Modal Control of Flexible Systems Using Distributed Sensing
Vibration and noise reduce the perceived quality, productivity, and efficiency of many mechanical systems. We have designed a modal controller for conservative flexible systems that uses distributed sensing. Spatial filtering of the distributed displacement and velocity measurements based on the system eigenfunctions prevents spillover instabilities in the closed-loop system. The proposed control is proven to stabilize a discrete set of controlled modes without destabilizing the remaining, residual modes. We then apply the theory to a single flexible link robot arm and experimentally demonstrate the feasibility of the proposed control strategy. The experiments use high speed video feedback with image processing to determine the spatial beam curve. The controller quickly damps the first modal response without causing instability in the remaining modes.
The experimental testbed consists of thin flexible beam actuated at one end by a switched reluctance motor (SRM) and carrying a payload mass of 0.1 [kg].
The following control hardware is used :
The time derivative calculations are implemented using a standard, backwards difference/filtering algorithm. The control algorithms are written in C++ and implemented using the QMotor real-time control environment.
Figure (a) shows a photograph of the experimental setup as seen by the camera. The camera viewing area is square and does not include the entire link. This simplifies the image processing. A snapshot, the beam centerline pixel data, and a best fit cubic polynomial are shown in Figures (b)-(d). The four time-varying polynomial coefficients are then transmitted via a fast, dedicated TCP/IP connection to the other PC, where the control algorithm and other I/O operations associated with the flexible link robot are implemented.
The objective of the experiment is to regulate the angular displacement of the flexible link robot arm to a setpoint of 20[deg] starting from an initial angle of 0[deg].
A PD control Law is initially implemented with the control gains tuned to achieve the best performance. The proposed Modal controller is then implemented and its performance is compared with that of the PD Controller.