Robust control of a flexible link robot and rigid link robot: Theory, simulation, and experiment
Abstract
The goal is to design a controller for multi-link flexible robots that ensures accurate joint trajectory tracking and fast vibration damping. Two methods are followed, theoretical and experimental. The theoretical approach comprises derivation of dynamic model, design of a robust controller, stability analysis of the designed controller, and computer simulations. The experimental approach includes verifications of the dynamic model and real time implementations of the controller. Dynamic equations are derived using Hamilton's principle and Lagrange's equations. From the dynamic equations derived by Lagrange's equation, it is found that the flexible motion significantly influences nonlinear terms, centrifugal and Coriolis terms, rather than the inertia matrix. Discrepancies were found between the model and the physical robot become smaller when the actuator's dynamics are included in the model. Two submodels, one slow and one fast submodel, are derived applying singular perturbation technique to the model. A robust controller is developed for the slow submodel that represents the rigid link robot. A velocity feedback controller is developed for the fast submodel that represents the flexible motion. The stability of the composite controller consisting of a robust controller for the slow submodel and a velocity feedback controller for the fast submodel is analyzed by a composite Lyapunov function. From the analysis, it is shown that the composite controller stabilizes a flexible robot and guarantees trajectory tracking of the joint motion and the suppression of the flexible motion if the perturbation parameter is less than a value whose bound is obtained analytically. Experiments on SAM, RALF, and RALF with SAM at its tip are performed to verify the mathematical analysis. Experimental results show excellent trajectory tracking of joint motion and fast suppression of flexible motion. The effectiveness of the inertial forces of SAM on the control of the flexible motion of RALF is demonstrated by simulations and experiments, where SAM is mounted at the tip of RALF.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- 1992
- Bibcode:
- 1992PhDT........46L
- Keywords:
-
- Computerized Simulation;
- Control Stability;
- Control Systems Design;
- Controllers;
- Robot Control;
- Trajectory Planning;
- Vibration Damping;
- Actuators;
- Centrifugal Force;
- Coriolis Effect;
- Dynamic Models;
- Feedback Control;
- Liapunov Functions;
- Linkages;
- Real Time Operation;
- Robustness (Mathematics);
- Stability Tests;
- Mechanical Engineering