The possibility of introducing PIDD2 controllers into adaptive automatic control systems using the proposed algorithm for finding the optimum adjusting parameters of the specified controller is considered. The carried out analysis of the structural implementation of the PIDD2 controller and the estimation of the filter time constants of the first and second order differentiation units made it possible to formulate the structure of the PIDD2 controller-based adaptive automatic control system. The proposed algorithm for finding the optimum adjusting parameters of the PIDD2 controller consists in a purposeful procedure for finding the optimal point with the maximum value of the transfer factor of the controller in the parameter space, taking into account the preset stability margin. In determining the steps of the algorithm, the structural and parametric optimization of the filters of the differentiation links is performed, which make it possible to reduce the problem only to the search for adjusting parameters of the controller. The work of the proposed algorithm is illustrated by the example of an automatic control system, where the mathematical model of the heat exchanger unit of the fuel combustion engine of the internal combustion engine is the controlled object. Analysis of transient processes and frequency responce of the simulated system shows the qualitative superiority of the adaptive automatic control system with the optimally tuned PIDD2 controller over the conventional automatic system with a PID controller. The versatility of the algorithm and the ability to periodically adjust the adjustments of the controller are also noted.