I am already studying PID control and some how to some extent I have understood it except one main confusion. When the difference between reference input \$r(t)\$ and current output value \$y(t)\$ is zero, \$e(t)\$ will be zero and hence \$u(t)\$ will also be zero, so how will then the plant act or work when its input \$u(t)\$ is zero?
Best Answer
No, e(t) being zero does not imply that u(t) is also zero. It only implies that the output of the "P" process is zero.
Remember, the "I" and "D" processes have memory — they depend on the past behavior of e(t). u(t) is zero only if the sum of all three processes is zero.