Servo Loop Simulator

A PID controller's step response is determined by the interplay of proportional gain (Kp), integral gain (Ki), derivative gain (Kd), and the plant's natural frequency and damping ratio. This simulator integrates a second-order plant model in real time as gains are adjusted, plotting the resulting position step response and reporting overshoot, settling time to within 2%, steady-state error, and a stability classification (overdamped, near-critical, underdamped, or oscillating). Plant parameters — natural frequency in Hz and damping ratio ζ — allow the tool to represent mechanical stages, galvo mirrors, piezoelectric actuators, or other physical systems. Diverging responses are detected automatically and flagged as unstable. Use it to develop intuition for PID tuning, to estimate achievable bandwidth, or to check whether a proposed gain set is stable before applying it to hardware.