Asymptotic Position Research Articles

High-precision motion servo control of double-rod electro-hydraulic actuators with exact tracking performance

Comprehensive effects coming from measurement noises, matched and mismatched uncertainties make it difficult for electro-hydraulic servo systems to further attain high-accuracy tracking level. The existing control strategies often consider these control issues one-sidedly. Accordingly, we develop two different control strategies combining integral robust control and direct adaptive control for high-precision position control of double-rod electro-hydraulic systems to account for these control issues concurrently. Specially, by skillfully introducing a filtered error function, a novel desired compensation adaptive control framework will be integrated into the controller design to reduce environmental noises. Moreover, an improved noise-alleviation method is proposed to achieve high-accuracy calculation of the standard sign function in nonlinear integral robust terms. Furthermore, each of the control algorithms can guarantee asymptotic position tracking performance in general. Comparative experiments and simulation results show the evident superiorities of the developed control strategies.

Dual-loop integral sliding mode control for robust trajectory tracking of a quadrotor

This paper presents a novel control scheme for the trajectory tracking in a quadrotor. First, the kinematics and dynamics models of the quadrotor with uncertainties are developed by Newton–Euler method. For the nonlinear and coupling dynamic, unmodeled uncertainties and external disturbances, an effective linear extended state observer is designed to estimate them. Then, the overall quadrotor system is divided into two subsystems: translational subsystem and rotational subsystem. For the rotational subsystem, the attitude controller is designed with a dual-loop integral sliding mode control method, and the designed controller is able to track the desired attitudes and angular velocities simultaneously. For the translational subsystem, a globally asymptotic stability position controller based on the hyperbolic functions is designed, and the application of hyperbolic functions can provide a bounded and smooth control input. In the end, both simulation and experiment results are provided to verify the effectiveness of the designed control strategy.

Coordinated Attitude Synchronization and Tracking Control of Multiple Spacecraft Over a Communication Network With a Switching Topology

This paper investigates the coordinated attitude synchronization and tracking problems of multiple rigid-body spacecraft subject to inaccurate inertial parameters. Two adaptive distributed control algorithms are developed based on communications among spacecraft connected through a switching communication network, which allow each switching subgraph to be disconnected. In the first place, by introducing an adaptive strategy for the inertial parameters, a distributed attitude synchronization control algorithm is designed. In particular, a gain selection criteria is specified for the asymptotic attitude synchronization under uniform joint connectivity. In the second place, for the coordinated attitude tracking problem, we first develop a distributed observer for each spacecraft to estimate the reference information associated with a leader over a switching network with uniform joint quasi-strong connectivity. Then, we propose an adaptive tracking scheme such that each spacecraft tracks the estimated information. Finally, numerical examples are given to validate the effectiveness of two proposed adaptive distributed control algorithms.

Simple saturated relay non‐linear PD control for uncertain motion systems with friction and actuator constraint

This study addresses the problem of robust fast and high-precision positioning of uncertain one-degree-of-freedom mechanical systems with friction and actuator constraint. The proposed control is constructed within the framework of saturated proportional–derivative (PD) plus relay action. Global asymptotic positioning stability is proven by Lyapunov's direct method with Barbalat's lemma. The appealing features of the proposed control are that it is fairly easy to construct with simple intuitive structure and the absence of modelling parameter in the control law formulation, and thus it is ready to implement for practical applications. An additive feature is that the proposed control embeds the PD action within one saturation function and hence it omits the elaborating embedment of the control gains within the requested constraint. Another feature is that the proposed approach can be explicitly upper bounded a priori and thus, it has the ability to protect the actuator from saturation completely and to ensure global asymptotic stability featuring fast transient and high steady-state positioning. Numerical simulations and real experimental results demonstrate the effectiveness and improved performance of the proposed approach.

Sufficient Conditions for the Existence of Asymptotic Quiescent Position for One Class of Differential-Difference Systems

The time-delay systems are considered and the limiting behavior of their solutions is investigated. The case in which the solutions have the trivial equilibrium that may not be an invariant set of the system is studied. The notion of an asymptotic quiescent position for the trajectories of delayed systems is introduced. Its stability is analyzed by the method of Lyapunov functions using the Razumikhin approach. Sufficient conditions for the existence of an asymptotic quiescent position for one class of the systems of differential-difference equations are established. Some illustrative examples of nonlinear differential equations with delay that have an asymptotic quiescent position are given and the sufficient conditions are applied to them.

Nonlinear Asymptotic Attitude Estimation Using Double GPS Receivers and Gyro

We present an asymptotically convergent nonlinear attitude estimator using a rate gyro and GPS. Double-difference (DD) carrier phase measurements are provided by at least two GPS antennas. The unknown integer ambiguity factor related to GPS carrier phase measurement is estimated along with the attitude. An observability condition is derived to guarantee the convergence of the estimator when a single baseline vector is available with more than four satellites in view. A systematic procedure for tuning observer parameters is also presented. Finally, the experimental test from a light fixed-wing aircraft illustrates the performance of the proposed observer.

Faster Positioning of One Degree-of-Freedom Mechanical Systems With Friction and Actuator Saturation

This paper concerns with faster positioning of one degree-of-freedom (1DOF) mechanical systems with friction and actuator saturation. A very simple but quite effective saturated relay proportional-derivative (PD) control is proposed. The proposed control is conceived within the framework of nonlinear PD methodology. It is accomplished by adding a relay position error for friction compensation to the saturated PD control law. For faster transient with bounded input, a saturated nonlinear function is introduced. Lyapunov's direct method is employed to prove global asymptotic positioning. The appealing advantages of the proposed control are that it is fairly easy to construct without involvement of any modeling parameter and has the ability to avoid the actuator saturation. Numerical example and experiments demonstrate the effectiveness and improved performance of the proposed approach.

Disturbance Observer-based Trajectory Following Control of Robot Manipulators

Robotic manipulators are usually subject to different types of disturbances. If the effects of such disturbances are not taken into account, it can lead to unsatisfactory tracking performance of the robot and may even destabilize the robot control system. In this paper a novel nonlinear disturbance observer-based controller is designed for robotic manipulators. Previous disturbance observer-based controllers which are designed for robotic systems undergo the restricting assumption that the external disturbance is constant. In this paper a novel two-stage procedure is proposed to design a disturbance observer that improves disturbance attenuation ability of current disturbance observer-based controllers. The proposed method can cope with non-constant disturbance. Furthermore, it is shown that even for the fast time varying disturbance, the controller achieves satisfactory tracking performance. The proposed controller guarantees semi-global asymptotic position and velocity tracking and moreover, removes restrictions of previous studies on the number of degrees of freedom (DOFs), joint types, and manipulator configuration. The effectiveness of the proposed method is verified against different types of external disturbance applied on the robot manipulator and the results are compared with the results of previous methods. Furthermore, the results support the theoretical conclusions.

A simple nonlinear PD control for faster and high-precision positioning of servomechanisms with actuator saturation

Abstract This paper investigates the problem of high performance motion control for servomechanisms subject to actuator saturation. A very simple but quite effective nonlinear proportional-derivative (PD) control is proposed for faster and high-precision positioning of such systems. The particular reasoning behind our concern on nonlinear PD (NPD) control is that most of practical servomechanisms so far are still controlled by classic proportional-integral-derivative (PID)/PD or nonlinear PID (NPID)/NPD algorithms and these controls do not explicitly take into account actuator constraint. Lyapunov’s direct method is employed to prove global asymptotic positioning stability. The appealing advantages of the proposed control are that it has simple intuitive structure with high computational efficiency and does not involve modelling parameter. An additive feature is that the proposed control has the ability to ensure that actuator constraint is not breached, and thus it completely avoids the instability and degraded or unpredictable motion and thermal or mechanical failure from excessive torque. Simulations and experimental results demonstrate that the proposed approach offers a comparable result over the existing model-dependent nonlinear controls and a much improved performance over the commonly-used model-independent linear PD control for servomechanisms with actuator constraint.

Trajectory tracking of constrained robotic systems via a hybrid control strategy

In this paper, a novel hybrid coordinated control scheme is proposed for robotic systems with full-state constraints. Asymmetric barrier Lyapunov functions (ABLFs) in backstepping design procedure are employed and corresponding backstepping controller is presented to prevent full-state constraints violation. Energy-based Hamilton control is utilized to provide Hamilton controller. Hybrid control method, which includes both backstepping and Hamilton control, is considered for improving asymptotic position tracking performance. Asymptotically stability of the closed-loop system is analyzed in Lyapunov sense. It is shown that proposed hybrid controller can effectively enhance response speed and tracking accuracy while ensuring that full-state constraints are not violated. Simulation example is provided to illustrate the feasibility and advantage of control algorithm.

Tronquée Solutions of the Third and Fourth Painlevé Equations

Recently in a paper by Lin, Dai and Tibboel, it was shown that the third and fourth Painlev\'e equations have tronqu\'ee and tritronqu\'ee solutions. We obtain global information about these tronqu\'ee and tritronqu\'ee solutions. We find their sectors of analyticity, their Borel summed representations in these sectors as well as the asymptotic position of the singularities near the boundaries of the analyticity sectors. We also correct slight errors in the paper mentioned.

Simple relay non‐linear PD control for faster and high‐precision motion systems with friction

This study addresses the problem of robust faster and high-precision positioning of uncertain one-degree-of-freedom mechanical systems with friction. A very simple relay non-linear proportional-derivative (PD) controller is proposed. Global asymptotic positioning stability is proven by Lyapunov's direct method invoking Barbalat's lemma. The appealing features of the proposed control are that it is fairly easy to construct with simple intuitive structure and without reference to modelling parameter and the ability to ensure global asymptotic positioning stability featuring faster transient and higher steady-state precision. Simulations and experiments demonstrate the effectiveness and improved performance of the proposed approach.

Sufficient conditions for the existence of an asymptotic quiescent position in time-delay systems

Sufficient conditions for the existence of an asymptotic quiescent position in time-delay systems

An acceleration-based hybrid learning-adaptive controller for robot manipulators

The robust periodic trajectory tracking problem is tackled by employing acceleration feedback in a hybrid learning-adaptive controller for n-rigid link robotic manipulators subject to parameter uncertainties and unknown periodic dynamics with a known period. Learning and adaptive feedforward terms are designed to compensate for periodic and aperiodic disturbances. The acceleration feedback is incorporated into both learning and adaptive controllers to provide higher stiffness to the system against unknown periodic disturbances and robustness to parameter uncertainties. A cascaded high gain observer is used to obtain reliable position, velocity and acceleration signals from noisy encoder measurements. A closed-loop stability proof is provided where it is shown that all system signals remain bounded and the proposed hybrid controller achieves global asymptotic position tracking. Results obtained from a high fidelity simulation model demonstrate the validity and effectiveness of the developed hybrid controller.

Globally asymptotic attitude estimation for accelerated aerial vehicles

This paper addresses the attitude estimation problem for rigid bodies moving in 3D-space with not negligible and time varying acceleration. For this case, we propose a simple and efficient globally asymptotic attitude estimation by using measurements from low-cost IMU and GPS. It consists of an observer based on proportional-integral (PI) term with discontinuous switching function to estimate the linear acceleration in the inertial frame for which we obtain global exponential convergence, along with a complementary filter for raw vectors from IMU to remove noise and bias. For this one, we get global asymptotic convergence of the observer taking into account gyro bias. Thereafter the filtered data is processed with an algebraic algorithm (e.g. TRIAD) for the attitude estimation. Note that when no gyro bias is considered, we obtain global exponential convergence for the overall system. To show the importance of filtering these raw vectors and the convergence behaviour of the proposed observers, simulation results are also given.

Stability of the asymptotic quiescent position of perturbed homogeneous nonstationary systems

Stability of the asymptotic quiescent position of perturbed homogeneous nonstationary systems

A learning control algorithm for periodic robot synchronization: Experimental results

SummaryA repetitive learning control algorithm, that achieves asymptotic joint position tracking for robotic manipulators characterized by uncertain dynamics and performing a repetitive task, can be theoretically and experimentally endowed with a recursive period identifier. Experimental results illustrate its application to a 2‐link robot master‐slave synchronization problem, in which the joint positions of the master, ie, “periodic” with uncertain and even time‐varying period, are only available at runtime.

Robust MPC-Based Fault-Tolerant Control for Trajectory Tracking of Surface Vessel

A robust control method, based on a model predictive control, is developed for the trajectory tracking of a surface vessel with sensor failures. The kinematic model of a surface vessel is first obtained. The Lyapunov stability theory and linear matrix inequalities are then adopted to produce a closed-loop system that can have a fault-tolerant capability against sensor failures and to subsequently obtain the simulated results of a fault-tolerant controller through solving the linear matrix inequalities. The asymptotic tracking position, heading angle, and the velocities of the surface vessel can be obtained using the inputs of incomplete state information in the simulation. The feasibility and effectiveness of the proposed control method have been verified through simulation results.

Strong gravitational lensing—a probe for extra dimensions and Kalb-Ramond field

Strong field gravitational lensing in the context of both higher spacetime dimensions and in presence of Kalb-Ramond field have been studied. After developing proper analytical tools to analyze the problem we consider gravitational lensing in three distinct black hole spacetimes—(a) four dimensional black hole in presence of Kalb-Ramond field, (b) brane world black holes with Kalb-Ramond field and finally (c) black hole solution in f(T) gravity. In all the three situations we have depicted the behavior of three observables: the asymptotic position approached by the relativistic images, the angular separation and magnitude difference between the outermost images with others packed inner ones, both numerically and analytically. Difference between these scenarios have also been discussed along with possible observational signatures.

A New Robust Controller Formulation for the Full–State Feedback Position Tracking of a Small–Scaled Unmanned Model Helicopter

This work focuses on the robust attitude tracking control problem for a small– scaled unmanned helicopter where the actual system inputs, namely the elevator servo input, the aileron servo input and the rudder servo input, are used in the controller formulation. The design process is divided into two parts. Initially the problem is transformed into a second order system with an uncertain non–symmetric input gain matrix by utilizing some reasonable simplifications for the rotor model under the hovering flight conditions. Then a novel robust control methodology is utilized via a matrix decomposition method. The stability of the overall system is ensured by Lyapunov type analysis where asymptotic position tracking is ensured. Numerical simulation results are presented to demonstrate the efficiency of the proposed method.