Pole assignment control design for time–varying time–delay systems using radial basis functions

Abstract

Systems with time-varying time delays present a particularly challenging control problem. They have been observed across a wide array of domains, from hydraulic actuators to insulin delivery control systems. Control systems that address system time-delays, nonlinearities and uncertainty are the subject of much research but, whilst the specific concept of varying time delays is sometimes acknowledged (for example in the control of hydraulic manipulators), this appears to be less widely investigated than some other types of nonlinearity. In part motivated by recent research into internal multi-model control, as similarly applied to systems with unknown time-varying delays, the present work utilises a Gaussian radial basis function to switch between two or more partial controllers. Each partial controller is based on a linear model with a (time-invariant) time delay. The new algorithm is developed and evaluated via simulation using a non-minimal state space (NMSS) framework, with pole assignment as the design criterion. Simulation results suggest that it yields improved performance in comparison to a simpler switching approach and the equivalent linear control system. However, laboratory examples and further research into robustness and stability is required in the next step.

A linear regression variable time delay estimation algorithm for the analysis of hydraulic manipulators

“…The time delay is subsequently estimated by comparing the predictions to the current measured response. Reference [16] builds on this idea in the context of time delay variations. Fig.…”

“…The method has been successfully used to estimate the wide range of delays observed in the experimental data, and is providing insight into the variable time delay behaviour. In future work, the authors are developing new SDP models and control systems to exploit these results [16].…”

“…Both these approaches are limited to time-invariant delays. However, recent research by the present authors has investigated how to obtain improved manipulator control performance [16], and this has motivated a re-examination of the experimental data to highlight the scenarios in which the time-delay varies.…”