Modified fast discrete-time PID formulas for obtaining double precision accuracy

Proportional integral derivative (PID) controllers are widely used across various industries. This paper presents a new modified PID controller based on integer origin raw data, which are equivalent to classic PID controller based on floating-point actual values. These new formulas presented in new PID controller provide a mathematical approach to the 'Classic PID Formula', 'Subtractor Formula' and 'Scaling Formula', which form the basis of classic PID controller. The approach integrates these three formulas and separates them into integer and real value by applying the properties of associativity and commutativity. This method uses origin raw data as input to perform integer-based computation and performs floating-point operations once. This resulted in faster computation time and energy savings, while showing accuracy comparable to the existing double precision formulas.