Robust tuning of Two-Degree-of-Freedom (2-DoF) PI/PID based cascade control systems

A design approach for Two-Degree-of-Freedom (2-DoF) PID controllers within a cascade control configuration that guarantees robust and smooth control is presented in this paper. The use of a cascade control configuration comes into place when the use of an additional (intermediate) sensor provides the possibility for a compensation of a load-disturbance before it affects the output variable. The rationale of operation associated to both the inner and outer controllers determines the need of good performance for disturbance attenuation (regulation) as well as set-point following (tracking). Therefore, the use of 2-DoF controllers is introduced. However, the use of 2-DoF controllers, introduces additional parameters that need to be tuned appropriately. Specially for the case of PI/PID controllers there are not known clear auto-tuning guidelines for such situation. The approach undertaken in this paper provides the complete set of tuning parameters for the inner (2-DoF PI) controller and the outer (2-DoF PID) controller. The trade-off among control system performance (measured in terms of closed-loop response speed) and robustness allows to derive a recommendation for the design-parameter lower limit. The design equations are formulated in such a way that a non-oscillatory response is specified for both the inner and outer loop. A side advantage of providing the complete set of parameters is that it avoids the need for the usual identification experiment for the tuning of the outer controller.