A perturbation analysis of spillover in closed-loop distributed-parameter systems

The design of controllers for distributed-parameter systems from truncated modal system descriptions is inherently conducted in ignorance of the actuator and sensor coupling to the unmodeled modes. The real presence of this coupling, referred to here as spillover, can cause significant changes in the expected closed-loop system behavior. To examine the effects of spillover, this coupling is treated as a perturbation to the truncated modal distributed system dynamic model with a scale parameter of smallness ??. Perturbation power series in ?? are derived for the spillover-induced shift in each closed-loop pole location. Providing that ?? = 1 is within the region of convergence of a particular series, that series is evaluated at ?? = 1 to obtain a pole shift expression for the associated pole. The resulting expressions are simple and yield considerable insight into the nature of spillover.