Pilot modeling based on time-delay synthesis

Abstract

A review of some human pilot models of the years 1970-1990 -the Kleinman-Baron-Levison optimal control model, the Davidson-Schmidt modified optimal control model, and the Hess optimal control model -has been presented from the perspective of a new model based on the optimal control synthesis of time-delay systems. In the first of the listed models, the 'central nervous' reaction of the pilot is naturally defined as a pure time delay in the measurement equation of the system. In the framework of the optimal control theory, the pilot's behavior is modeled by linear quadratic regulator gain and Kalman-Bucy filter with a linear predictor. Starting from this optimal model of the 1970s, the other two models assumed the Padé approximation of the pure time delay, thus eliminating the linear predictor. In this article, the pure time delay of pilot reaction was reconsidered and divided, for convenience, into two equal parts: for the output measurement equation and for the input control. The pilot model problem has been first defined in the framework of rigorous time-delay synthesis and then solved by making reference to the control separation and duality principles. A closed-form expression of the solution is thereby obtained. The proposed model was then compared by numerical simulations with Kleinman and Hess consacrated models. The analysis of the results shows that this new pilot model is described by a simplified representation, instead denoting similar performance versus previous optimal models -which contains additional insertions as Kleinman-Baron predictor or Padé approximation, respectively. Finally, joint evaluation of the proposed model and Kleinman and Hess models with respect to the well-known Neal-Smith criterion confirms the consistency and viability of the employed strategy as a possible tool for pilot-induced oscillations phenomenon investigation.

Dealing with actuator rate limits. Towards IQC-based analysis of aircraft-pilot system stability

“…The solution to the LQG problem (4a), (5) is given by the following system of equations Proof. See [23]. Remark 2.2.…”

“…T a denotes the transpose to a vector (matrix) a . Based on the separation principle and the duality principle [29], [30], the solution of pilot OCM was obtained in two steps [23]. The first step in the synthesis of the pilot OCM was finding of the LQR solution.…”

“…Numerical evaluation of pilot synthesis proposed above follows exactly the line described in [23]. The mathematical model concerns the hovering control of a VTOL-type aircraft [24].…”

“…Assumption 2.1. As it was done in [23], the total inherent delay 2 of the pilot input  is shared, for convenience, into the  component for observation and  effective CN decision feedback component (Fig. 2).…”

“…In the paper [23], our approach was to eliminate the Padé approximations of the central nervous block frequently used in the literature and to assume the natural representation of the time delay in control input ( Further on, the actuating neuromuscular block is modeled, as usually [23]- [25], by the lag block               0 for 0 t ; : dynamics (1). Thus, the two blocks (1) and (3), in state space form, will be given by the system…”