This paper demonstrates the design of loop-shaping controller for a linear time invariant (LTI) system with input saturation constraint. The design problem has been formulated in the four-block synthesis framework, which is equivalent to normalized coprime factor robust stabilization problem. The shaped plant is represented as a polytopic linear parameter varying (LPV) system while saturation nonlinearity is considered. For a polytopic model, the LTI loop-shaping controllers have been designed at each vertex of the polytope using linear matrix inequalities, and subsequently controllers are scheduled by adopting a certain interpolation procedure. The proposed controller ensures the stability and robust -performance of the closed-loop system due to vertex property of the polytopic LPV shaped plant. The effectiveness of the design method has been illustrated through a numerical example.
Design of Loop-Shaping Controller for LTI System With Input Saturation: Polytopic Gain Scheduled Approach
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Patra, S., Sen, S., and Ray, G. (December 2, 2010). "Design of Loop-Shaping Controller for LTI System With Input Saturation: Polytopic Gain Scheduled Approach." ASME. J. Dyn. Sys., Meas., Control. January 2011; 133(1): 014506. https://doi.org/10.1115/1.4001328
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