Cascaded Sliding-Mode Observer for High-Order Systems with Lower-Triangular Structure

Motivated by state estimation and adaptive control of large-scale complex power systems, this paper proposes a cascaded sliding-mode observer for high-order systems with lower-triangular structure and not necessarily in Byrnes-Isidori Normal Form. Key information about the known nonlinear terms of the system is integrated into different blocks of the proposed observer. Under appropriate parameter design rules, the states of the proposed observer will quickly reach and slide on the intersection of sliding surfaces. During this sliding phase, the estimation errors rapidly converge to negligibly small values, determined by a parameter of the observer. Compared with standard high-gain observers and classical high-gain parameter embedded sliding-mode observers, the proposed observer achieves similar estimation error convergence speed with smaller gain coefficients. Moreover, the peaking phenomenon of the proposed observer is less severe. Besides, the structure of the proposed observer is more flexible than that of some well-known cascaded high-gain observers as there is no restriction on the dimension of the blocks of the proposed observer. Simulation studies are carried out on a fifth-order nonlinear system and a 10-machine 48-bus power system to further demonstrate the features of the proposed observer and its application on adaptive transient stability control of wind farms penetrated power systems.