Uniform damping control: discretization and optimization

AbstractThis paper develops the control discretization and control optimization processes for the uniform damping of structures. A distributed uniform damping control is first shown to represent a first-order approximation to an associated globally optimal solution. This approximation is shown to be accurate for moderate to low levels of damping. The implementation of uniform damping control with discrete control forces is then demonstrated, using a subdomain approach, whereby a transformation of coordinates is carried out and a resulting subdomain polynomial expansion is truncated. Control laws are developed for one, two, and three discrete control forces per subdomain. Next, a steepest descent method is developed for the optimal assignment of control gains and the locations of the control forces. As a general rule the number of modes that can be uniformly damped is twice the number of control forces. The control discretization and associated optimization processes are illustrated via the control of a cantilever beam