Gain scheduled SPR controllers for nonlinear flexible systems

The problem of scheduling strictly positive real (SPR) dynamic compensation for control of nonlinear flexible systems which exhibit collocated inputs and outputs is explored. The major application is the robust motion control of structurally flexible systems whose dynamics possess significant configuration dependence. Included in this class are flexible robot manipulators. The issue of designing a linear time-invariant SPR compensator for control of a nonlinear system is examined. Controller performance is enhanced by scheduling a series of such designs and a scheduling algorithm is developed which preserves robust stability with respect to the nonlinear plant model. Global asymptotic stability of equilibrium setpoints is proven when the scheduled SPR compensator is used in conjunction with a proportional feedback gain. A numerical example employing a two-link flexible manipulator is used to illustrate the approach and compare the efficacy of different scheduling algorithms.