Decentralized Robust PID Controller Design Using Disk Margins Specifications

Many industrial processes are multi-input and multi-output. One challenge during controller design is to ensure both performance and robustness of the closed-loop in the presence of coupling between the loops. One way to ensure robustness in the frequency domain is by using disk margins. They represent a family of complex-valued uncertainties that account for simultaneous gain and phase variations in the frequency response. In this paper, a frequency-based decentralized robust proportional-integral-derivative controller design method is proposed. An optimization problem is used to achieve zero steady-state error for constant setpoints. The uncertainty is expressed using an output multiplicative model. To ensure robust stability, constraints on the disk margins are imposed using a multiloop approach. The problem is formulated using linear matrix inequalities. Simulation results validate the proposed method in comparison to other decentralized robust controllers presented in the literature. In the examples, the designed controllers resulted in a closed-loop that meets performance requirements and robust stability.