The HHC Algorithm for Helicopter Vibration Reduction Revisited

The Higher-Harmonic Control (HHC) algorithm is re-examined from a rigor-ous control theory-oriented perspective. A brief review of the history and developments of HHC is given, followed by a careful development of the al-gorithm. The paper proceeds to perform an analytic convergence and ro-bustness analysis. On-line identification with the adaptive variant of the al-gorithm is also addressed. A new version of the algorithm, relaxed HHC, is also introduced and shown to have beneficial robustness properties. Some numerical results comparing these variants of the HHC algorithm applied to helicopter vibration reduction are also presented. The results presented in this paper unify and extend previous work on the higher-harmonic control algorithm. Nomenclature 0n Zero matrix of size n × n A Matrix relating plant input and output between updates A? Adjoint matrix of A, (Ā)T D Matrix defined to be TTQT+R Ff Exponential window In Identity matrix of size n × n J Quadratic-form cost function JT̂, ∞ Converged cost function for adaptive control JT,α, ∞ Converged cost function for relaxed control Kk+1 Matrix defined to be ∆uTk+1Pk+1 k Integer index between control inputs m Number of harmonics in control input M Matrix defined to be D−1(TTQ+ ST) Nb Number of rotor blades Pk Matrix defined as (∆Uk∆UTk) −