Observability of Self-Sensing System Using Extended Kalman Filter

Nomenclature Bp = input matrix (l m) Cp = diagonal piezoelectric capacitance matrix (m m) In = unit matrix (n n) K = constant-charge stiffness matrix (l l) l = number of DOF of structure M = mass matrix (l l) m = number of piezoelectric actuators Ok n = zero matrix (k n) Q = charge vector (m 1) V = voltage vector (m 1) w = external force vector (l 1) x = displacement vector (l 1) z = state vector in Eq. (7) (2l 1) ze = extended state vector in Eq. (10) [ 2l m 1] e = observer gain matrix [ 2l m m] = diagonal modal damping matrix (l l) = modal displacement vector (l 1) = eigen matrix (l l) = diagonal constant-charge modal stiffness matrix (l l)