Quasi-linear H2/H.INF./LTR Control of Vertical Parallel Flexible Structures Connected by a Spring.

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The quasi-linear H2/H∞/LTR control method is presented for the robust control of hardnonlinear multivariable systems. The hard nonlinear elements such as Coulomb friction, dead-zone and backlash are replaced by their random input describing functions (RIDF) to develop a quasi-linear model for designing a quasi-linear H2/H∞ controller. However, a nonlinear correction term appears in the coupled Riccati equations when the quasi-linear H2/H∞ method is applied for a quasi-linear model. It is shown that a nonlinear correction term can be ignored using the loop transfer recovery (LTR) under the appropriate condition. Thus, the quasi-linear H2/H∞ controller can be synthesized by introducing the inverse random input describing function (IRIDF). To show the effectiveness of the proposed control method, it will be applied to a flexible parallel inverted pendulum with Coulomb friction. The results of simulation show that the proposed control method is robust to nonlinear effects and the vibration of end tip.