Partial pole placement with minimum norm controller

— The problem of placing an arbitrary subset (m) of the (n) closed loop eigenvalues of a nth order continuous time single input linear time invariant(LTI) system, using full state feedback, is considered. The required locations of the remaining (n − m) closed loop eigenvalues are not precisely specified. However, they are required to be placed anywhere inside a pre-defined region in the complex plane. The resulting non-uniqueness is utilized to minimize the controller effort through optimization of the feedback gain vector norm. Using a variant of the boundary crossing theorem, the region constraint on the unspecified (n−m) poles is translated into a quadratic constraint on the characteristic polynomial coefficients. The resulting quadratically constrained quadratic program can be approximated by a quadratic program with linear constraints. The proposed theory is demonstrated for power oscillation damping controller design, where the eigenvalues corresponding to poorly damped...

• Type: Journal
• Year: 2010
• Where: CDC
• Authors: Subashish Datta, Balarko Chaudhuri, Debraj Chakraborty
• Keywords: Arbitrary Subset, CDC 2010, Characteristic Polynomial, Control Systems, Vector Norm