We have developed a digital signal processor-based system for real-time control of the ISTTOK plasma position based a low-cost Digital Signal Processor (DSP) board. A novel plasma shape reproduction method was developed using a Cauchy-condition expansion applied to the vacuum region around the plasma. This method showed to be best suited than classic methods such as Legendre-Fourier Expansion (LFE) or Current Filaments (CF), particularly in small tokamaks with passive stabilizers conductors where the presence of strong eddy currents can cause significant errors in magnetic field sensors. We discuss the accuracy of this method by correlating against measurements from a microwave interferometer diagnostic. We present an implementation in the DSP system that allows the real time control of the plasma position with a required 1-ms period.