Multiple PID tuning by non-iterative LMI

Robust control gained importance in the last decades as a tool for complex systems to achieve expected performance under the most varied possible operational conditions. Thus, convex programming constrained by linear matrix inequalities has been used by several authors to tune multiple PID loops addressing model uncertainties and system stability. However, the computational costs are high for large systems because the original problem is bilinear, for which iterative techniques are proposed. This work proposes a non-iterative technique to maximize system decay rate constrained by an upper bound on ℋ norm. The Lyapunov matrix is expressed as a function of control gain matrices by an equivalence relation and is eliminated as a decision variable. Because it is non-iterative, the proposed technique is suitable for high-sized systems and can achieve solutions with reduced computational cost as good as the iterative approaches.