Polytopic Linear Models Based Output Tracking Control of a Single-Link Flexible Joint Robot Manipulator

Document Type : Research Article


1 Department of Electrical Engineering, Shahid Beheshti University

2 Department of Electrical Engineering, Shaihid Beheshti University


In this paper, to solve the output tracking problem of a single-link flexible joint manipulator, polytopic linear models (PLMs) of the dynamics are made to take advantage of this method. Although linear control methods are very useful due to their powerful theories and simplicity, they can only be used in a neighborhood of the equilibrium point. One way to solve this problem is a PLMs based method that linearizes the dynamics around several operating points. Therefore, in this paper, after calculating the PLMs of the manipulator, a state feedback control is applied to the derived linear dynamics that are augmented with the dynamics of the output tracking error. For constructing PLMs, an extended method is used to decompose the scheduling space, which is the segregation method improved with an extra aggregation. In order to avoid creating a large number of local models, an axis-oblique decomposition strategy is used instead of an axis-orthogonal decomposition. In addition, the scheduling functions of the PLMs are determined such that overlaps between the regions are avoided. By this selection, the output tracking problem becomes as a Linear Matrix Inequality (LMI) problem instead of a bilinear matrix inequality problem which is more difficult to solve and may not lead to an optimal global solution.


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