Observer-based feedback linearisation of nonlinear ultrasonic systems

At high vibration amplitudes, piezoelectric transducers exhibit nonlinear characteristics (Blackburn and Cain, J Appl Phys 100:114101, 2006; Aurelle et al., Ultrasonics 34:187–191, 1996; Hall, J Mater Sci 36:4575–4601, 2001) due to its material properties. The result is a resonance frequency shift and the occurrence of the jump phenomenon. The jump phenomenon may cause a collapse of the vibration amplitude in forced excitation systems. This nonlinear behaviour is often associated with a discrete spectrum of overtones. In order to linearise the nonlinear system a control circuit was implemented with the aim to eliminate the overtones in the response of the nonlinear system. This paper gives a theoretical and experimental study of damping higher harmonics using a discrete Luenberger observer implemented in a feedback linearisation loop. The Luenberger observer monitors the electrical charge which is proportional to the displacement and uses this information to generate a feedback voltage in order to achieve linear behaviour. Thus, the observer’s output is used to create a linearisation term added to the excitation voltage to eliminate the nonlinearity. In relation to the linearised system, there is no occurence of the jump phenomenon and the phase is linear within the operation band. This simplifies the implementation of a resonance control system.