Robust and minimum norm dynamic compensator design for partial eigenvalues assignment problems in singular vibration systems

This paper considers robust and minimum norm dynamic compensator design for studying partial eigenvalues assignment problems in singular vibration systems. The new partial eigenvalues assignment methods are proposed by using dynamic compensator. The parametric dynamic compensator expressions are derived for solving partial eigenvalues assignment problems using the corresponding characteristic equations and no spill property. Quadrature rectangle decomposition method is adopted to design the dynamic compensator gains. The optimal energy consumption control problem is discussed by designing the minimum norm dynamic compensator in singular vibration systems. A new gradient-based optimization method is proposed to discuss the robust and minimum dynamic compensator design by establishing the gradient formulas of objective functions. Simulation examples are provided to verify the main results.