Patent ID: 7706899

Claim:
An apparatus for controlling a system, comprising: a fixed controller comprising: a fixed proportional-integral-derivative (PID) controller; and a fixed feedforward controller, in which the fixed PID controller and the fixed feedforward controller are configured to receive a reference command and to produce a fixed controller output comprising a fixed PID and a fixed feedforward controller command; an adaptive cascade controller comprising: an adaptive cascade PID controller; and an adaptive feedforward controller, in which the adaptive cascade PID controller and the adaptive feedforward controller are configured to receive the reference command and to produce adaptive controller output comprising an adaptive cascade PID and an adaptive feedforward command; and means for adding the fixed controller output and the adaptive cascade controller output to produce a control command for a controlled system, the controlled system providing a measure of an output and a rate of change of the output as feedback to the fixed controller and the adaptive controller, and wherein z = - ( ⅆ / ⅆ t + K pp ) n - 1 ⁢ e z I = ∫ z ⁢ ⅆ t , where n is a dominant order of a process, I is time, K pp >0 is a selected scalar gain, e=r−y is a tracking error for the reference command r, and y is the output.