This paper studies repetitive control (RC) with linear phase lead compensation to precisely track periodic trajectories in piezo-based scanning probe microscopes (SPMs). Quite often, the lateral scanning motion in SPMs during imaging or fabrication is periodic in time. Because of hysteresis and dynamic effects in the piezoactuator, the tracking error repeats from one scanning period to the next. Commercial SPMs typically employ PID feedback controllers to minimize the tracking error; however, the error repeats from one operating cycle to the next. Furthermore, the residual error can be excessively large, especially at high scan rates. A discrete-time repetitive controller was designed, analyzed, and implemented on an experimental SPM. The design of the RC incorporates two phase lead compensators to provide stability and to minimize the steady-state tracking error. Associated with the lead compensators are two parameters that can be adjusted to control the performance of the repetitive controller. Experimental tracking results are presented that compare the performance of PID, standard RC, and the modified RC with phase lead compensation. The results show that the modified RC reduces the steady-state tracking error to less than 2% at 25 Hz scan rate, an over 80% improvement compared to PID control.

In this paper, an analog velocity feedback controller is considered for active vibration suppression of a thin plate for attenuation of sound levels in the frequency range of 0–100 Hz. The active control methods can be applied to interior cavity noise reduction, as encountered for instance in automotive applications. For that purpose, a simplified experimental vibro-acoustic cabin model was built in our laboratory and developed methodologies are demonstrated on the set-up. The set-up includes a rectangular box (1 × 1 × 2 m) which is separated with a flexible thin plate (1 × 1 × 0.001 m) to obtain two enclosed cavities: the passenger compartment (PC) and the engine compartment (EC). The vibration control is applied only on the flexible plate since the walls enclosing the cavities are made of more rigid material (wood filled concrete). By employing piezoelectric patch as actuator and laser doppler vibrometer as vibration sensor, an analog proportional velocity feedback controller is designed and built experimentally for suppressing the low-frequency modes of the flexible plate. In order to attenuate only lower-frequency structural modes of the thin panel, pre-filters are also included in analog circuit. The vibration of thin plate and sound in the passenger compartment is measured for controller-inactive and active cases while disturbing the thin plate via shaker. By measuring vibration and sound response, closed and open loop experimental frequency responses are obtained and presented. The aim of this experimental study is to investigate performance of active vibration control applications on acoustic attenuation as the first step towards robust structural acoustic control.