Thermoelastic martensitic phase transition in Ni-Ti based shape memory alloys enables designing micro- and nanotools that are controlled by small changes in temperature (~10°С). This makes it feasible creating a new generation of complex microrobotical systems for manipulation and treatment of various nanoobjects in nanoindustry, medicine, nanoelectronics, etc. This work deals with the development of a physical and mathematical model for the micro manipulation system. The system under investigation pertains to shape memory composite nanotweezers with the composition Ti2NiCu/Pt located at the tip of a tungsten microneedle. The activation and control of the nanotweezers is done by heating them by the passage of an electric current flowing through a microdiode located in the needle. The microdiode serves the twin purpose of Joule heating and temperature sensing/measurement so as to close the feedback loop of the control system. The prototype of the control system was manufactured and tested. The data from the simulation were compared with those from the preliminary experiments. © 2016 Trans Tech Publications, Switzerland.