## Publica

Hier finden Sie wissenschaftliche Publikationen aus den Fraunhofer-Instituten. # Model based control of a piezo-actuated axis

**Abstract**

This paper presents the physical state space model of the static und dynamic behaviour of a piezo-actuated axis exemplified by a drilling bar. The piezo-actuated axis consists of an amplifier, a piezo-actuator and a solid state joint. Depending on the physical and mechanical equations, a linear state space model was derived to specify the static and dynamic behaviour of the piezo-actuated axis. The starting model parameters are fitted to measured data by an optimisation algorithm based on Newton's method. The linear model of the piezo-actuated system cutting edge is a useful support to design simple linear controllers like PID elements. The measured closed loop frequency response of the model based control is compared to simple linear controllers like PID elements. The PID controller can be easily extended with a Notch filter to damp the natural frequency of the system. The optimised model of the piezo-actuator can be used to design extensions of standard control structures like IMC controllers. The state space model of the piezo-actuated axis can be used to design a state space controller with a Kalman filter and PI-tracking control. This control extends the bandwidth of the axis up to 520 Hz, which is 65 Hz better than a Notch filter control. Unfortunately, the design of a Kalman filter is very time consuming and the control structure is very susceptible to parametric changes in the controlled system. Thus, the Notch filter control achieves the best rate between use and effort.