Output regulation for redundant plants via orthogonal moments

In this paper we address the output regulation problem for redundant plants, namely systems possessing more control inputs than regulated outputs, with focus on the specific opportunity and difficulty deriving from the additional inputs. The former consists in the fact that, having a wealth of input configurations achieving the same steady-state behavior, it is possible to optimize additional performance criteria while preserving the primary task of output regulation. The latter stems from the fact that the naive approach of replicating the required internal model of the exosystem on each input channel leads to loss of observability/detectability of the cascaded interconnection of the internal model and the plant, thus preventing the achievement of overall closed-loop stability: The main result of this paper consists in the design of an inner auxiliary control loop that allows to break the above conflict between advantages and drawbacks of redundant plants. The result is then revisited by exploiting the orthogonal moments of the plant at the exosystem's frequencies. Differently from classic moments, which, for an asymptotically stable plant, describe the relation between inputs and steady-state output response, orthogonal moments characterize the input directions that yield zero steady-state output response at given frequencies.