asymptotic convergence. Advantages of the proposed fast transient tracking differentiator include the easy implementation with intuitive structure and high computational efficiency and faster transient and higher noise attenuation for both small and large initial estimation errors. The proposed fast transient tracking differentiator can be applied to a large class of motion systems by cascading to a robust output feedback proportional–derivative control for fast and high-precision positioning with position measurement only. Numerical simulation and real-time experimental comparisons demonstrate that the proposed approach provides an easygoing model-free output feedback solution for fast and accurate velocity reconstruction and high-performance positioning of uncertain motion systems with position measurement only.

Nonlinear Tracking Differentiator Based Prescribed Performance Control for Space Manipulator

Nonlinear Tracking Differentiator Based Prescribed Performance Control for Space Manipulator

Generalized Variable Gain ADRC for Nonlinear Systems and Its Application to Delta Parallel Manipulators

In this paper, a novel generalized variable gain active disturbance rejection control (VGADRC) method is proposed for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> -th order nonlinear system. The generalized VGADRC, including generalized variable gain tracking differentiator (VGTD), generalized variable gain extended state observer (VGESO), and generalized variable gain controller (VGC), incorporates error-based variable gains to achieve desired control performance. Moreover, the stability analysis of VGADRC is performed, and the existence of feasible solutions are discussed and expressed explicitly. Finally, the generalized VGADRC method is applied to delta parallel manipulators, and the numerical simulation results and experiment results are presented to illustrate the effectiveness of the proposed method.

A Novel Reduced-Order Generalized Differentiator With Zero-Phase Lag and Improved Noise Attenuation

The differentiator is widely used in power converter control to improve the control performance. However, the noise attenuation and phase lag always challenge the digital implementation of the differentiator. The existing differentiators, such as the high-pass filter, nonideal generalized integrator, and the discrete-time optimal control-based tracking differentiator, all face the same incompatible contradiction between noise attenuation and phase lag. The multiple second-order general differentiators lack polarity-selective property and suffer a huge computational burden. To address these issues, this letter proposes a novel reduced-order generalized differentiator (ROGD). Then, different discretization versions of the proposed ROGD and existing differentiators are discussed and compared to demonstrate that the proposed ROGD can achieve excellent performance for differentiation estimation with zero-phase lag and improved noise attenuation at the same time. The effectiveness of the proposed differentiator is finally verified by the differentiator simulation and the experiments of the grid-forming control where the differentiator is used.

On a novel tracking differentiator design based on iterative learning in a moving window

On a novel tracking differentiator design based on iterative learning in a moving window

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.

Dynamical analysis and accelerated adaptive backstepping funnel control for dual-mass MEMS gyroscope under event trigger

This paper investigates an adaptive backstepping funnel control scheme with an event-triggered mechanism for a chaotic dual-mass Micro-Electro-Mechanical Systems (MEMS) gyroscope. The mathematical model of the dual-mass micro-gyroscope is first developed based on a mutual mechanical coupling. Then, its inherent nonlinear characteristics under different spring and coupling coefficients, all of which have noticeable impacts on the system sensitivity, are fully examined through phase and Lyapunov exponent diagrams. In order to methodically address the control problem involving the uncertainty, the slow convergence, the constraint violation, the “item explosion” and the communication resource waste, an accelerated adaptive backstepping funnel controller is proposed by combining the type-2 sequential fuzzy neural network (T2SFNN), the speed function, the asymmetric funnel boundaries, the accelerated exponential integral tracking differentiator (AEITD) and the event-triggered mechanism. The recommended scheme not only well resolve the above issues, but also guarantee the prescribed performance requirements and the boundedness of all signals in closed-loop system. Finally, the effectiveness of the control scheme is substantiated through several simulated results.

Model predictive control–based compound control strategy for ducted rockets gas flow with anti-regulation suppression

Variable flow ducted rockets are excellent candidates for propulsion systems in hypersonic vehicles. However, the anti-regulation characteristics of the gas flow not only decrease the stability of ducted rockets but also create difficulties in the control system design. In this study, a model predictive control (MPC)–based compound control algorithm that suppresses the anti-regulation is proposed. First, a mathematical model involving a gas flow regulation system was developed to describe and analyse the anti-regulation. Next, a fused feedback variable that included both the gas flow and the gas generator pressure signal was constructed. An MPC control system with the fused feedback variable was also designed. Then, to accurately predict the gas flow and the anti-regulation, a nonlinear disturbance observer was constructed. To evaluate the performance of the controller, two scenarios that were regulated by a tracking differentiator proportional–integral–derivative controller and a model reference adaptive control controller were constructed and compared. The theoretical results demonstrate that the proposed method exhibited a superior performance compared to previous methods by overcoming the supposed trade-off between the response rate and the anti-regulation of gas flow systems.