Question: A robot arm has natural frequency of 10 Hz and a damping ratio of 0.3 for motions in the vertical plane. Vertical position is denoted by x1 and vertical velocity by x2. The spectral density of velocity disturbances is 10. Calculate and plot P(t) and K(t) for a time interval of 0.2 sec, assuming P(0) = 0 and using the conventional Kalman-Bucy filter equations for the following measurement:
(a) Velocity only, R = 1.
(b) Position only, R = 1.
(c) Velocity and position, r11 = r22 = 1.