Issues in the Design of a Multirate Model‐Based Controller for a Nonlinear Drug Infusion System

Abstract

Multivariable controller design for the regulation of mean arterial pressure (MAP) and cardiac output (CO) in congestive heart failure patients is restricted by the limited frequency of CO sampling. Performance criteria for the controller specify maximum allowable transient settling times for both variables, and the design should account for the inherent multirate nature of the process in order to satisfy these criteria. We present a multirate model predictive control (MPC) design for MAP and CO regulation by combined infusion of sodium nitroprusside and dopamine, based on a comprehensive nonlinear model of the system. The multirate MPC algorithm is based on nonlinear quadratic dynamic matrix control. To reduce computation time, we introduce a selective linearization technique that linearizes the model on the basis of trends in the plant-model mismatch. The problem is complicated by restrictions on initial dopamine infusion, prescribed to avoid extremely slow responses. We present a novel rule-based override (RBO) to the MPC controller that uses a set of heuristics to initialize dopamine. The performance of the MPC/RBO controller is illustrated using simulation results.

A practical multiple model adaptive strategy for multivariable model predictive control

“…Another popular approach is to linearize the nonlinear analytical equations around the current measurement of the process variable at each sampling instance to obtain linear discrete state space equations (Gattu & Zafiriou, 1992Lee & Ricker, 1994;Gopinath et al, 1995). The states of the process are then estimated based on recursive identification techniques that involve the use of a Kalman filter.…”

“…Specifically, if the computations are based entirely on the model prediction (i.e. no constraints are active), the accuracy of the model has significant effect on the performance of the closed loop system (Gopinath, Bequette, Roy, Kaufman, & Yu, 1995). Hence, the capabilities of DMC will degrade as the operating level moves away from its original design level of operation.…”

The Design of Nonlinear Predictive Controllers: Application to a Drug Infusion System

“…Yu et al [9] and Gopinath et al [11] present lumped parameter models of the circulatory system. The forcing function is the time-varying elastance of the heart.…”

“…The nonlinear model is represented by 38 differential equations. A detailed description of the modeling equations and the procedure for solving them is given by Gopinath et al [11]. …”

“…Possible explanations are that the magnitude of the inverse response is negligibly small, or that the constant relative order assumption is no longer valid at the higher doses. The input multiplicities have a clearer explanation from a physiological standpoint (see Gopinath et al [11] for details). The steady-state responses shown here are supported by the experimental results ofOingrich and Roy [14].…”