Bifurcation analysis for PID-controller tuning based on a minimal neuromuscular blockade model in closed-loop anesthesia

The problem of PID-controller tuning in an automatic drug administration system for neuromuscular blockade (NMB) in closed-loop anesthesia is considered. Contrary to the usual practice of tuning PID-controllers on the basis of a linearized model or online tests, bifurcation analysis based on a minimally-parametrized Wiener model for NMB is utilized. The parsimony of the mathematical model is instrumental in minimizing the number of bifurcation parameters. It appears that the equilibrium of the closed-loop system defined by the setpoint of the controller undergoes Andronov-Hopf bifurcation at a point in the model parameter space giving rise to sustained nonlinear oscillations. A model-based PID-controller tuning procedure is suggested that guarantees a certain settling time and robustness margin of the resulting loop. The tuning procedure is illustrated on mathematical models identified from patient data.