Using Matlab, model a PID controller feedback system for a plant with a gain of 0.05 and a lag of 50ms. Simulate a reference input of the unit step function rising at time t=0. Calculate the integral of the error, e(t), over a one second interval. Your simulation should graph the reference input, r(t), and the plant output, y(t), and output the net error.
Find suitable values for the controller constants (Kp, Ki, Kd) that minimize net error and produce acceptable control.
The purpose of this assignment is not to discover ideal control constants for a completely made-up system. It is to get you to explore the simulation to get a feel for how such a feedback control system can behave. To that end, here are a list of starter questions to get you thinking and playing.
Write up a brief report to accompany your simulation source code that includes thoughtful, well-written responses to these questions, as well as any other relevant observations you take away from the exercise.