Practical Tracking Control of a Class of Uncertain Surface Vessels Under Weak Assumptions on Uncertainties and Reference Trajectories

2021 ◽  
Author(s):  
Jian Li ◽  
Wenqing Xu ◽  
Zhaojing Wu ◽  
Yungang Liu
Keyword(s):  
Tracking Control ◽  
Broad Class ◽  
Tracking Error ◽  
Reference Trajectory ◽  
Unknown Parameters ◽  
Related Literature ◽  
Surface Vessels ◽  
Control Scheme ◽  
Reference Trajectories ◽  
Theoretical Results

Abstract This paper is devoted to the tracking control of a class of uncertain surface vessels. The main contributions focus on the considerable relaxation of the severe restrictions on system uncertainties and reference trajectory in the related literature. Specifically, all the system parameters are unknown and the disturbance is not necessarily to be differentiable in the paper, but either unknown parameters or disturbance is considered but the other one is excluded in the related literature, or both of them are considered but the disturbance must be continuously differentiable. Moreover, the reference trajectories in the related literature must be at least twice continuously differentiable and themselves as well as their time derivatives must be known for feedback, which are generalized to a more broad class ones that are unknown and only one time continuously differentiable in the paper. To solve the control problem, a novel practical tracking control scheme is presented by using backstepping scheme and adaptive technique, and in turn to derive an adaptive state-feedback controller which guarantees that all the states of the resulting closed-loop system are bounded while the tracking error arrives at and then stay within an arbitrary neighborhood of the origin. Finally, simulation is provided to validate the effectiveness of the proposed theoretical results.

scholarly journals Finite-Time Adaptive Fuzzy Control for Nonlinear Systems with Unknown Backlash-Like Hysteresis

2021 ◽  
Author(s):  
Shuzhen Diao ◽  
Wei Sun ◽  
Le Wang ◽  
Jing Wu
Keyword(s):  
Fuzzy Control ◽  
Finite Time ◽  
Fuzzy Systems ◽  
Tracking Error ◽  
Adaptive Fuzzy Control ◽  
Finite Time Stability ◽  
Adaptive Fuzzy ◽  
Intermediate Variable ◽  
Control Scheme ◽  
Theoretical Results

AbstractThis study considers the tracking control problem of the nonstrict-feedback nonlinear system with unknown backlash-like hysteresis, and a finite-time adaptive fuzzy control scheme is developed to address this problem. More precisely, the fuzzy systems are employed to approximate the unknown nonlinearities, and the design difficulties caused by the nonlower triangular structure are also overcome by using the property of fuzzy systems. Besides, the effect of unknown hysteresis input is compensated by approximating an intermediate variable. With the aid of finite-time stability theory, the proposed control algorithm could guarantee that the tracking error converges to a smaller region. Finally, a simulation example is provided to further verify the above theoretical results.

scholarly journals A model reference adaptive variable impedance control method for robot

2021 ◽  
Vol 336 ◽  
pp. 03005
Author(s):  
Xinchao Sun ◽  
Lianyu Zhao ◽  
Zhenzhong Liu
Keyword(s):  
Real Time ◽  
Tracking Control ◽  
Control Method ◽  
Impedance Control ◽  
Tracking Error ◽  
Reference Trajectory ◽  
Control Parameters ◽  
Model Reference ◽  
Force Tracking ◽  
Model Reference Adaptive

As a simple and effective force tracking control method, impedance control is widely used in robot contact operations. The internal control parameters of traditional impedance control are constant and cannot be corrected in real time, which will lead to instability of control system or large force tracking error. Therefore, it is difficult to be applied to the occasions requiring higher force accuracy, such as robotic medical surgery, robotic space operation and so on. To solve this problem, this paper proposes a model reference adaptive variable impedance control method, which can realize force tracking control by adjusting internal impedance control parameters in real time and generating a reference trajectory at the same time. The simulation experiment proves that compared with the traditional impedance control method, this method has faster force tracking speed and smaller force tracking error. It is a better force tracking control method.

Adaptive multi-dimensional Taylor network tracking control for a class of switched nonlinear systems with input nonlinearity

2020 ◽  
Vol 42 (13) ◽  
pp. 2482-2491
Author(s):  
Shan-Liang Zhu ◽  
De-Yu Duan ◽  
Lei Chu ◽  
Ming-Xin Wang ◽  
Yu-Qun Han ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Tracking Control ◽  
Low Cost ◽  
Tracking Error ◽  
Switched Nonlinear Systems ◽  
Nonlinear Functions ◽  
Input Nonlinearity ◽  
Control Approach ◽  
Adaptive Tracking Control ◽  
Control Scheme

In this paper, a multi-dimensional Taylor network (MTN)-based adaptive tracking control approach is proposed for a class of switched nonlinear systems with input nonlinearity. Firstly, the input nonlinearity is assumed to be bounded by a sector interval. Secondly, with the help of MTNs approximating the unknown nonlinear functions, a novel adaptive MTN control scheme has the advantages of low cost, simple structure and real time feature is developed via backstepping technique. It is shown that the tracking error finally converges to a small domain around the origin and all signals in the closed-loop system are bounded. Finally, two examples are given to demonstrate the effectiveness of the proposed control scheme.

Region-Reaching Control of a Flexible-Joint Manipulator

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
J. W. Yu ◽  
X. H. Zhang ◽  
J. C. Ji ◽  
J. Y. Tian ◽  
J. Zhou
Keyword(s):  
Control Problem ◽  
Tracking Control ◽  
Control Algorithm ◽  
Objective Functions ◽  
Flexible Joint ◽  
Point Tracking ◽  
Control Scheme ◽  
Lyapunov Stability Analysis ◽  
Flexible Joint Manipulator ◽  
Theoretical Results

Abstract This paper addresses the region-reaching control problem for a flexible-joint robotic manipulator which is formulated by Lagrangian dynamics. An adaptive control scheme is proposed for the manipulator system having two constrained regions which are constructed by selecting appropriate objective functions. The two joints of the flexible-joint manipulator can be, respectively, confined in different regions, and this gives more flexibility than the traditional fixed-point tracking control. By performing a straightforward Lyapunov stability analysis, a simple control algorithm is established to provide a solution for the region-reaching control problem. Finally, numerical simulations are given to validate the theoretical results.

Adaptive control of a class of non-linear systems preceded by backlash-like hysteresis

2014 ◽  
Vol 24 (5) ◽  
Author(s):  
JIANPING CAI ◽  
LUJUAN SHEN ◽  
FUZHEN WU
Keyword(s):  
Differential Equation ◽  
Adaptive Control ◽  
Linear Systems ◽  
Tracking Error ◽  
Robust Adaptive Control ◽  
Unknown Parameters ◽  
Control Scheme ◽  
Non Linear ◽  
Non Linear Systems ◽  
Robust Adaptive

We consider a class of uncertain non-linear systems preceded by unknown backlash-like hysteresis, which is modelled by a differential equation. We propose a new state feedback robust adaptive control scheme using a backstepping technique and properties of the differential equation. In this control scheme, we construct a new continuous function to design an estimator to estimate the unknown constant parameters and the unknown bound of a ‘disturbance-like’ term. The transient performance of the output tracking error can be guaranteed by the introduction of pre-estimates of the unknown parameters in our controller together with update laws. We do not require bounds on the ‘disturbance-like’ term or unknown system parameters in this scheme. The global stability of the closed-loop system can be proved.

Cross-Coupling Controller for Five Degree-of-Freedom Coplanar Nanostage

2013 ◽  
Vol 284-287 ◽  
pp. 1788-1793
Author(s):  
Van Tsai Liu
Keyword(s):  
Tracking Control ◽  
Tracking Error ◽  
Cross Coupling ◽  
Degree Of Freedom ◽  
Creep Model ◽  
Contour Error ◽  
Viscoelastic Creep ◽  
Control Scheme ◽  
Optimization Parameters ◽  
Cross Coupling Control

The proposed approach is to design a tracking controller for five degree-of-freedom coplanar nanostage which can provide high precision applications. This study propose a viscoelastic creep model, it was modeled as a series connection of springs and dampers to describe the creep effect. Then, utilize a PI controller using Taguchi method to search the optimization parameters to suppress the tracking error. Finally, a cross-coupling control scheme is proposed to eliminate the contour error which is typical in dual-axes tracking control problem. The developed approaches are numerically and experimentally verified which demonstrate performance and applicability.

scholarly journals Tracking Control Based on Recurrent Neural Networks for Nonlinear Systems with Multiple Inputs and Unknown Deadzone

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
J. Humberto Pérez-Cruz ◽  
José de Jesús Rubio ◽  
E. Ruiz-Velázquez ◽  
G. Solís-Perales
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Exponential Convergence ◽  
Broad Class ◽  
Tracking Error ◽  
The State ◽  
Control Law ◽  
Reference Trajectory ◽  
Uncertain Dynamics ◽  
The Difference

This paper deals with the problem of trajectory tracking for a broad class of uncertain nonlinear systems with multiple inputs each one subject to an unknown symmetric deadzone. On the basis of a model of the deadzone as a combination of a linear term and a disturbance-like term, a continuous-time recurrent neural network is directly employed in order to identify the uncertain dynamics. By using a Lyapunov analysis, the exponential convergence of the identification error to a bounded zone is demonstrated. Subsequently, by a proper control law, the state of the neural network is compelled to follow a bounded reference trajectory. This control law is designed in such a way that the singularity problem is conveniently avoided and the exponential convergence to a bounded zone of the difference between the state of the neural identifier and the reference trajectory can be proven. Thus, the exponential convergence of the tracking error to a bounded zone and the boundedness of all closed-loop signals can be guaranteed. One of the main advantages of the proposed strategy is that the controller can work satisfactorily without any specific knowledge of an upper bound for the unmodeled dynamics and/or the disturbance term.

scholarly journals Observer-Based Decentralized Tracking Control with Preview Action for a Class of Nonlinear Interconnected Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Xiao Yu
Keyword(s):  
Tracking Control ◽  
Controller Design ◽  
Tracking Error ◽  
State Feedback Control ◽  
Control Action ◽  
Linear Matrix ◽  
Reference Trajectory ◽  
Integral Control ◽  
Control Approach ◽  
Output Tracking Control

In this paper, for the first time, the observer-based decentralized output tracking control problem with preview action for a class of interconnected nonlinear systems is converted into a regulation problem for N augmented error subsystems composed of the tracking error dynamics, the difference equation of the state observer, and the available future reference trajectory dynamics associated with each individual subsystem. The developed innovative formulation of an observer-based decentralized preview tracking control scheme consists of the integral control action, the observer-based state feedback control action, and the preview action of the desired trajectory. The controller design feasibility conditions are formulated in terms of a linear matrix inequality (LMI) by using the Lyapunov function approach to ensure the existence of the suggested observer-based decentralized control strategy. Furthermore, both decentralized observer gain matrices and decentralized tracking controller gain matrices can be efficiently and simultaneously computed through a one-step LMI procedure. Stability analysis of the closed-loop augmented subsystem is carried out to illustrate that all tracking errors asymptotically converge toward zero. Finally, a numerical example is provided to demonstrate the effectiveness of the suggested control approach.

scholarly journals Adaptive Fuzzy H∞ Robust Tracking Control for Nonlinear MIMO Systems

2015 ◽  
Vol 15 (1) ◽  
pp. 34-45
Author(s):  
Sanxiu Wang ◽  
Kexin Xing ◽  
Zhengchu Wang
Keyword(s):  
Tracking Control ◽  
Mimo Systems ◽  
Tracking Error ◽  
Approximation Error ◽  
Nonlinear Function ◽  
Robust Tracking ◽  
Robust Tracking Control ◽  
Fuzzy Logic Systems ◽  
Adaptive Fuzzy ◽  
Control Scheme

Abstract In this paper an adaptive fuzzy H∞ robust tracking control scheme is developed for a class of uncertain nonlinear Multi-Input and Multi-Output (MIMO) systems. Firstly, fuzzy logic systems are introduced to approximate the unknown nonlinear function of the system by an adaptive algorithm. Next, a H∞ robust compensator controller is employed to eliminate the effect of the approximation error and external disturbances. Consequently, a fuzzy adaptive robust controller is proposed, such that the tracking error of the resulting closed-loop system converges to zero and the tracking robustness performance can be guaranteed. The simulation results performed on a two-link robotic manipulator demonstrate the validity of the proposed control scheme.

Trajectory Preshaping for High-Speed Articulated Systems

1995 ◽  
Vol 117 (3) ◽  
pp. 304-310 ◽  
Author(s):  
Zvi Shiller ◽  
Hai Chang
Keyword(s):  
High Speed ◽  
Industrial Robot ◽  
Correction Term ◽  
Tracking Error ◽  
Feedback Controller ◽  
Reference Trajectory ◽  
Direct Drive ◽  
Unknown Parameters ◽  
Tracking Errors ◽  
Articulated Systems

This paper presents a method for reducing the tracking errors of articulated systems, moving along specified paths at high speeds. It consists of preshaping the reference trajectory to account for the dynamics of the feedback controller. The trajectory is assumed to be feasible, satisfying the known manipulator dynamics and the actuator constraints. The correction term, added to the nominal trajectory, is computed by filtering the nominal control inputs through the inverse of the feedback controller. A learning procedure is also presented to account for unknown parameters of the feedback controller and for unmodeled dynamics. It consists of an iterative parameter optimization that minimizes the tracking error along the path at each joint. The initial guesses for this optimization are selected to ensure that the tracking error is not worse than the error with no preshaping. The method is demonstrated experimentally for the UCLA Direct Drive Arm and for the AdeptOne industrial robot, achieving mean tracking errors as low as 0.11 mm at top speeds of 1.8 m/s.

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