The article deals with the development of a mathematical model of the external cylindrical grinding process taking into account the restoration of the system parameters. The possibility of stabilizing the quality of finished products at the operations of external cylindrical grinding due to the stabilization of quality parameters based on monitoring the parameters of the technological system is considered. An unambiguous connection has been established between the output signal y(t) and the numerical sequence of the set quantization period T. The mathematical description of the process of digital signal processing was based on their representation as a function of discrete time. The obtained mathematical model is used for diagnostics and control of the external cylindrical grinding process, taking into account the restoration of the system parameters. The paper confirms that the type of disturbance and the type of deviation of the output variable actual values of a grinding system can be determined depending on the number of machined parts. This allows for adaptive control and correction of external round grinding, as well as the possibility of calculating the time interval in which it is necessary to change the values of the output variables.