We consider combined control in automatic control systems for technological objects trajectory movements. We present research results of the system disturbance invariance ensuring on the example of the technological manipulator that implements hydrocutting of the oil pipelines. Control is based on the propositions of the fourth modified invariance form with the use of bootstrapping methods. The paper presents analysis of results obtained by two different correction methods. The essence of the first method lies in injection of additional component into the already established control signal and formation of the channel for that component. Control signal correction during the signal synthesis stage in the control device constitutes the basis for the second method. Research results have shown high efficiency of application for both correction methods. Both methods have roughly the same precision. We have shown that the correction in the control device is preferable because it has no influence on the inner contour of the system. We have shown the necessity of the block usage with the variable transmission coefficient, which value is determined by technological trajectory parameters. Research results can be applied in practice for improvement of the precision specifications of automatic control systems for trajectorial manipulators.