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Tensor Product Based Polytopic LPV System Design of a 6-DoF Multi-strut Platform

Fangwu Ma, Jinhang Li*, Liang Wu, and Daofa Yuan
International Journal of Control, Automation, and Systems, vol. 20, no. 1, pp.137-146, 2022

Abstract : Multi-strut platform is widely used for precise instrument vibration isolation. In this paper, a NewtonEuler based 6-DOF 12-strut platform model is proposed. Nonlinearity of platform dynamic component is derived by establishing polytopic linear parameter varying (LPV) system. To guarantee the linearization accuracy of LPV system while reducing model elements to a real-time computing level. Tensor product(TP) model transformation and truncated high-order singular value decomposition(HOSVD) are used to decompose LPV system high-order tensor into unique principle basis. Then low-rank approximation of system is implemented by discarding minor singular basis vectors, for the sake of minimizing storage space and computing complexity. And then the parameter varying system is represented by convex combination of discretized system vertexes. So quadratic regulator method can be applied to vertex linear time-invariant subsystem controller to construct the global controller. Performance of the proposed multi-strut platform is demonstrated through hardware in loop simulation.

Keyword : "Convex combinationpolytopic LPV, HOSVD, multi-strut platform, tensor product. "

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