The article presents the models of technological systems and the parameters of the control object allowing one to seek rational control algorithms, the choice of structure of the control system and synthesis of correction devices. The generalized and detailed structural schemes of controlling the elastic-deformable state during working on low-rigidity shafts while applying the tensile force as well as with additional feedback and transfer functions of technological systems, considering the assumptions made and the results of theoretical and experimental testing. The structure of the control object and the dependencies describing the system and considering the specificity of forming the section of the machined surface of the elastic-deformable low-rigidity shafts at longitudinal feeds. As a result of the research a method of increasing the accuracy of controlling the parameters of dynamic systems at the change of the longitudinal feed and regulating the parameters of the elastic-deformable state of low-rigidity elements by introducing correction devices in form of negative feedback in accordance with the cutting force. Moreover, the possibility of creating adaptive units which are not very sensitive to the change of parameters in turning and grinding.