Are there set limitations on closed loop systems?

Shreesh P. Mysore, 30 Sep 02

There are several limitations to what can be achieved using a closed loop system and these lead to tradeoffs which are common in engineering. For instance, in the cruise control example, if you provide a step input of 10mph to the system, you cannot have a closed loop system that "tracks" the step, i.e., follows it exactly. The cruise control system will get to the new speed after a delay, or after a delay and overshoot+oscillations, or will settle to a speed very close to the commanded speed. A tradeoff will occur if one requires that the time taken for the new speed to be reached be <1 unit and the speed overshoot be <0.5mph. More generally, if one requires that the performances of the system in different regimes of its operation be all within strict limits, then there are mathematical bouunds on what can be achieved. You will encounter more of this in the course.