Robust Stabilization and Tracking Control for a Class of Switched Nonlinear Systems

This work is concerned with the contouring control problem of robotic manipulators using the method of equivalent errors. The method was previously proposed for multi-axis motion systems with emphasis on machine tools applications. It is shown in this paper that the method of equivalent errors is equally applicable to robot manipulators. For robotic systems, a desired path usually is described in terms of the position of the end-effector (task space), but the system dynamics are described in generalized coordinates (joint space). The proposed method utilizes the forward kinematics to transform the desired path in the task space into that in the joint space. As such, the equivalent errors can be defined easily. Two examples contouring free-form paths are studied numerically to demonstrate the effectiveness of the proposed method. One is a two-link robot manipulator, and the other is a 6-DOF Stewart platform. Three controllers for the system with and without uncertainty are considered. The simulation results demonstrate the excellent performance of the proposed method and verify the effectiveness of its application to the contouring control problem of robotic systems, even with uncertainty and higher degrees of freedom.

“…Integrating the (n − 1) equivalent contour errors given by (3) and one tangential error given by (5), we can form n equivalent errors:…”

Section: Methods Of Equivalent Errorsmentioning

confidence: 99%

“…Robot manipulators have found broad applications in industry. The control issues of these systems have been important research topics [1][2][3][4][5]. In many situations, such as painting, welding, and deburring, it is required that the end effector of the robot manipulator follows a specific path.…”

Section: Introductionmentioning

confidence: 99%

Contouring Control of Robot Manipulators Based on Equivalent Errors

Chen¹,

Chou²

2013

“…For example, in , Chang et al addressed the problem of designing robust tracking control for a large class of uncertain nonlinear chaotic systems. In , Niu et al addressed the problem of robust stabilization and tracking control for a class of switched nonlinear systems via the multiple Lyapunov functions appoach. In this paper, we consider the tracking control of general‐form single‐input single‐output (SISO) nonlinear system described by

({, \begin{matrix} array \dot{x} = f (x) + g (x) u, \\ array y = h (x), \end{matrix})

where

boldx = {[x_{1}, x_{2}, \dots, x_{n}]}^{normalT} \in {double-struckR}^{n}

is the state vector,

u \in double-struckR

is the control input,

y \in double-struckR

is the output, and the functions f :

{double-struckR}^{n} \to {double-struckR}^{n}

, g :

{double-struckR}^{n} \to {double-struckR}^{n}

and h :

{double-struckR}^{n} \to double-struckR

are continuous and smooth (as differentiable as needed).…”

Section: Introductionmentioning

confidence: 99%

“…In light of the complexity and uncertainty of nonlinear systems, which widely exist in scientific and engineering fields, many efforts have been devoted to the solving of nonlinear system problems [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. As an important part of nonlinear system problems, the tracking control of nonlinear systems has attracted much attention in recent decades [6,7,9,10,[14][15][16][17]. For example, in [15], Chang et al addressed the problem of designing robust tracking control for a large class of uncertain nonlinear chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

“…For example, in [15], Chang et al addressed the problem of designing robust tracking control for a large class of uncertain nonlinear chaotic systems. In [16], Niu et al addressed the problem of robust stabilization and tracking control for a class of switched nonlinear systems via the multiple Lyapunov functions appoach. In this paper, we consider the tracking control of general-form single-input single-output Manuscript received April 5, 2016; revised September 18, 2016;accepted November 13, 2016. The authors are with the School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China; with the SYSU-CMU Shunde International Joint Research Institute, Foshan 528300, China; and also with the Key Laboratory of Autonomous Systems and Networked Control, Ministry of Education, Guangzhou 510640, China.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

ZD, ZG and IOL Controllers and Comparisons for Nonlinear System Output Tracking with DBZ Problem Conquered in Different Relative‐Degree Cases

Mao

Zhang

et al. 2017

This paper considers the output tracking control of general‐form single‐input single‐output (SISO) nonlinear system, which may encounter the problem of division by zero (DBZ). First, via the Zhang dynamics (ZD) method, a ZD controller is proposed. Then, based on the ZD controller with the aid of gradient dynamics (GD) method, a Zhang‐gradient (ZG) controller is proposed. For comparison, the conventional input‐output linearization (IOL) controller is presented. The ZD, ZG and IOL controllers are compared in different relative‐degree cases (i.e., the standard relative‐degree case, the loose relative‐degree case and the DBZ relative‐degree case). Note that the ZG controller is valid in three relative‐degree cases, while the ZD and IOL controllers are valid only in the standard relative‐degree case and the loose relative‐degree case. In addition, performances of ZD and ZG controllers are guaranteed via theoretical analyses and computer simulations for the output tracking of general‐form nonlinear system with the DBZ problem conquered.

A Condition for Boundedness of Solutions of Bidimensional Switched Affine Systems With Multiple Foci and Centers

Zhu

2017

This paper studies boundedness of solutions of bidimensional switched affine linear systems. Every subsystem of the systems has a single stable/ unstable focus/ center and all the equilibria pairwise differ. By using the multiple polar coordinate systems method, this paper proposes a condition of boundedness of solutions of such switched systems under periodic/ quasi-periodic switching paths. The condition is also shown a sufficient condition of global asymptotic region stability of such switched systems with respect to a region containing all multiple equilibria. A global asymptotic region-stabilizing control, a periodic/ quasi-periodic switching path, and a corresponding algorithm are all designed for such switched control systems. An illustrative example demonstrates the effectiveness and practicality of our new results.