Application of the observer/Kalman filter identification method to unknown time-delay disturbed systems and the associated optimal digital tracker design

Many practical systems are described as unknown multi-input-multi-output (MIMO) time-delay systems with unknown disturbances. The properties and performance of multi-time-delay MIMO systems are quite different compared to delay-free systems, in particular if the time-delay is long. In addition, for practical implementation digital controllers are often required instead of analog controllers. This paper presents: (i) an overview of the mathematical modelling based on the observer/Kalman filter identification (OKID) method, with some insight on known/unknown MIMO systems; (ii) a study of the pole-zero maps of the identified delay-free system and the known/unknown time-delay system for various sampling periods; (iii) a development of the explicit pole-zero map of the sampled-data MIMO neutral system with multiple discrete and disturbed time delays; (iv) an utilisation of the OKID method for known/unknown time-delay sampled-data MIMO systems with unknown disturbances; (v) an extension of the existing equivalent-input-disturbance (EID) estimator, to determine a robust tracker for the unknown time-delay system with unknown disturbances; and (vi) an investigation on the unknown time-delay system with stable or unstable zeros to determine which traditional or customised tracker can be applied. In addition, simulation studies are performed on the relationship between pole-zero maps and delay times.