Harmonic Analysis of a PZT Poly-Actuator

Similar to combustion engines comprising multiple cylinders engaged with a crankshaft, multiple piezoelectric stack actuators (PSA) engaged with a common output rod can produce smooth, long stroke motion with desired properties. In particular, when equally spaced multiple units are arranged to push sinusoidal gear teeth on the output rod, the system exhibits unique collective behaviors thanks to "harmonic" effects of the multiple units. For example, although the force-displacement characteristics of individual units are highly nonlinear, the undesirable nonlinearity, including singularity, may be eliminated. Here we present harmonic analysis and control of a class of actuators consisting of multiple driving units engaged with a sinusoidal transmission, termed a harmonic poly-actuator. Through theoretical analysis we obtain 1) conditions on the unit arrangement to eliminate their nonlinearity from the output force, 2) control algorithms for coordinating the multiple units to generate a commanded force with desired force-displacement characteristics, and 3) a method for compensating for output force ripples due to possible misalignment and heterogeneity of individual units. The control algorithms are implemented on a prototype harmonic poly-actuator with six units of PSAs. Experiments demonstrate the unique features of the poly-actuator exploiting the harmonic properties of the system.