Automatic recovery from nonlinear oscillations in PID-controlled anesthetic drug delivery

The problem of recovering from nonlinear oscillations in a PID-controlled drug delivery system for the neuromuscular blockade (NMB) in closed-loop anesthesia is considered. The NMB system dynamics portrayed by a Wiener model can exhibit sustained nonlinear oscillations for physiologically feasible values of the model parameters and realistic PID gains. Such oscillations, also repeatedly observed in clinical trials, lead to under- and over-dosing of the administered drug and undermine patient safety. This paper proposes an bifurcation analysis-based tuning policy for the proportional PID gain that ensures automatic recovery from those oscillations. It is shown that with a time-varying proportional PID gain, the type of equilibria of the closed-loop system remains the same as in the case of constant controller gains and no additional types of complex nonlinear behaviors are introduced by these auxiliary dynamics. The recovery time is also evaluated in simulation over a database of individualized patient models.