New Tuning Rules of PI+CI Controllers for First-Order Systems

The reset control is a simple nonlinear control approach where the states of the controller are conducted to zero when a particular condition is satisfied. The PI+CI is a controller that mixes the simplicity of PI controllers with the benefits of a reset action to mitigate the fundamental limitations of linear control. However, the tuning of this kind of controller, with three parameters, two for the linear part and one for the nonlinear one, is not trivial. In this paper, simple tuning rules for PI+CI are proposed for both tracking and regulation problems, assuming first-order dynamics for the plant. The resulting control scheme, for which the reset coefficient is computed from exponential functions, is simulated and compared with an ideal PI+CI where the reset coefficient is obtained using rules available in the literature. Similar results are obtained for the tracking problem, and optimal performance based on the Integral Absolute Error (IAE) is also obtained for the regulation problem. These new rules, in contrast to those already existing in the literature, depend only on closed-loop specifications. Furthermore, the framework based on the minimization of IAE, used to obtain the proposed rules, makes it possible to consider for the first time the tracking and regulation problems simultaneously, i.e., cases where setpoint changes and disturbance arrivals can occur at the same time before reaching a new steady state. The results are validated using a set of study cases.