Consider the system defined by x1 x2 0 1 0 1x1 x2 0 10u y

Consider the system defined by {x_1 x_2} = [0 1 0 -1]{x_1 x_2} + [0 10]u y = [1 0]{x_1 x_2} (a) Design a full state-feedback controller such that the desired closed-loop poles have a natural frequency omega_n = 3 rad/s and a damping ratio zeta = 0.5. Make sure to give the equation of the full state-feedback controller. (b) Design a full-order estimator such that the estimator-poles have omega_n1 = 15 rad/s and zeta = 0.5. Make sure to give the dynamics equation of the full-order estimator. (c) Determine the state-space form of the compensator with combined control law and estimator.

Solution

a. second order equation is gives byw²/s²+2sw_n+p²

^{from the given question we can substitute the values in the above equations and finally we get the solutions as below}

9/s²+3s+9

b. similarly from the given information if we submit the values we will get the answer as

225/s²+75s+25