The use of wavelets for efficient, active control of distributed parameter systems

For active control of distributed parameter systems, such as a vibrating structures or acoustical noise fields, meeting the requirements of control over a high bandwidth and over a large spatial extent in general requires the use of a large number of sensors and actuators. For systems with large numbers of sensors and actuators, standard controller designs are faced with the computational and communications bottleneck of having to map, in real time, sensor outputs into actuator inputs to give optimal closed-loop performance. Unfortunately current control methodologies do not take this bottleneck into account, and designs resulting from using these methods are difficult do implement for large systems. In this paper we present an active control methodology that handles this bottleneck via a new multiscale/multirate theory of hierarchical design based on the wavelet transform. Our theory enables the development of efficient and highly scalable implementations of control systems using multiprocessor architectures. This paper covers a description of our multiscale control approach and simulation results on an Euler-Bernoulli beam.