NQG/H infinity/LTR control for a hard nonlinear servo system

In this paper we propose a new nonlinear controller design method, called n onlinear quadratic Gaussian/H-infinity/loop transfer recovery (NQG/H-infini ty/LTR), for nonlinear servo systems with hard nonlinearities such as Coulo mb friction, dead-zone. We consider a H-infinity performance constraint for the optimization of statistically linearized systems, by replacing a covar iance Lyapunov equation into a modified Riccati equation of which solution leads to an upper bound of the nonlinear quadratic Gaussian (NQG) Performan ce. As a result, the nonlinear correction term is included in coupled Ricca ti equation, which is generally very difficult to have a numerical Solution . To solve this problem, we use the modified loop shaping technique and sho w some analytic proofs on LTR condition. Finally, the NQG/H-infinity/LTR co ntroller is synthesized by inverse random input describing function techniq ues (IRIDF). It is shown that the proposed design method has a better perfo rmance robustness to the hard nonlinearity than the LQG/H-infinity/LTR meth od via simulations and experiments for the timing-belt driving servo system that contains the Coulomb friction and dead-zone.