Robust PID control of propofol anaesthesia: Uncertainty limits performance, not PID structure

New proposals to improve the regulation of hypnosis in anaesthesia based on the development of advanced control structures emerge continuously. However, a fair study to analyse the real benefits of these structures compared to simpler clinically validated PID-based solutions has not been presented so far. The main objective of this work is to analyse the performance limitations associated with using a filtered PID controller, as compared to a high-order controller, represented through a Youla parameter.

The comparison consists of a two-steps methodology. First, two robust optimal filtered PID controllers, considering the effect of the inter-patient variability, are synthesised. A set of 47 validated paediatric pharmacological models, identified from clinical data, is used to this end. This model set provides representative inter-patient variability Second, individualised filtered PID and Youla controllers are synthesised for each model in the set. For fairness of comparison, the same performance objective is optimised for all designs, and the same robustness constraints are considered. Controller synthesis is performed utilising convex optimisation and gradient-based methods relying on algebraic differentiation. The worst-case performance over the patient model set is used for the comparison.

Two robust filtered PID controllers for the entire model set, as well as individual-specific PID and Youla controllers, were optimised. All considered designs resulted in similar frequency response characteristics. The performance improvement associated with the Youla controllers was not significant compared to the individually tuned filtered PID controllers. The difference in performance between controllers synthesized for the model set and for individual models was significantly larger than the performance difference between the individual-specific PID and Youla controllers. The different controllers were evaluated in simulation. Although all of them showed clinically acceptable results, the robust solutions provided slower responses.

Taking the same clinical and technical considerations into account for the optimisation of the different controllers, the design of individual-specific solutions resulted in only marginal differences in performance when comparing an optimal Youla parameter and its optimal filtered PID counterpart. The inter-patient variability is much more detrimental to performance than the limitations imposed by the simple structure of the filtered PID controller.