The use of the term "process dead time" can mislead us in terms of recognizing the many sources of dead time. Also we don't often take into account the profound effect of the speed and the entry point of a disturbance into the process. Here we use a short cartoon video as the basis of how avoiding a collision with a car running a red light is analogous to a difficult control problem.
In the video Cartoon-Car-Collision provided by Aimee Ubriaco of MYNAH Simulation Technologies for a Lunch-n-Learn I recently did on "The Key Characteristics of Dynamic Terms and Responses", we can learn a lot more than expected. A couple of slides Car-Collision-Process-Control-Analogy from the MYNAH presentation detail how various driver and car actions relate to process control.
To summarize; the total loop dead time is the sum of the time to recognize the impending collision (measurement delay), to make a decision (controller execution delay), to move the leg to the brake (final control element delay), and to noticeably decelerate after the brake is applied (process delay). The disturbance is unmeasured because the car swerving around the line of traffic and running the red light is unseen and unpredictable. Therefore feedforward control is not possible and the driver is relying totally on feedback control. The errant car is traveling very fast and is consequently nearly a step disturbance. Even worse, the disturbance is on the process output thereby bypassing any moderating effects of the driver and car process dynamics. In contrast a change in grade would be a more gradual input disturbance that the driver could more readily deal with.