Minimum-Fuel Control of Second-Order Systems with Real Poles

Abstract

The controlled system has the transfer function G(s)=K/(s-λ1)(s-λ2). The control input is u(t), |u(t)|≤1, and the out put is y1(t). the control which forces any initial state y1(0), ẏ1(0) to the terminal state y1(T), ẏ1,(T), such that -K/Λ1Λ2≤y1(T)≤K/λ1λ2, ẏ1(T)=0, and which minimizes the fuel, F(T)=∫0T |u(t)|dt is determined. The phase plane is divided into three sets G-, G+, and G0; if the state is in G- then u(t)=-1 is used; if the state is in G+, then u(t)=+1 is used; if the state is in G0, then u(t)=0 is used.