Optimal nonlinear controller design for flexible robot manipulators

Abstract

Developing nonlinear adaptive and robust controllers for a two-link flexible robot arm is the main objective of this research. Two different modelling techniques are used to overcome model accuracy problems and these two are evaluated comparatively. These are FEM(Finite Element Method) as a reduced order approximate model and PDE (Partial Differential Equations) approach as an exact model. Since FEM model needs modal truncation, unknown disturbances can excite neglected high-frequency modes generated by the nonlinearities of the plant. The second approach is modelling the flexible robot arms by PDE which are known to provide exactness. In order to improve the important features of flexible links such as low mass and moments of inertia and high natural frequencies, optimal shape design can result in nonuniform cross-section of links. Furthermore, a high fundamental frequency is desired since it implies a large bandwidth that will allow for fast motion without causing serious vibration problems and for stable endpoint control. The main results of the study are robust regulation of the rigid modes and suppression of elastic vibrations of the flexible robot arm. The dynamic state feedback controller is used to achieve this goal in FEM approach. In the first part of this research the adaptive internal model approach, in parallel with a robust stabilizer, has been modified to manage totally unknown disturbances that can include neglected higher modes of the uniform flexible links as well as large parameter uncertainties such as tip mass changes. The stabilizer part of the controller which has been introduced for the first time in this research in conjunction with nonlinear systems, is optimized successfully with a new efficient evolutionary algorithm. In the second approach (PDE) of this research, the control of a two-link flexible arm with nonuniform cross-section by design is improved by employing the Lyapunov method. LaSalle's invariance principle, extended for infinite dimension, is used in order to prove the asymptotic stability of the closed loop system without any modal truncation as opposed to former approaches in literature. Besides, large parameter uncertainties such as tip and hub mass changes in PDE approach are also handled effectively by the proposed nonlinear controller.