Discrete Fractional-Order PID Control

This code implements PID parameter regulation using a discrete fractional-order control algorithm. The algorithm represents an advanced control technique that achieves superior accuracy through finer system analysis and control capabilities. It utilizes fractional calculus principles to better accommodate complex system dynamics and time-varying characteristics. The implementation likely involves discretization methods (such as Grünwald-Letnikov or Tustin approximation) to handle fractional-order derivatives and integrals digitally. Key functions may include fractional-order operator realization, parameter adaptation logic, and stability monitoring mechanisms. Furthermore, the algorithm can incorporate adaptive control strategies for dynamic parameter adjustment, ensuring compatibility with diverse systems and operating environments. The discrete fractional-order control approach thus provides an efficient and flexible control solution suitable for widespread applications including mechanical manufacturing, chemical processes, aerospace systems, and other industrial domains.