Synthesis of control and observation laws power system based on generalized formula Ackermann for MIMO systems

Abstract

For an electric power system (EPS), as a dynamic system with many inputs and many outputs (Multi Inputs Multi Outputs System − MIMO), compact analytical formulas are obtained for calculating the coefficients of the controller matrix and the observer matrix of the state of the solution of the synthesis problem, providing a given placement of eigenvalues along full state vector. These formulas are generalizations to MIMO systems of the well-known Ackermann formula used to design the control of systems with one input and many outputs (Single Input Multi Outputs System − SIMO). The approach is based on the transformations used in the original multi-step (multilevel) decomposition method, as well as a nondegenerate similarity transformation in the form of the Kalman controllability matrix. The obtained formulas are applicable to dynamic systems, for which the dimension of the state space is a multiple of the dimension of the inputs (controls). This limitation is removed by using the Yokoyama transform. These formulas differ in terms of parameterization of the set of equivalent laws. An example of the synthesis of a control law for a synchronous generator in a complex EPS is considered in order to preserve the existing modes of electromechanical oscillations and meet additional requirements (roughness with respect to disturbances and/or increased sensitivity to changes in controlled parameters in a given region or frequency band).