Method and apparatus for improved control of piezoelectric positioners

An apparatus for control of a piezoelectric positioner, comprising:

• (a) position sensor means for measuring the position state of the piezoelectric positioner and for providing a measured position state signal related to the position state of the piezoelectric positioner;
• (b) control means for generating a control signal to drive the piezoelectric positioner to a commanded position, wherein the control signal includes position and velocity state components, and wherein the control means includes
• means for comparing a commanded position state signal and the measured position state signal to form a position state error signal and
• means for deriving the position state component of the control signal from the position state error signal, and
• means for comparing an estimated velocity state signal with a commanded velocity state signal to form a velocity state error signal, and
• means for multiplying the velocity state error signal and a velocity state gain to form the velocity state component of the control signal;
• and
• (c) a velocity observer means for modeling a velocity state of the piezoelectric positioner and for providing the estimated velocity state signal as an output to the control means, wherein the estimated velocity state signal is related to the modeled velocity state of the piezoelectric positioner, including
• means for receiving the measured position state signal as an input and means for correcting the modeled velocity state in response to the measured position state signal,
• wherein the velocity observer modeling means includes model gains having gain values relative to estimates of a physical mass, a physical damping, and a physical stiffness of the piezoelectric positioner, and
• means for modeling a position state of the piezoelectric positioner and for providing an estimated position state signal related to the modeled position state of the piezoelectric positioner and
• means for comparing the measured position state signal and the estimated position state signal to form an observer position state error signal and
• means for using the observer position state error signal in a feedback loop to drive the estimated position state signal to equal the measured position state signal.

A piezoelectric positioning system, comprising:

• (a) a piezoelectric positioner;
• (b) drive means responsive to a control signal for driving the piezoelectric positioner to a commanded position defined by the control signal, wherein the control signal includes a velocity state component;
• (c) position sensor means for measuring the position state of the piezoelectric positioner and for providing a measured position state signal related to the position state of the piezoelectric positioner;
• (d) control means for generating the control signal, including means for comparing an estimated velocity state signal with a commanded velocity state signal to form a velocity state error signal and means for multiplying the velocity state error signal and a velocity state gain to form the velocity state component of the control signal;
• and
• (e) a velocity observer means for modeling a velocity state of the piezoelectric positioner and for providing the estimated velocity state signal as an output to the control means, wherein the estimated velocity state signal is related to the modeled velocity state of the piezoelectric positioner, and wherein the velocity observer means includes means for receiving the measured position state signal as an input and means for correcting the modeled velocity state of the piezoelectric positioner in response to the measured position state signal.

A piezoelectric positioner velocity observer, comprising:

• (a) means for receiving a measured position state signal corresponding to a physical position of a piezoelectric positioner;
• (b) means for modeling a velocity state of the piezoelectric positioner and means for correcting the modeled velocity state of the piezoelectric positioner in response to the measured position state signal, and wherein the means for modeling the velocity state of the piezoelectric positioner includes model gains having gain values relative to estimates of a physical mass, a physical damping, and a physical stiffness of the piezoelectric positioner;
• and
• (c) means for providing an estimated velocity state signal corresponding to the modeled velocity state of the piezoelectric positioner as an output from the means for modeling.

An improved scanned probe microscope of the type comprising a piezoelectric positioner having a probe attached to a first end of the positioner and a means for coarse positioning of the probe adjacent to a sample attached at a second end of the positioner, means for applying a voltage differential between the probe and the sample whereby a tunneling current from the sample is generated which is exponentially proportional to a position of the probe from the sample, and means for applying a scanning signal to the positioner to scan the probe laterally across the sample, wherein the improvement comprises:

• (a) drive means responsive to a control signal for driving the piezoelectric positioner to a commanded position defined by the control signal to position the probe at a commanded distance from the sample, wherein the control signal includes a velocity state component;
• (b) means for deriving the position state of the piezoelectric positioner from the tunneling current and for providing a measured position state signal related to the position state of the piezoelectric positioner;
• (c) control means for generating the control signal, including means for comparing an estimated velocity state signal with a commanded velocity state signal to form a velocity state error signal and means for multiplying the velocity state error signal and a velocity state gain to form the velocity state component of the control signal;
• and
• (d) a velocity observer means for modeling a velocity state of the piezoelectric positioner and for providing the estimated velocity state signal as an output to the control means, wherein the estimated velocity state signal is related to the modeled velocity state of the piezoelectric positioner, and wherein the velocity observer means includes and means for receiving the measured position state signal as an input and means for correcting the modeled velocity state of the piezoelectric positioner in response to the measured position state signal.

A method for the control of a piezoelectric positioner, comprising the steps of:

• (a) applying a control signal to the piezoelectric positioner to control a physical position of the positioner;
• (b) modeling the position and the velocity response of the piezoelectric positioner to the control signal;
• (c) measuring the physical position of the positioner;
• (d) comparing the measured position of the positioner to the modeled position response of the positioner to obtain a model position state error signal;
• (e) integrating the model position state error signal;
• (f) multiplying the integrated model position state error signal by a model integration gain;
• (g) applying the integrated model position state error signal multiplied by the model integration gain to the model of the position response to drive the modeled position response to equal the measured position;
• (h) comparing the modeled velocity response of the positioner to a commanded velocity signal to obtain a physical velocity state error;
• and
• (i) multiplying the physical velocity state error by a physical velocity state gain to form a velocity component of the control signal.

A method for the control of a piezoelectric positioner, comprising the steps of:

• (a) applying a control signal to the piezoelectric positioner to control a physical position of the positioner;
• (b) modeling the position and the velocity response of the piezoelectric positioner to the control signal;
• (c) measuring the physical position of the positioner;
• (d) comparing the measured position of the positioner to the modeled position response of the positioner to obtain a model position state error signal;
• (e) multiplying the model position state error signal by a model velocity gain to form a model velocity state feedback signal;
• (f) applying the model velocity state feedback signal to the model of the velocity response of the positioner;
• (g) integrating the model position state error signal;
• (h) multiplying the integrated model position state error signal by a model integration gain;
• (i) applying the integrated model position state error signal multiplied by the model integration gain to the model of the position response to drive the modeled position response to equal the measured position;
• (j) comparing the modeled velocity response of the positioner to a commanded velocity signal to obtain a physical velocity state error;
• and
• (k) multiplying the physical velocity state error by a physical velocity state gain to form a velocity component of the control signal.

A method for the control of a piezoelectric positioner, comprising the steps of:

• (a) applying a control signal to the piezoelectric positioner to control a physical position of the positioner;
• (b) determining an estimated physical mass of the piezoelectric positioner;
• (c) determining an estimated physical damping of the piezoelectric positioner;
• (d) determining an estimated physical stiffness of the piezoelectric positioner;
• (e) modeling the position and the velocity response of the piezoelectric positioner to the control signal based on the estimated physical mass, the estimated physical damping, and the estimated physical stiffness;
• (f) measuring the physical position of the positioner;
• (g) comparing the measured position of the positioner to the modeled position response of the positioner to obtain a model position state error signal;
• (h) integrating the model position state error signal;
• (i) multiplying the integrated model position state error signal by a model integration gain;
• (j) applying the integrated model position state error signal multiplied by the model integration gain to the model of the position response to drive the modeled position response to equal the measured position;
• (k) comparing the modeled velocity response of the positioner to a commanded velocity signal to obtain a physical velocity state error;
• and
• (l) multiplying the physical velocity state error by a physical velocity state gain to form a velocity component of the control signal.