Local Nonsmooth ℋ_∞-synthesis Under Friction/Backlash Phenomena

Abstract

The robust control of mechanical systems has attracted considerable research interest (see, e.g., related surveys compiled in [10] and [199]). The existing controllers from [19, 20, 44, 68, 225], which were derived via the nonlinear ℋ_∞-control approach coupled to the feedback linearization techniques, as well as passivity-based controllers from [187], are widely used in practice due to their robustness and simplicity of implementation. However, the frictional influence and backlash effects, as well as the fact of the incompleteness of the state measurements, were ignored in these studies, that severely limited the achievable performance and their practical utility. The nonsmooth ℋ_∞-synthesis of Chap. 7 is, in principle, capable of accounting for hard-to-model friction forces and backlash effects. It is the latter approach that is applied in the present chapter to regulation problems for a frictional mechanical manipulator and for a servomechanism with backlash, both with incomplete measurements. Due to the nature of the approach, the resulting regulators yield the desired robustness properties against the discrepancy between the real friction/backlash phenomenon and that described in the model.