Compensation for canonical second order systems for eliminating peaking at the natural frequency and increasing bandwidth

A method of eliminating peaking and increasing bandwidth of a canonical second order system having a system frequency, and a resonant-prone mechanism having a mechanism frequency, said method comprising:

• forming a control loop for said resonant-prone mechanism, said control loop including a forward path and a feedback path;
• adding gain into said forward path of said control loop for said resonant-prone mechanism wherein said gain interjected includes a ratio of the square of the system and mechanism frequencies;
• and
• adding a phase lead or feedback factor (H-factor) into said feedback path of said control loop for said resonant-prone mechanism, said phase lead being a complex ratio of said system and mechanism frequencies.

A method of eliminating peaking and increasing bandwidth of a resonant-prone Fast Tool Servo system having a piezo actuator, a system frequency, and a mechanism frequency, said method comprising:

• forming a control loop for said resonant-prone system, said control loop including a forward path and a feedback path;
• adding gain into said forward path of said control loop of said system, wherein said gain added includes a function of the system and mechanism frequencies;
• and
• adding a phase lead or feedback factor (H-factor) into said feedback path of said control loop of said system, said phase lead being a complex ratio of said system and mechanism frequencies.

A fast tool servo system having a piezo actuator, a system frequency, and a mechanism frequency, comprising:

• a piezo-drive linear actuator;
• a fast tool servo;
• a control loop having a forward path and a feedback path;
• gain electronics to provide a gain component for adding gain into a forward path of said control loop of said system, wherein said gain added includes a function of the system and mechanism frequencies;
• and
• phase electronics to a phase component for adding a phase lead or feedback factor (H-factor) into a feedback path of said control loop of said system, said phase lead being a complex ratio of said system and mechanism frequencies.

A method of mitigating overshoot settling time for a scanning tunneling microscope using a piezo-electric positioner, having a piezo actuator, a system frequency, and a mechanism frequency, said method comprising:

• forming a control loop for said system, said control loop including a forward path and a feedback path;
• adding gain into said forward path of said control loop of said system, wherein said gain added includes a function of the system and mechanism frequencies;
• and
• adding a phase lead or feedback factor (H-factor) into said feedback path of said control loop of said system, said phase lead being a complex ratio of said system and mechanism frequencies.

A scanning tunneling microscope using a piezo-electric positioner, having a piezo actuator, a system frequency, and a mechanism frequency, comprising:

• a scanning tunneling microscope;
• a piezo-electric positioner;
• a control loop having a forward path and feedback path;
• gain electronics to provide a gain component for adding gain into said forward path of said control loop of said system, wherein said gain added includes a function of the system and mechanism frequencies;
• and
• phase electronics to provide a phase component for adding a phase lead or feedback factor (H-factor) into said feedback path of said control loop of said system, said phase lead being a complex ratio of said system and mechanism frequencies.