In this paper we address the controlled complete AutoRegressive Moving Average Independent Process Analysis (ARMAX-IPA; X-exogenous input or control) problem, which is a generalization of the Blind SubSpace Deconvolution (BSSD) task. Compared to our previous work that dealt with the undercomplete situation, (i) here we extend the theory to complete systems, (ii) allow an autoregressive part to be present, (iii) and include exogenous control. We investigate the case when the observed signal is a linear mixture of independent multidimensional ARMA processes that can be controlled. Our objective is to estimate the ARMA processes, their driving noises as well as the mixing. We aim efficient estimation by choosing suitable control values. For the optimal choice of the control we adapt the D-optimality principle, also known as the 'InfoMax method'. We solve the problem by reducing it to a fully observable D-optimal ARX task and Independent Subspace Analysis (ISA) that we can solve. Numerical examples illustrate the efficiency of the proposed method.