The propeller of an airship is connected to a DC motor. The motor is being controlled using a PI controller. The PI controller has a proportional gain of Kp = 2, and an integral gain of Ki = 0.5, and the controller's input is the speed error, which is the difference between the desired and measured speeds. It follows the equation:
Output = Kp×Error + Ki×∫Error dt
If the desired speed is 500 rpm and the measured speed is 480 rpm, what will be the controller's output after 10 seconds?
My approach: Considering 10 seconds to be an instance, I assumed the error signal to be independent of time. Thus, output= 2(20) + (0.5)(20)(10)= 140
This feels wrong on so many levels but I am not able to figure out how else to go about this. Anyone ?