Dominant pole placement for multi-loop control systems

This paper proposes a method for multiloop PI controller design which can achieve dominant pole placement for TITO (two input two output) processes. It is an extension of the original dominant pole design for SISO systems. Unlike its SISO counterpart, where the controller parameters can be obtained analytically, the multiloop version amounts to solving some nonlinear equation with complex coefficients, for which closed-form formulae are not possible. This is not surprising as the coupling between loops makes the closed-loop characteristic equation depend on both unknown controllers in a nonlinear way, and hence difficult to solve analytically. A novel approach is developed to solve the equation using a “generalized root locus” method, in which the solution to our pole placement problem is found from a suitable intersection point between the “root locus” and the positive real axis. The design procedure is given and simulation examples are provided to show the effectiveness of the proposed method and comparisons are made with the BLT method