Avoiding excessive zero crossings in reset control

Abstract

In the present world, a new development in technology every other year is anticipated. Robots and motion stages in the high-tech sector are required to work at higher speeds being stable, more precise, and power-efficient. Linear controllers have served well but are falling short to continue with the trend. Reset elements can enhance the performance of linear filters like PID by overcoming the bounds of linear control. As the name implies, reset elements reset their state/ states, thus induce nonlinearity. This nonlinearity provides reduced phase lag with similar magnitude behaviour as linear elements. With such behaviour or by adding linear filters with reset elements, both the steady-state and transient response can be improved. The tracking precision is not needed to be compromised over stability and noise rejection. The reset control has its downsides. The resetting action (nonlinearity) produce higher-order harmonics in the output. The number and instant of resets occurring are vital in determining the closed-loop sensitivities. Ideally, only two resets should occur in one period of the reference frequency. But due to higher-order harmonics, multiple resets (zero crossings) can occur, which makes analytical closed-loop estimation difficult. This thesis provides an amplitude threshold criteria on higher-order harmonics to avoid the multiple zero crossings. Controllers following such a threshold can help benefit the system from nonlinearity rather than being adversely affected by it. An example of a control scheme with reset and linear elements for a motion stage is presented that satisfies the amplitude threshold. No multiple resets in the input signal to the reset element for any reference frequency were confirmed.