Microcontroller implementation of dynamically adaptable control of stepper motor with continuous second derivative of speed curve

Stepper motor control is well known and in literature thoroughly studied subject for parameters of position, speed and acceleration. Stepper motor speed control with dynamically adoptable parameters of target speed and maximal allowed acceleration, requiring continuous change of acceleration (continuous second derivative of speed function) presents challenge to microcontroller implementation on factors of processing power and/or available memory array. Authors failed to find this kind of algorithm described in available literature, and consider it important for practical solutions of speed control in physical systems susceptible to oscillations. Paper offers theoretical basics and presents methods for construction of control algorithm.