Prototyping of a LQG Compensator for a Compliant Positioning System with Friction

With increasing demands on speed and accuracy of positioning systems, friction and compliance which are present in every mechanical system have to be actively influenced by control. This requires to abandon the wide-spread classical (PI, PID) control concepts and apply more advanced approaches. LQG (linear quadratic Gaussian) control is one of the candidates which is capable to do active vibration damping and disturbance (friction) compensation, allowing for a high control bandwidth, strong disturbance rejection, and precise positioning with rapid changes of speed and acceleration. If properly designed and implemented, LQG control also shows a high robustness against external disturbances, nonlinear system behaviour, and plant parameter variations. Although control engineers have the theoretical background which is well explained in most control design textbooks, e.g.[1][2], one can still hear argueing against LQG control with the more demanding theory, the complex computational tasks, the difficulty to find appropriate design parameters, and the more demanding implementation issues. These arguments mostly originate from the lack of knowledge about the systematic procedure for design and implementation of LQG control, and about the extensive support given by recent development environments [3] for system modelling, analysis, design, simulation and rapid prototyping of control systems. In order to at least improve the knowledge about the procedure of LQG design and implementation, the aim of this paper is to show a straightforward approach for the position control of a compliant positioning system with friction. Since it has already been applied to other positioning devices, the approach can be seen as a sample for highly dynamical and precise position control design.