This paper presents a semi-adaptive control approach to closed-loop medication infusion problems. The rationale underlying this approach is to design a controller that can adapt model parameters with a large impact on the model's fidelity while fixing the remaining parameters at nominal values. In this paper, a control-oriented model for this purpose is derived via system identification and sensitivity analysis of a low-order model capturing the direct dose-response relationship Using the model thus derived, a model-reference adaptive controller and a composite adaptive controller are designed and compared with each other. In-silico simulation results using remifentanil's effect on respiratory rate as an example indicate that both controllers can regulate the output at commanded set points. Copyright (c) 2016 John Wiley & Sons, Ltd.