Uncertain Polytopic LPV Modelling of Robot Manipulators and Trajectory Tracking

作者：Jabali Mohammad Bagher Abolhasani; Kazemi Mohammad Hosein

来源：International Journal of Control Automation and Systems, 2017, 15(2): 883-891.

DOI：10.1007/s12555-015-1432-1

• LMI
• LPV system
• nonlinear systems
• polytopic representation
• robot manipulator
• robust design

This research work proposes a full state systematic feedback control design method for some classes of non-linear systems which are forced to follow a specific desired trajectory, such as robotic systems, using uncertain polytopic linear parameter-varying (LPV) modelling approach. An LPV representation of the system is generated from linearization of its usual Lagrangian equation about a desired state trajectory and is reduced to an uncertain polytopic one. A vector of scheduling signals from the desired trajectory information is produced to construct the LPV model. The control gain matrix is derived by solving a set of linear matrix inequalities (LMIs) that returns the sufficiently small value of the time derivative of the Lyapunov function. A sufficient condition is proposed to guarantee the asymptotic stability of the closed-loop LPV systems against the uncertainties on the vertices. The proposed scheme is applied to controller synthesis of a two-degree-of-freedom robotic manipulator trajectory tracking problem.

• 出版日期2017-4