Patent ID: 7645124

Claim:
A method to control a system exhibiting stick-slip behavior and having unmeasurable states comprising the steps of: receiving an electrical torque parameter, a crank angle parameter, and a crank speed parameter; estimating the unmeasurable states; sending estimates of the unmeasurable states to a regulator wherein the regulator is one of a linear quadratic regulator, a binomial full state feedback regulator, a Bessel full state feedback regulator, and an ITAE ((integral of time multiplied by the absolute value of error) full state feedback regulator; and regulating the system to minimize differences between reference states and the estimates wherein the system is a down-hole pump system and the unmeasurable states are pump angle and pump speed and the regulator structure has a gain [k 1 ;k 2 ;k 3 ;k 4 ] that corresponds to a gain for errors of a reference vector x*=[Ac*, Wc*, Ap*, Wp*] minus four system states {circumflex over (x)}=[Â c , Ŵ c , Â p , Ŵ p ] where Ac* is a a crank angle command, Wc* is a crank speed command, Ap* is a pump angle command, Wp* is a pump speed command, Â c is a crank angle position, Ŵ c is a crank speed, Â p is a pump angle estimate, and Ŵ p is a pump speed estimate.