Two-Degree-of-Freedom PID Controllers Structures

As in most of the existing industrial process control applications, the desired value of the controlled variable, or set-point, normally remains constant (regulatory control or disturbance rejection operation) but needs to be changed (servo-control or setpoint tracking operation) we are mainly interested in the two-degree-of-freedom (2DoF) implementation of the PID control algorithms. The extra parameter that the 2DoF control algorithm provides is used to improve their servo-control behavior while considering the regulatory control performance and the closed-loop control system robustness [1–5]. This 2DoF feature can be incorporated both into a PI or a PID control algorithm. Although all the controllers with a proportional integral (PI) control algorithm are implemented in the same way, have the same transfer function, this is not the case with commercial controllers with proportional integral derivative (PID) control algorithms. In fact, usually, the control algorithm implementation is manufacturer dependent and not all of its variations are available in the same controller. Even more, the controllers manufacturers use different names for the same PID algorithm [6]. The diversity of the PID control algorithms is evident in [7]. In addition, it would be the case that a tuning rule of interest had been obtained using a control algorithm different from the one implemented in the controller to tune. In this case, controller parameters conversion is required that will also indicate if the pursued equivalent controller exists. On that basis, the most widely used PID control algorithms are presented in this chapter by also providing conversion formulae that allows to convert the parameters of one algorithm from those obtained for another formulation. As it will be seen this conversion will not always be possible, showing some formulations are more general than others.