Robust Reset Control using Adaptive / Iterative Learning Control

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Abstract

Reset controllers can outperform PID controllers and may introduce phase advantage compared to linear PID control. However, in general, reset controllers do not have the same steady state properties as linear controllers, like removing steady state errors. In case of model mismatches and disturbances, this may cause limit cycles (persisting oscillations) in the closed response when (constant) references are tracked. The occurrence of these limit cycles is very unwanted in mechatronic precision systems, since the response does not converge to the desired set-point.

To avoid / remove limit cycles in the response, some reset control methods are currently available. Examples are PI+CI controllers, reset controllers that reset to non-zero values and reset controllers with (adaptive) feedforward. Although the existing methods can be used to overcome the limit cycle problem, they are often dependent on the model of the system or are a trade-off between linear and nonlinear control. Hence, the existing methods are not very robust in general or do not use the full advantage of reset control.

In this thesis, a simple and robust fixed instant adaptive reset controller is developed for a minimum phase SISO system that can be stabilized by standard PID control. The presented adaptive reset algorithm detects if a limit cycle is present and adapts the after reset value in an iterative way until the limit cycle is removed. Although no mathematical proof is given, the idea behind the presented method is explained. Simulations and measurements are performed to show that the algorithm is able to get rid of limit cycles caused by model mismatches and constant input disturbances. Furthermore, it is shown that the adaptive algorithm can be applied to zero-crossing reset as well.