Simulation Studies of a Prototype EMA Controller for Time-Varying Linear and Nonlinear Systems

Due to the lack of a general mathematical theory for linear time-varying (LTV) dynamical systems, the control of LTV systems has been a difficult task. Recently, a unified linear system theory has been developed for the class of LTV systems of the form: y⁽ⁿ⁾ + an(t)y^(n-1) +...+ a2(t)¿ + a1(t)y = bn+1(t)u⁽ⁿ⁾ + bn(t)u^(n-1) +... + b2(t)¿ + b1(t)u, based on a unified time-varying eigenvalue concept [6]-[10]. Using that theory, a novel controller design technique, called EMA control, has also been developed for LTV systems [11]. In this paper three simulation case studies of the EMA controller are presented to exemplify its applications in time-varying linear and nonlinear control systems found in aerospace industries. The nonlinear systems in these simulation studies were treated either by local linearization, or simply as a time-varying linear system whose coefficients ¿i(t) are dependent on the states y^(k)(t), k = 0,1,...,n-1. The success of the EMA control technique presented in this paper demonstrates its usefulness.