Q4.An auto-pilot system of an aircraft requires speed data relative to the ground. In order to avoid the installation of an expensive speed sensor such as Doppler radar or inertial system, the speed is to be estimated by an observer. The state equation in observer canonical form in longitudinal axis is given as E- - + y(t) = [30][*] Where x₁ (t) is the speed state variable and x₂ (t) is the position state variable. Using Lüenberger's method, design the observer and sketch the system block diagram by OPAMPS. (Hint: Lüenberger's Method: 281-60 = (1) 2(t) = F2(t) + Gu(t) + Hy(t) (2) Where G = DB (3) DA-FD = HC (4) The design of the observer essentially consists of solving Eq. (4) for D and obtaining G from Eq. (3). The stability of F and the linear independence of D with respect to C must be provided as a secondary condition. The solution exists if A and F have unequal eigenvalues. For our case, choose,
