A H∞-weighting scheme for PID-like motion control

For motion control systems PID- or lead-lag-controllers serve well and are industrial standard. But often flexible modes of the mechanism endanger the stability of the control loop and thereby limit the bandwidth of the loop. Tuning and augmenting the controller becomes difficult and expensive at this point. Robust control design methods, first of all the μ-synthesis, offer a straight design formalism to overcome this problem. Anyhow, the crucial point in H_∞ and μ-synthesis is the proper choice of weighting functions. In most of the known applications of robust control, the weighting functions were shaped ad-hoc. It is often not clear to the engineer how to express the given technical specifications in terms of H_∞-weighting functions. In fact, theory does not give an answer to this question up to now. Therefore, in this paper a H_∞-weighting scheme is presented that leads to closed-loop response similar to the established one obtained by PID-control in the rigid-body range. In this way PID-like high performance motion controllers can systematically be designed in the presence of structural flexibilities. In contrast to other guidelines on weighting functions, the exact shape of the weighting functions is given as well as specific numbers of their parameters.