Load varying polytopic based robust controller design in LMI framework for a 2DOF stabilized platform

This paper tackles the problem of payload uncertainties through polytopic system formulation and robust controller design for a 2DOF parallel manipulator. Typically, such platforms are used as a base for different payloads, e.g., satellite antenna and camera in oceangoing crafts. Traditionally, these kinds of manipulators are modeled through a time varying nonlinear model, thus providing the rationale for a nonlinear or adaptive controller. Uncertainties due to load variations present a significant challenge for robust control design. In this paper, the authors have proposed a novel and practical approach to solve the variant payload dilemma for the stabilized platform. The novelty lies in extracting different linear models with distinct load conditions using the system identification method and quantifying them into a convex hull to formulate a polytopic system. A regulator is then designed by mixed H₂/H∞ synthesis with pole-placement constraints in a linear matrix inequality (LMI) framework to compensate output disturbances. The results are comparedwith a Riccati-based H∞ loop shaping controller. It is shown through simulations and experiments that an LMI design is a better choice for achieving robustness as well as performance. The hallmark of this work is the successful testing of the control strategy on a stabilized platform with heavy asymmetric satellite antenna to reject the tides' effect in a deep, turbulent sea.