Tuning of multivariate PID controllers based on characteristic matrix eigenvalues, Lyapunov functions and robustness criteria

A tuning criterion for multiple input-multiple output (MIMO) PID controllers based on characteristic matrix eigenvalues and Lyapunov functions was suggested. In this method, the tuning problem is stated as an optimization one in which the Lyapunov quadratic index variation with respect to dynamic parameters was minimized with constrains in eigenvalues. Proposed criterion was applied to the multivariate controls of a distillation column, and a nonlinear biochemical reactor.