Coursework – Controller Design for Administering Insulin to Diabetic Patients

Background

Type I diabetes, or insulin-dependent diabetes mellitus (IDDM), is an endocrine carbohydrate metabolic disorder in which blood sugar is increased from the normal 70-100 mg/dL range as a result of insufficient secretion of insulin by the β-cells of islets of Langerhans present in the pancreas. As current clinical treatment methods are “open-loop” in nature, it is thought that “closed-loop” control approaches (often referred to as “artificial” β-cells) can result in good glycaemia control over extended periods of time and also mimic the glucose control in healthy persons.

Professor Robert S. Parker, when he was at the University of Pittsburgh, USA developed a detailed physiological model of the human glucose-insulin system. A Simulink implementation of this model is available on the coursework folder (diabetesOL.mdl and sfundiabetes.m) and should be treated as a diabetic patient throughout this coursework. This model has two inputs, namely insulin delivery rate (manipulated variable) and meal disturbance (disturbance). The only output of the model is blood glucose concentration (controlled variables). The meal disturbance (γmeal) represents the absorption rate of glucose into the gut from a meal taken by a diabetic patient and is modelled as

1

𝛾meal  = 60𝑠 + 1  𝐺empt

Here 𝐺empt is the gastric emptying rate function. For a 15 g meal, 𝐺empt can be approximated by a trapezoidal wave form, as shown in Figure 1

Figure 1: Gastric emptying rate function for a 15 g meal.
The control objective is to keep the glucose concentration level of the patient within the normal 70-100 mg/dL range for 400 minutes, once the 15 g meal is consumed. Preferably, the glucose concentration should settle at its nominal value in 400 minutes. The nominal value of the insulin delivery rate is 22.3 mU/min and should not exceed 115 mU/min.

Tasks

To design suitable controllers, perform the following tasks:

1) Design appropriate step tests, collect data and identify FOPTD models using 63.2% and fraction incomplete methods. It is recommended that you perform both negative and positive step tests to account for nonlinearity. Check the validity of the identified models through visual comparison of predicted and observed output responses, and calculation of integral square error (ISE) values. You should use the better model for controller design in subsequent steps [25 marks]

2) Design PI and PID controllers using Ziegler-Nichols method. Note that the ultimate gain and ultimate period required for using this method should be obtained from the FOPTD model identified in part

a) and not by performing experiments on the patient [25 marks].

3) Implement the controllers designed in part a) on the patient (Simulink model). Fine tune your controllers to meet control objectives, if necessary. Explain the reasoning behind the different steps taken during fine tuning [25 marks].

4) Compare the performance of the different controllers from part 3) by calculating the integral absolute error (IAE) of blood glucose concentration and total insulin delivered. Which controller would you recommend and why? [15 marks].

5) Write a report which contains the technical details of each task (1 – 4) with a presentation and discussion of results [10 marks].

Notes

• You need to download the files diabetesOL.mdl and sfundiabetes.m from the coursework folder and keep them in the same directory on your computer.
• You should submit a report detailing the technical development of each tasks, the results and discussions. Use of graphics wherever possible is strongly encouraged.
• Your report should not exceed 8 sides of A4 paper, minimum font size 11 pt and minimum margin 2 cm on all sides.
• Your report may contain some Matlab code (if used) to illustrate how the results are generated. No need to put all Matlab code into an appendix.
• While it’s fine to discuss amongst yourselves how to approach this coursework in general, plagiarism will not be tolerated. Your reports will be checked by the Turnitin system.
• You should consider writing your report guided by the marking sheet below.