Digital PID Control Algorithm for Continuous Systems

This code implements PID parameter adjustment through a digital control algorithm for continuous systems. The algorithm utilizes sensor measurements to detect errors within the system and computes control signals based on these errors to correct system behavior. The PID controller, a widely-used control mechanism, calculates control signals by integrating past errors (integral term), current errors (proportional term), and predicted future errors (derivative term), resulting in enhanced system stability. The implementation includes functions for error sampling, discrete-time difference calculations for derivative action, and numerical integration for the integral component. Additionally, the code supports switching between multiple control modes—such as position control, velocity control, and force control—through configurable parameters and mode-selection logic, allowing adaptation to diverse system requirements. Each mode employs specific gain tuning and signal processing methods tailored to the control objective.