#### Date of Award

1-1-2011

#### Document Type

Campus Access Dissertation

#### Department

Chemical Engineering

#### First Advisor

Edward P Gatzke

#### Abstract

Diabetes mellitus is a pancreatic disease associated with cardiovascular malfunction. With the growing number of diabetic patients worldwide, along with the hassle of the treatment, it becomes imperative to find ways to accurately control diabetes with very little user interaction. This work presents development of the required methods for a fully itegrated control scheme to control nonlinear biological systems. First, the noisy measurement data must be filtered. Additionally, the model parameters may change over time. For both of these purposes, an unscented Kalman filter (UKF) may be used. This is a sigma-point model-based method capable of calculating the mean and covariance of a noisy signal, assuming the noise is Gaussian. While usually a state estimation method, this work presents a novel way to apply this method to parameter estimation by augmenting the dynamic model to include the parameters as states with a zero time derivative. This allows for the accurate parameter estimation needed to update the model parameters periodically. If the convergence of this method is slow, a novel iterative procedure is shown in which the same group of data is filtered repeatedly, using the final values of one iteration as the initial values of the following iteration. This allowed determination of adequate results with less data. Following this filtering, it is important to calculate disturbances and unknown inputs. In a diabetic patient, this is where the glucose intake is calculated. In order to perform this estimation, a moving horizon estimator (MHE) was applied. While usually used for parameter estimation, this work presents a different approach in order to calculate the disturbances. If the disturbance appears on the model equations, it is possible to treat it as a model parameter. As a result, the MHE was capable of determining the magnitude of a meal in the diabetic patient model with as little as 2.59% error. The final step to this integrated control procedure is the controller itself. As is usually done, the MHE procedure was paired with a model-predictive control (MPC) routine. MPC allows for future constraint violations to be corrected by extrapolating the model into a future prediction horizon, calculating inputs in the near future that will maintain the future values within their constraints. If the state filtering was accurate, and the MHE provides with the meal values, the MPC can readily determine the amount of insuling required to drive the subcutaneous glucose down below dangerous levels. While it proved too aggressive for the system initially, by taking advantage of the ability of the MPC to bound inputs the MPC showed that it was indeed possible to apply predictive control to the diabetic patient model. Thus, this work shows an information loop which occurs between three mathematical online methods. This information loop provides the initial values for each iteration but the first one, as each output is used as the initial value for the following routine. While the methods in this work are specific, it may be possible to apply the same concept using other procedures instead.

#### Recommended Citation

Rivera-Montalvo, A. A.(2011). *Fully-Integrated Control: Noise Filtering, Parameter Estimation, Disturbance Determination and Predictive Control of Biological Nonlinear Processes.* (Doctoral dissertation). Retrieved from http://scholarcommons.sc.edu/etd/593