Answer Happy

Linear System Theory
Q1. Translational motion of a ballistic missile continuously acquires sufficiently exact position values from its standard navigation aid GPS. However, in addition it 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 translational dimension is given as d X₁ (t) A- ==3*₂8]+4₂0 u(t) -X₂ (t) y(t) = [0_1][x₂] Where x₁ (t) is the speed state variable and x₂ (t) is the position state variable, u(t) is the acceleration variable. The design criteria for the observer are as follows: Damping ratio, <= 0,707, and Natural frequency, wn = 3 rad/s a) Design the observer, b) Locate the poles of the onserver on s- plane, c) Sketch the system block diagram by OPAMPS, d) Obtain the unit step response of the system by using MATLAB simulation.