A discussion of Chaplin & Smith´s patent for the cancellation of repetitive vibrations

Considers a method proposed by Chaplin and Smith (1986) for the cancellation of repetitive vibrations. Direct implementation of the concepts of the patent is not straightforward, because of the lack of precise information regarding certain components, and because of the absence of guidelines for the design of a system with satisfactory stability and performance properties. This paper proposes a specific algorithm based on the concepts of the patent and provides an approximate analysis which is found useful to obtain a closed-loop system with predictable dynamic characteristics. Simulations demonstrate the validity of the approximation and the success of the design. A tendency of the algorithm for convergence towards undesirable operating states is identified, and an improved version is derived. The resulting algorithm is compared to another algorithm proposed for the same purposes. While the structure and properties of the schemes are similar, a significant difference is found in the steady-state characteristics of the algorithms. Although the patent concerns the specific problem of repetitive vibrations, the algorithms of the paper are applicable to a broad range of control problems where periodic disturbances of unknown frequency must be rejected