An Investigation of the Human As An Optimal Controller in Closed Loop Systems

This thesis is written to present the findings of the author resulting from An Investigation of the Human as an Optimal Controller in Closed Loop Systems. In Chapter 1, a summary of the past efforts to characterize the human is presented. Although by far incomplete, the examples chosen indicate the basic methods employed in these characterizations. All of these characterizations have been along the line of what is the operator\u27s transfer function, rather than how does the operator weigh his performance. In an effort to answer this question, it is postulated that the operator uses a form of a quadratic performance index. In Chapter 2, the mathematics and problem are formulated. The problem is written in the modern control theory state variable format. A cost functional is derived and minimized. The resulting Riccati differential matrix equation is found to be of order 2n x 2n, whereas the plant only had an order n x n. In Chapter 3, the optimal control law is investigated with respect to previously developed models. It is seen that within certain restrictions, the optimal control law is compatible with human transfer functions. In Chapter 4, the plant, model and optimal control law are simulated and typical data is presented. The steady state solutions to the Riccati differential matrix equation are presented. The optimal controller is then removed and. the human inserted as the controller. Examination of the data obtained reveals that the human in this task can operate equal to an optimal controller. Chapter 5 presents certain conclusions regarding the operator\u27s ability to function as an optimal controller and hints as to possible additional areas suitable for investigation