Estimation and control of a resonant plant prone to stick-slip behavior
First Claim
1. 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 [k1;
k2;
k3;
k4] 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.
3 Assignments
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Accused Products
Abstract
A method and apparatus are provided for estimating and/or precluding stick-slip, or other oscillatory or resonant behavior, through use of a virtual transducer, which precludes the need for having sensors located adjacent to a driven element of the system, or adjacent contact surfaces at which the stick-slip relative motion may occur. Parameters measurable at a drive mechanism are utilized for controlling a system in a manner which precludes stick-slip, or other oscillatory or resonant behavior, of the driven element. Relative motion between contacting surfaces in the driven element, prone to stick-slip behavior, is controlled such that, after sufficient force is applied by the drive element to overcome static friction forces between the contacting surfaces and break them free from one another, relative motion between the surfaces is maintained at a high enough relative speed that the surfaces are precluded from statically contacting one another, so that stick-slip behavior is precluded.
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Citations
7 Claims
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1. A method to control a system exhibiting stick-slip behavior and having unmeasurable states comprising the steps of:
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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 [k1;
k2;
k3;
k4] 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. - View Dependent Claims (4, 5, 6, 7)
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2. A method to control a system exhibiting stick-slip behavior and having unmeasurable states comprising the steps of:
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receiving an electrical torque parameter, a crank angle parameter, and a crank speed parameter; estimating the unmeasurable states with a finite difference state estimator; sending estimates of the unmeasurable states to a 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, wherein the step of estimating the unmeasurable states with a finite difference state estimator comprises the steps of estimating the pump angle in accordance with the equation - View Dependent Claims (3)
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Specification