Method and apparatus for reducing resonance in a dual inertia system

• US 6,144,181 A
• Filed: 09/21/1998
• Issued: 11/07/2000
• Est. Priority Date: 09/21/1998
• Status: Expired due to Term

• Current Assignee: Allen-Bradley Company LLC (Rockwell Automation, Inc.)
• Original Assignee: Rockwell Technologies, LLC (Teledyne Technologies Incorporated)
• Inventors: Rehm, Thomas J., Schmidt, Peter B.
• Primary Examiner(s): SALATA, ANTHONY J
• Application Number:
  US09/158,184
• Time in Patent Office: 778 Days
• Field of Search: 318/569-572, 318/609, 318/610, 318/611, 318/616-620, 318/621, 318/624
• US Class Current: 318/629
• CPC Class Codes: G05B 5/01 electric

Abstract

A method and apparatus for minimizing resonant oscillations in a dual inertia system characterized by minimally stable poles and both a resonant frequency and an anti-resonant frequency, the apparatus including a notch filter which is tuned so that notch filter zeros essentially cancel the minimally stable poles and so that at least one notch pole is located at the intersection of a real axis and an system anti-resonant zero radius on a root-loci plot, thereby rendering an exceptionally stable system, the method for tuning the notch filter as described.

Claims

1. A method for use in a configuration including a controller and a dual energy system, the system including a drive component and a load component, the controller controlling the drive component and the drive component driving the load component, the system characterized generally by a second order transfer function including two system resonant poles and two system zeros and having a resonant frequency ω

_r and an anti-resonant frequency ω

_ar, the method for minimizing resonance, the method comprising the steps of;

providing a notch filter characterized by a Laplace domain transfer function;

##EQU15## where A is a tuning variable, R is a damping term and ω

_n is a natural frequency; and

tuning the transfer function such that natural frequency ω

_n is equal to resonant frequency ω

_r and a damping term R=(ω

_ar /ω

_r)+(ω

_r /ω

_ar).

2. The method of claim 1 further including the steps of, prior to providing, determining both the system resonant frequency ω

_r and the system anti-resonant frequency ω

_ar.

3. The method of claim 2 wherein the step of determining the system resonant frequency includes the steps of determining a motor velocity error signal indicating the difference between a commanded motor velocity and an actual motor velocity and performing a Fast Fourier Transfer on the error signal to determine the system resonant frequency.

4. The method of claim 3 wherein the motor and load components are linked together via a shaft and the shaft is characterized by a spring constant k, the motor is characterized by a motor inertia J_m and the load is characterized by a load inertia J_l, each of the load and motor inertias J_l and J_m are known and the step of determining the anti-resonant frequency ω

_ar includes solving the equation;

##EQU16## to determine the value of constant k and then solving the equation;

##EQU17##

5. A method for use in a configuration including a controller, a dual energy system and a notch filter, the system including a drive component and a load component, the controller controlling the drive component and the drive component driving the load component, the system characterized generally by a second order transfer function including two system resonant poles and two system zeros and having a resonant frequency T_r and an anti-resonant frequency T_ar, the notch filter characterized by a second order transfer function also having two poles and two zeros, the method for minimizing resonance and comprising the steps of:

selecting notch filter transfer function zeros to cancel the system resonant poles wherein the notch filter transfer function in the Laplace domain is ##EQU18## where A is a tuning variable, R is a damping term and ω

_n is a natural frequency; and

selecting notch filter poles so that both notch filter poles are on the real axis of a root-loci s-plane and one of the poles is on the real axis at a radius which is equal to the magnitude of the system zeros, the step of selecting notch filter poles including the step of tuning the notch filter such that natural frequency ω

_n is equal to resonant frequency ω

_r and damping term R=(T_ar /T_r)+(T_r /T_ar).

6. The method of claim 5 further including the steps of, prior to selecting the notch filter zeros, determining both the system resonant frequency ω

_r and the system anti-resonant frequency ω

_ar.

7. The method of claim 6 wherein the drive component is a motor and the method further includes the steps of determining a motor velocity error signal indicating the difference between a commanded motor velocity and an actual motor velocity and performs a Fast Fourier Transfer on the error signal to determine the system resonant frequency.

8. The method of claim 7 wherein the motor and load components are linked together via a shaft and the shaft is characterized by a spring constant k, the motor is characterized by a motor inertia J_m and the load is characterized by a load inertia J_l, each of the load and motor inertias J_l and J_m are known and the step of determining the anti-resonant frequency ω

_ar includes solving the equation;

##EQU19## to determine the value of constant k and then solving the equation;

##EQU20##