<p>This thesis aims to design a controller to apply medication to patients with hypothyroidism, a disease that occurs due to the underacting thyroid gland. The body cannot produce sufficient thyroid hormones, which leads to an increase in the production of hormones in the pituitary gland. The thyroid malfunctioning could lead to other associated conditions like nausea, fatigue, heart conditions, higher cholesterol, and elevated blood pressure. Thus, it is essential to ensure that the levels of thyroid hormones, Triiodothyronine (T3) and Thyroxine (T4), are healthy. The production of these hormones is governed by the hypothalamus-pituitary-thyroid (HPT) axis, a part of the endocrine system. This illness cannot be cured but can be regulated entirely through medication. The standard practice to control hypothyroidism in patients is to prescribe a constant daily dosage of synthetic T4 (i.e., levothyroxine) and, in some cases, an additional dose of synthetic T3 (i.e., Liothyronine). In this thesis, simulation studies are performed where two patients with varying levels of hypothyroidism are prescribed constant doses of synthetic hormones. The medications initially help the patients but are unsuccessful in maintaining healthy ranges. Using model predictive control, an observer-controller-based compensator is proposed to prescribe varying medication doses as inputs based on the patient's requirement. The inputs are quantized to be practically implemented in a real patient scenario. This compensator successfully improves the patient's hormone levels toward healthy values and ensures that the hormone trajectories follow the body's circadian rhythm.  </p>