Least squares based self‐tuning control of dual‐rate systems

A polynomial transformation technique is used to obtain a frequency‐domain model for a dual‐rate system in which the output sampling period is an integer multiple of the input updating period. Based on this model, a self‐tuning control algorithm is proposed by minimizing output tracking error criteria from directly the dual‐rate input–output data. Convergence properties of the algorithm are analysed in detail in the stochastic framework. The output tracking error at the output sampling instants has the property of minimum variance. It is shown that the control algorithm can achieve virtually optimal control asymptotically, ensuring the closed‐loop systems to be stable and globally convergent. A simulation example illustrates the self‐tuning scheme presented.