NQG/H.INF./LTR Control for a Hard Nonlinear Servo System.

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