New Approach of Tracking Control for a Class of Non-Minimum Phase Linear Systems

2007 ◽  
Author(s):  
Bo Xie ◽  
Bin Yao
Keyword(s):  
Linear Systems ◽  
Trajectory Planning ◽  
Tracking Control ◽  
Controller Design ◽  
Tracking Error ◽  
Trajectory Design ◽  
Minimum Phase ◽  
Control Approach ◽  
Tracking Controller ◽  
Phase Systems

The paper presents a new tracking control approach for a class of non-minimum phase linear systems. The proposed approach consists of two parts: trajectory planning and tracking controller design. The trajectory planning is solved as an optimization problem to improve the achievable transient performance under the fundamental constraints associated with perfect tracking of non-minimum phase systems. The recently proposed adaptive robust tracking controller for a class of non-minimum phase systems is then applied to guarantee that the tracking error dynamics can be stabilized with bounded internal states. The effectiveness of the proposed approach is illustrated through simulation on tracking control of a second order non-minimum phase linear system. Further works are underway to extend the proposed control strategy and trajectory design to a class of non-minimum phase nonlinear systems.

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.

Multi-dimensional Taylor network-based adaptive control for nonlinear systems with unknown parameters

2020 ◽  
pp. 014233122095335
Author(s):  
Lei Chu ◽  
Yuqun Han ◽  
Shanliang Zhu ◽  
Mingxin Wang
Keyword(s):  
Nonlinear Systems ◽  
Tracking Control ◽  
Control Method ◽  
Controller Design ◽  
Tracking Error ◽  
Unknown Parameters ◽  
Nonlinear Characteristics ◽  
Control Approach ◽  
Closed Loop Systems ◽  
Adaptive Laws

This paper presents an adaptive multi-dimensional Taylor network (MTN) control approach for a class of nonlinear systems with unknown parameters. MTN is employed to identify unknown nonlinear characteristics existing in the system, and then a novel adaptive MTN tracking control method is proposed, via backstepping technique. In the controller design, double adaptive laws are designed and appropriate Lyapunov functions are chosen to overcome the difficulties caused by the unknown parameters. The designed controller can guarantee that all the variables in the closed-loop systems are bounded and the tracking error can be arbitrarily small. Finally, simulation results are presented to verify the effectiveness of the proposed approach.

Tracking Control of Non-Minimum Phase Systems Using Filtered Basis Functions: A NURBS-Based Approach

2015 ◽  
Author(s):  
Molong Duan ◽  
Keval S. Ramani ◽  
Chinedum E. Okwudire
Keyword(s):  
Tracking Control ◽  
Phase Error ◽  
Approximate Model ◽  
Basis Functions ◽  
Minimum Phase ◽  
Tracking Errors ◽  
Model Inversion ◽  
B Spline ◽  
Phase Systems ◽  
Zero Phase

This paper proposes an approach for minimizing tracking errors in systems with non-minimum phase (NMP) zeros by using filtered basis functions. The output of the tracking controller is represented as a linear combination of basis functions having unknown coefficients. The basis functions are forward filtered using the dynamics of the NMP system and their coefficients selected to minimize the errors in tracking a given trajectory. The control designer is free to choose any suitable set of basis functions but, in this paper, a set of basis functions derived from the widely-used non uniform rational B-spline (NURBS) curve is employed. Analyses and illustrative examples are presented to demonstrate the effectiveness of the proposed approach in comparison to popular approximate model inversion methods like zero phase error tracking control.

scholarly journals A COMPARISON OF LYAPUNOV AND FUZZY APPROACHES TO TRACKING CONTROLLER DESIGN

2020 ◽  
Vol 1 (2) ◽  
pp. 54-57
Author(s):  
Tan- Sang Le ◽  
Le Hong Hieu
Keyword(s):  
Mobile Robots ◽  
Lyapunov Stability ◽  
Tracking Control ◽  
Controller Design ◽  
Final Goal ◽  
Tracking Controller

There are numerous types of locomotion of mobile robots. Therein, the most widespread type of locomotion is motion using wheels. The task of robot is transport themselves from place to place. And tracking control is always an important problem to appply robots in practice. The robot has to reach the final goal by following a referenced trajectory. The paper proposes two methods based on the lyapunov stability standard and fuzzy law. Then, we simulate the algorithms to evaluate the results.

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.

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