A straightforward method for tuning of Lyapunov-based controllers in semi-active vibration control applications

Abstract Lyapunov-based control is an attractive strategy for semi-active vibration control as it has a mathematical basis ensuring stability in the sense of Lyapunov and great flexibility in the design. Unfortunately, that flexibility complicates the controller tuning since it involves the construction of a weighting matrix, which is usually done by trial-and-error. In this work, a straightforward (closed form) method to construct such a matrix is proposed. The proposed method is based on penalizing vibrational modes according to their contributions to the response in the uncontrolled case. For this purpose, a new concept of Generalized Modal Contribution Factor is developed. This takes into account the following: spatial distribution of the excitation, knowledge of the frequency content of the excitation, and control objective. The capability of the proposed tuning method is demonstrated through a numerical example.