A "paper-pilot" model is sometimes utilized in aircraft control design and analysis to represent the pilot in the loop. A block diagram of an aircraft with a pilot "in the loop" is shown in Figure CP6.5. The variable Ñ‚ represents the pilot's time delay. We can represent a slower pilot with Ñ‚ = 0.6 and a faster pilot with Ñ‚ = 0.1. The remaining variables in the pilot model are assumed to be K = 1, Ñ‚1 = 2, and Ñ‚2 = 0.5. Develop an m-file to compute the closed-loop system poles for the fast and slow pilots. Comment on the results. What is the maximum pilot time delay allowable for stability?
Figure CP6.5
An aircraft with a pilot in the loop.

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Pilot model Elevator Aircraft model servo 10 S 10 0 s23s 6) (sTs+2)