Polynomial operator-based digital controller structures of high stability performance and computation efficiency

In this paper, the optimal controller structure problem is investigated with finite word length (FWL) consideration. Based on the polynomial operator concept, a new sparse controller structure is proposed. This structure is efficient in terms of implementation and can be optimized to reduce FWL effects. A pole modulus sensitivity based stability measure is derived and the optimal controller structures are defined as those that maximize the proposed measure. The problem of finding optimal sparse structures is solved using exhaustive searching with a practical consideration. A design example is given, which shows that the newly developed structure can beat the fully parametrized optimal state-space realization in terms of both computation efficiency and stability performance.