Inherent limitations of linear control, including PID, are Bode's phase-gain relationship and the waterbed-effect. Literature showed that reset control can overcome these limitations. The 'Constant in Gain, Lead in Phase' (CgLp) reset element was developed, which can be used in combination with a conventional PID approach. The benefit is that CgLp increases the broadband phase without altering the gain.

Recently, a continuous reset (CR) CgLp was proposed to eliminate the discontinuous output of the CgLp, which for example, excites resonances in mechanical structures. Unfortunately, CR CgLp is more sensitive to measurement noise than CgLp due to CR CgLp taking the derivative of its input, amplifying noise. This causes resets to occur more frequently. Literature has shown that these excessive resets can deteriorate the system performance.

The main contribution of this work is to improve the noise robustness of CR CgLp by implementing a filter on the measurement line to attenuate measurement noise. The attenuation of noise causes a reduction of excessive resets. Two filters are designed and critically compared. First, a low-pass filter succeeded by a lead element (LL). Second, an accelerometer-aided Kalman filter (aaKF). These were validated in practice on a precision-positioning stage.

Simulations have shown that the proposed designs improve performance of CR CgLp. The overshoot of CR CgLp could be reduced by 32% and IAE could be reduced by 53%. Besides this, CR CgLp with aaKF showed to outperform a PID controller with similar bandwidth and phase margin. The overshoot could be reduced by 46% and the IAE by 34%.

Test results on a physical setup have shown that the LL filter could improve the IAE of a step response by 13% compared to a CR CgLp without filter. Compared to PID control, the CR CgLp with LL filter has a superior transient response.