Dominant pole placement for multi-loop control systems

This paper proposes a method for multi-loop PI controller design which can achieve dominant pole placement for two input two output processes. It is an extension of the original dominant pole design (PID Controllers: Theory, Design, and Tuning, Instrument Society of America, Research Triangle park, NC, 1995.) for SISO systems. Unlike its SISO counterpart, where the controller parameters can be obtained analytically, the multi-loop version amounts to solving some coupled nonlinear equation with complex coefficients, for which closed-form formulae are not possible. A novel approach is developed to solve the equation using a ''root trajectory'' method, in which the solution to our pole placement problem is found from intersection points between the ''root trajectories'' 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.