Multi-loop PID controllers design with reduced loop interactions based on a frequency-domain direct synthesis method

A novel direct synthesis (DS) method for simultaneous and non-iterative design of multi-loop PID controllers for stable multivariable processes is presented in this article. We deal with the specifications of the desired closed-loop dynamics, which is a critical design decision in the DS method, for designing multi-loop controllers. Control loop interactions in multi-loop control systems are usually undesirable but unavoidable due to inter-channel interactions of multivariable processes. The main feature of the method is that the multi-loop control design aims at reducing the interactions among loops. The proposed DS method specifies the design target in terms of the frequency response of the desired closed-loop transfer function (CLTF) and synthesizes the controllers in the frequency domain. We develop an approach to effectively specify the desired closed-loop frequency response to achieve improved control performance by minimizing the sum of the magnitude of the interactive parts in the desired CLTF matrix. With the desired closed-loop frequency response and a process model, the frequency response of an ideal multi-loop controller is synthesized and then approximated to a PID controller. We provide simulation studies of three industrial benchmark processes and a nonlinear quadruple tank system to illustrate the design result and performance of the proposed method and make comparisons with several existing methods. Our results prove the effectiveness of the frequency-domain DS method. The proposed multi-loop PID controllers achieve reduced loop interactions and provide satisfactory overall performance.