Reducing the effect of truncation error in spatial and pointwise models of resonant systems with damping

This paper is concerned with finding analytical solutions to the problems of reducing the effect of truncation error in models of resonant systems that include damping. Pointwise and spatial models of resonant systems are both considered in the paper. It is known that the truncation of an infinite-dimensional model produces errors in the zero locations and zero-frequency content of the system. Our approach is to add a feedthrough term to the truncated model to reduce the uncertainty caused by neglected dynamics. This will improve the accuracy of the model by reducing the errors in the zero locations and zero-frequency content of the system, which is important in ensuring the closed-loop system's robustness when a feedback controller is implemented. The optimal feedthrough terms are determined by minimising the weighted ℋ₂ norm and spatial ℋ₂ norm of the error systems associated with the pointwise and spatial models, respectively. The existence of analytical solutions for optimal feedthrough terms allows models of resonant systems to be compensated in a straightforward manner. Simulation results are presented to demonstrate the effectiveness of our approach in reducing the effect of truncation error.