Controller design for haptic systems under delayed position and velocity feedback

This thesis considers controller design for haptic systems under delayed position and velocity feedback. More precisely, a complete stability analysis of a haptic system, where local dynamics are described by some second-order mechanical dynamics, is presented. Characteristic equation of this system with time delays involves quasipolynomials. By a change of variables in the characteristic equation, stability conditions are obtained analytically and regions are plotted by using Matlab. Next, using two optimization techniques (H∞ and stability margin optimization) optimal choice for the controller gains is proposed. H∞ optimization minimizes tracking error between devices while avoiding large control action inputs. H∞ analysis requires high computational cost for accurate results due to its dependency to frequency domain. On the other hand, stability margin optimization defines a cost function that expresses the trade-off between system bandwidth and robustness with low computational cost. The derived results are tested on a three degree of freedom real-time experimental platform to illustrate the theoretical results. Finally robustness analysis is performed for optimal parameters to find allowable delay perturbations