The measurement or sensor element in a feedback system is important to the accuracy of the system [6]. The dynamic response of the sensor is important. Most sensor elements possess a transfer function
Hs = k / τs + 1
Suppose that a position-sensing photo detector has τ = 4μs and 0.999 < k < 1.001. Obtain the step response of the system, and find the k resulting in the fastest response-that is the fastest time to reach 98% of the final value.