The effect of link flexibility on planar manipulators using an adaptive tracking controller

The objective of this paper is to propose a general method for finding the effects of flexible links on the tracking performances using adaptive tracking controllers (ATC). The Lagrange–Euler equation is used to formulate the dynamic equations of motion. The equations of motion of the flexible manipulator in a vector–matrix form are coupled, nonlinear, and second–order differential equations. To obtain the effects of the flexible links on the controller, a rigid–based ATC is used to control a rigid, and its equivalent flexible, dynamic model, respectively. The proposed method has no limitation on the number of links used. Two existing model reference adaptive control techniques, the gradient approach by using the modified MIT (MMIT) rule and the exact matching (EM), are applied. The exact matching adaptation mechanism is used in this study as a comparative reference for the tracking performance. Numerical simulation results indicate that the gradient approach has superior performance over other designs. The proposed method can be used as a design tool to reduce the weight of a manipulator to improve the efficiency. The method is not just for the adaptive controls, but it also can be used in any state space control schemes. A comparison of the tracking performance is also made for the MIT rule and the modified MIT rule.