Output prediction in systems with backlash

Abstract

Abstract

Systems exhibiting backlash pose a challenging prediction problem, since they involve state multiplicity for finite-order input-output models. Future outputs, given future inputs, cannot adequately be predicted using only a few past outputs and inputs, but are critically dependent on the internal state of these systems. In case the presence of steady state multiplicity is not known, a reliable predictor should be able to handle it without this explicit knowledge; in case the presence is known, the predictor would do well to be able to benefit from this knowledge even when the rest of the process might not be known.

Conventional empirical models such as feedforward neural networks cannot accurately represent systems that entail state multiplicity for their intrinsically limited input—output system representation. This work employs a state-feedback neural network structure, previously proposed by the authors, as an attractive solution to the problem of reliable output prediction for systems with hysteresis or backlash. By generating a state-space mapping of the system, the proposed network structure is able to store the relevant information in the state, thereby avoiding the information loss incurred by the input-output predictor. The feedback structure also yields more accurate multistep predictions.

The presented results for a simulation example of a backlash system demonstrate the superiority of the feedback structure over the feedforward network for achieving satisfactory prediction accuracy without explicit knowledge of the presence of backlash.