The Optimal Sequence for Reset Controllers

The PID controller is one of the most used controllers in the industry. However, fundamental limitations due to linearity restrict its performances when higher bandwidth, stability, and precision are required simultaneously in today’s high-tech industry. Reset control is a promising nonlinear control strategy which can overcome these limitations. But it also brings new problems. High order harmonics are introduced into the system because of non-linearity which lead to unwanted dynamics and deterioration of performances. So it is necessary to reduce them as much as possible. It is found that the sequence of different parts of a reset controller has effects on the magnitude of high order harmonics. Through high order sinusoidal input describing functions (HOSIDOFs) tool, the optimal sequence of the open loop in which the magnitude of high order harmonics is minimum is achieved for a general reset controller. The superiority of the suggested sequence in the closed-loop system is validated through both simulation and experiments at a Lorentz-actuated precision positioning stage.