Session: 07-12-01 Control Theory and Applications I

Paper Number: 70264

Start Time: Tuesday, 01:10 PM

70264 - A Novel Fractional Fixed-Time Sliding Mode Control Method for Spherical Robot Linear Motion Speed Control 

This paper studies the linear motion speed control problem of an underactuated spherical robot under the uncertainty of model parameters and unknown disturbances. A novel fractional fixed-time terminal sliding mode control incorporating with a nonlinear disturbance observer is proposed for the spherical robot to achieve fast stabilization and robust speed control.

First, a novel fixed time terminal sliding surface is proposed by adding a fractional differential operator in the traditional integer order fixed time terminal sliding surface. Based on the theory of fixed time convergence and fractional calculus, the fixed time convergence of the novel fractional sliding surface is proved, and the upper bound of settling time of the novel fractional fixed time sliding surface is also given.

The uncertain model parameters and unknown disturbances are treated as an unknown nonlinear function of the spherical robot. A nonlinear disturbance observer is designed to estimate the unknown nonlinear function. The convergence of the nonlinear observer is proved by Lyapunov stability theorem. Also, the convergence accuracy of the nonlinear observer is given.

Then a fractional hierarchical sliding mode speed controller is designed based on the novel fractional fixed time terminal sliding surface and the nonlinear disturbance observer. The spherical robot is divided into shell subsystem and inner pendulum subsystem. The novel fractional fixed time sliding surface is used in the first layer sliding surface of each subsystem. The second sliding surface is obtained by linear combination of the two first layer sliding surface. A double power reaching law is used for achieve a fixed time convergence of the second sliding surface. Through the Lyapunov stability theorem, the boundedness of the second layer sliding surface and the first layer sliding is achieved, and The stability of the whole system is guaranteed.

In order to illustrate the effectiveness and superiority of the proposed fractional hierarchical sliding mode controller, an integer order hierarchical sliding controller based on traditional integer order fixed time terminal sliding surface is designed. Some simulation work is done under some setting simulation conditions such as abrupt changes of rolling friction, model parameter errors. The spherical robot can track of desired speed under the action of two controllers. Compared to the integer order hierarchical sliding controller, the fractional hierarchical sliding mode controller has a shorter settling time and lower overshoot. When subjected to the abrupt changes of rolling friction, the spherical robot under two controllers can reach a new steady state without steady state error in a short time, but the fractional hierarchical sliding mode controller owns a shorter recovery time than the integer order one.  

Presenting Author: Ting Zhou Beijing Jiaotong University

Authors:

Zhou Ting Beijing Jiaotong University
Xu Yugong Beijing Jiaotong University
Wu Bin Beijing Jiaotong University