Control of a very flexible robot in gravity

This thesis presents several algorithms used to control a very flexible robot in gravity. The flexible arm is modelled using an assumed modes method to characterize the elastic behavior. Gravity is included in the model. Control algorithms are developed and simulated numerically. The control schemes include proportional-derivative (PD), linear quadratic regulator (LQR), and linear quadratic regulator with a prescribed degree of stability algorithms. The PD algorithms use only hub position and velocity for feedback. Simulations show fast response times with large overshoot and long settling times. The LQR algorithms have the benefit of modal feedback. These responses settle quicker than the responses obtained using PD controllers. The LQR responses are sensitive to the weighting factors used to derive the feedback gains. As expected, the simulation results indicated that the weighting factors, and consequently the feedback gains, should be modified for each payload. The LQR with the prescribed degree of stability gives improved results compared to the previous LQR. However, this scheme results in unstable responses for large prescribed degrees of stability due to system nonlinearities;The flexible arm robot used for the simulation study is then implemented in a test bed. The flexible arm is in the vertical plane. The PD control schemes give experimental results that are similar to the simulation results. Control algorithms with modal feedback yield shorter settling times than the PD algorithms. The experiments show higher order modes can become unstable as the hub velocity and first mode feedback gains are increased. The second mode feedback gain is found to have a stabilizing effect on these instabilities. A nonlinear controller based on varying the first mode feedback gain with position is presented. This controller results in smaller overshoot in some cases