Petko Petkov, Da Wei Gu and Mihail Konstantinov

SLICOT Working Note 2001-1: January 2001.

In this paper we apply some of the SLICOT routines in the mu-synthesis of a robust control system for a triple inverted pendulum. We consider the case of a mixed type uncertainty consisting of two complex uncertainties in the actuators, three real uncertainties in the moments of inertia and three real uncertainties in the viscous friction coefficients. Using the D-K iteration, a further fictitious complex uncertainty block is included and a mu-controller is constructed for which the closed-loop control system achieves robust stability and robust performance as requested. The influence of the individual uncertainty on the robust stability is investigated using mu-analysis. In addition a reduced order controller is found such that the robust stability and robust performance of the closed-loop system are preserved with the much lower order controller. In the design, the structured singular value mu is calculated with the SLICOT routine AB13MD and the model reduction toolbox in SLICOT is used in the model reduction of the mu controller. The computation experience shows that the SLICOT routines perform better than the counterpart routines in MATLAB in terms of speed and accuracy.