Design of controller for robots using the robust root locus of discrete time systems

A technique for generating multi-parameter root loci of a continuous time feedback system was introduced by Barmish and Tempo (1990). For uncertainties in l parameters of the plant, the robust root locus is reduced to a two-dimensional bounded subset of the complex plane. This is much better than treating the complete l-dimensional set and plotting a large number of ordinary root loci. In this paper, the authors extend this procedure to discrete time systems. A computational method for plotting the robust root locus of discrete time systems is developed. The graph of the locations of the poles of the transfer function of the closed loop system corresponding to each gain can be plotted readily and accurately with this method. The sensitivity of poles to the coefficients of the characteristic polynomial can thus be examined and the optimal tuning gain selected to reach a better robustness. Also a stricter bound of the zeros of the characteristic polynomial is given to further reduce the computation of the robust root locus. The technique is applied to the design of robot manipulators. Simulations of controller design for the PUMA 762 robotic disk grinding process are included