Method of controlling amplitude of mechanical excitation of a piezoelectric powered ultrasonic stack including under load

A method of controlling amplitude of mechanical excitation at an end of a piezoelectric powered ultrasonic stack including when it is under load to be at a desired amplitude set-point wherein a piezoelectric ultrasonic converter of the ultrasonic stack is excited by an ultrasonic power supply, comprising:

• determining in real time with a control loop feedback controller a true amplitude of mechanical excitation at the end of the piezoelectric powered ultrasonic stack including when the piezoelectric powered ultrasonic stack is under load by multiplying one of an amplitude of motional voltage exciting the piezoelectric ultrasonic converter and an amplitude of motional current exciting the piezoelectric ultrasonic converter by a cosine of a phase difference angle between the motional voltage and the motional current;
• and
• controlling in real time the ultrasonic power supply with the control loop feedback controller to control an output amplitude of at least one of output voltage and output current of the ultrasonic power supply so that the determined true amplitude of mechanical excitation at the end of the piezoelectric powered ultrasonic stack will be at the desired amplitude set-point.