Control Logic to Track Outputs of a Command Generator
Thomas L. Trankle, Arthur E. Bryson · Journal of Guidance and Control · 1978
A procedure is presented for synthesizing time-invariant control logic to cause the outputs of a linear plant to track the outputs of an unforced (or randomly forced) linear dynamic system. The control logic uses feedforward of the reference system state variables and feedback of the plant state variables. The feedforward gains are obtained from the solution of a linear algebraic matrix equation of the Lyapunov type. The feedback gains are the usual regulator gains, determined to stabilize (or augment the stability of) the plant, possibly including integral control. The method is applied here to the design of control logic for: 1) a second-order servomechanism to follow a linearly increasing (ramp) signal, 2) an unstable third-order system with two controls to track two separate ramp signals, and 3) a sixth-order system with two controls to track a constant signal and an exponentially decreasing signal (aircraft landing-flare or glide-slope-capture with constant velocity).