A new tuning of PID controllers based on LQR optimization

This paper presents a new analytical tuning of Proportional-Integral-Derivative controllers based on the well known Linear Quadratic Regulator optimization problem for a wide class of processes where its behaviour can be modelled with a constant time and a dead time delay. When the dead time delay can be approximated by a first order Padé proposal, the optimal control problem gives an analytical solution for the tuning of the PID parameters. And the results obtained with the original model, without approximation, gives very satisfactory performances. Also, the positive results obtained by simulation with this new PID control design respect to the conventional empirical formulas to tune PID controllers are very promises to apply in the future to the industrial processes.