Control of vibratory/oscillatory mixers

1. A method for controlling a vibratory/oscillatory mixer that comprises an actuator and a mechanical system containing a material to be mixed, the mechanical system being subjected to a plurality of oscillatory input force waveforms and vibrating in accordance with a plurality of associated oscillatory response waveforms, each of said oscillatory input force waveforms having an input force frequency and an input force amplitude and each of said associated oscillatory response waveforms having a response frequency and a response amplitude, the method comprising:

a step for accepting input from an operator of a desired operating condition for the mechanical system;

a step for operating the actuator at a first oscillatory input force waveform having a first frequency and a first input force amplitude to produce a first associated oscillatory response waveform within a primary mode of resonance in the mechanical system;

a step for measuring a first phase angle between said first oscillatory input force waveform and said first associated oscillatory response waveform and recording said first phase angle;

a step for controlling the actuator at a second oscillatory input force waveform having a second frequency to produce a second associated oscillatory response waveform;

a step for determining a second phase angle between said second oscillatory input force waveform and said second associated oscillatory response waveform and recording said second phase angle;

a step for calculating an undamped natural frequency, a damping ratio and operating points for maximum displacement, maximum velocity, maximum acceleration or maximum jerk for said mechanical system;

a step for driving the actuator at an operating frequency that causes the mechanical system to vibrate substantially at one of said operating points;

a step for repeating said operating, measuring, controlling, determining, calculating, and driving steps until the mechanical system is operating at said one of said operating points;

a step for adjusting said input force amplitude until said desired operating condition is reached;

a step for periodically testing the mechanical system to ensure that it is operating at said desired operating condition, and, if the mechanical system is not operating at said desired operating condition, repeating said operating, measuring, controlling, determining, calculating, driving, repeating, adjusting, and periodically testing steps until the mechanical system is operating at said desired operating condition;

a step for, during operation at said desired operating condition, calculating the amount of energy and/or power being absorbed by the material to be mixed;

a step for, during operation of said mechanical system, executing a supervisory algorithm; and

a step for terminating mixing.

2. A method for controlling a vibratory/oscillatory mixer that comprises an actuator and a mechanical system containing a material being mixed, the mechanical system being subjected to a plurality of oscillatory input force waveforms and vibrating in accordance with a plurality of associated oscillatory response waveforms, the method comprising:

(a) accepting input from an operator of a desired mixer operating condition;

(b) operating the actuator at a first oscillatory input force waveform having a first frequency and a first input force amplitude to produce a first associated oscillatory response waveform within a primary mode of resonance in the mechanical system;

(c) measuring a first phase angle between said first oscillatory input force waveform and said first associated oscillatory response waveform;

(d) operating the actuator at a second oscillatory input force waveform having a second frequency to produce a second associated oscillatory response waveform;

(e) measuring a second phase angle between said second oscillatory input force waveform and said second associated oscillatory response waveform;

(f) calculating an undamped natural frequency, a damping ratio and operating points for maximum displacement, maximum velocity, maximum acceleration or maximum jerk for said mechanical system;

(g) operating the actuator at an operating frequency that causes the mechanical system to vibrate substantially at one of said operating points;

(h) repeating steps (b) through (g) until the mechanical system is operating at said one of said operating points;

(i) adjusting said input force amplitude until said desired operating condition is reached;

(j) periodically testing the mechanical system to ensure that it is operating at said desired operating condition, and, if the mechanical system is not operating at said desired operating condition, repeating steps (b) through (j) until the mechanical system is operating at said desired operating condition;

(k) during operation at said desired operating condition, calculating the amount of energy and/or power being absorbed by the material being mixed;

(l) during operation of said mechanical system, executing a supervisory algorithm; and

(m) terminating mixing.

3. A method for controlling a vibratory/oscillatory mixer at a desired operating condition, the vibratory/oscillatory mixer comprising an actuator and a mechanical system containing a material to be mixed, the mechanical system being subjected to a plurality of oscillatory input force waveforms and vibrating in accordance with a plurality of associated oscillatory response waveforms, the method comprising:

operating the actuator at a first oscillatory input force waveform having a first frequency and a first input force amplitude to produce a first associated oscillatory response waveform within a primary mode of resonance in the mechanical system;

measuring a first phase angle between said first oscillatory input force waveform and said first associated oscillatory response waveform;

operating the actuator at a second oscillatory input force waveform having a second frequency to produce a second associated oscillatory response waveform;

measuring a second phase angle between said second oscillatory input force waveform and said second associated oscillatory response waveform;

calculating an undamped natural frequency, a damping ratio and operating points for said mechanical system;

operating the actuator at an operating frequency that causes the mechanical system to vibrate at one of said operating points;

adjusting said input force amplitude until said desired operating condition is reached; and

ensuring that the mechanical system is operating at said desired operating condition.

4. The method of claim 3 further comprising:

during operation at said desired operating condition, calculating the amount of energy or power being absorbed by the material to be mixed.

5. A system for controlling a vibratory/oscillatory mixer at a desired operating condition, the vibratory/oscillatory mixer comprising an actuator and a mechanical system containing a material being mixed, the mechanical system being subjected to a plurality of oscillatory input force waveforms and vibrating in accordance with a plurality of associated oscillatory response waveforms, the system comprising:

means for operating the actuator at a first oscillatory input force waveform having a first frequency and a first input force amplitude to produce a first associated oscillatory response waveform within a primary mode of resonance in the mechanical system;

means for measuring a first phase angle between said first oscillatory input force waveform and said first associated oscillatory response waveform;

means for operating the actuator at a second oscillatory input force waveform having a second frequency to produce a second associated oscillatory response waveform;

means for determining a second phase angle between said second oscillatory input force waveform and said second associated oscillatory response waveform;

means for calculating an undamped natural frequency, a damping ratio and operating points for said mechanical system;

means for operating the actuator at an operating frequency that causes the mechanical system to vibrate at one of said operating points;

means for adjusting said input force amplitude until said desired operating condition is reached; and

means for ensuring that the mechanical system is operating at said desired operating condition.

6. The system of claim 5 further comprising:

means for calculating the amount of energy or power being absorbed by the material being mixed during operation at said desired operating condition.

7. A system for controlling a vibratory/oscillatory mixer at a desired operating condition, the system comprising:

a mechanical system that is operative to contain a material being mixed;

an actuator;

a sensor; and

a controller;

wherein said controller is operative to cause said actuator to impose a first oscillatory input force waveform on said mechanical system, said first oscillatory input force waveform having a first frequency and a first input force amplitude, said first oscillatory input force waveform causing said mechanical system to vibrate in accordance with a first oscillatory response waveform within a primary mode of resonance in the mechanical system;

wherein said controller is further operative to cause said sensor to sense the signals required for said controller to determine a first phase angle between said first oscillatory input force waveform and said first oscillatory response waveform;

wherein said controller is further operative to cause said actuator to impose a second oscillatory input force waveform having a second frequency on said mechanical system, said second oscillatory input force waveform causing said mechanical system to vibrate in accordance with a second oscillatory response waveform;

wherein said controller is further operative to cause said sensor to sense the signals required for said controller to determine a second phase angle between said second oscillatory input force waveform and said second oscillatory response waveform;

wherein said controller is further operative to calculate an undamped natural frequency, a damping ratio and operating points for said mechanical system;

wherein said controller is further operative to cause said actuator to vibrate said mechanical system at one of said operating points;

wherein said controller is further operative to cause said actuator to adjust said input force amplitude until said desired operating condition is reached.

8. The system of claim 7 wherein:

said controller is operative to calculate the amount of energy or power being absorbed by the material being mixed during operation at the desired operating condition.

9. The method of claim 2 wherein said desired mixer operating condition is one or more of the following operating conditions for the mechanical system: a maximum energy efficiency, a maximum mixing rate or another specific mixing rate, a maximum acceleration amplitude or another specific acceleration amplitude, a maximum velocity amplitude or another specific velocity amplitude, a maximum displacement amplitude or another specific displacement amplitude, and a maximum jerk amplitude or another specific jerk amplitude, a desired amount of energy absorption by the material to be mixed, and one or more salient mixing attributes is reached.

10. The method of claim 9 wherein said salient mixing attributes include one or more of the following attributes of the material being mixed: a temperature, a pressure, a viscosity, a color, a tackiness, a homogeneity, and a separation.

11. The method of claim 2 wherein said actuator comprises a plurality of resonators and said desired mixer operating condition is one or more of the following operating conditions for the actuator: an equal drive current being transmitted to each resonator; an equal power being transmitted to each resonator; a minimum power for the actuator; a minimum apparent sound generated; or a constant voltage being imposed on each resonator.

12. The method of claim 2 wherein said calculating step comprises using said first and second phase angles (‘θ 1 ’ and ‘θ 2 ’) and said first and second frequency (‘ω 1 ’ and ‘ω 2 ’) to calculate said undamped natural frequency (‘ω n ’) and said damping ratio (‘ζ’) using the following relations:

ω

n

2

=

ω

2

2

·

ω

1

·

tan

⁡

(

θ

1

)

-

ω

1

2

·

ω

2

·

tan

⁡

(

θ

2

)

tan

⁡

(

θ

2

)

·

ω

1

-

tan

⁡

(

θ

1

)

·

ω

2

ζ

=

tan

⁡

(

θ

1

)

·

(

ω

n

2

-

ω

1

2

)

2

·

ω

1

·

ω

n

=

tan

⁡

(

θ

2

)

·

(

ω

n

2

-

ω

2

2

)

2

·

ω

2

·

ω

n

13. The method of claim 2 wherein said calculating step comprises calculating operating points for maximum displacement, maximum velocity, maximum acceleration, or maximum jerk for said mechanical system in accordance with a relation presented on FIG. 11 .

14. The method of claim 2 wherein said executing a supervisory algorithm step comprises: calculating a rate of change of said response amplitude and initiating said terminating step if said rate of change is above a desired value.

15. The method of claim 2 wherein said actuator comprises two resonators; and

wherein said oscillatory input force waveforms being produced by one of said resonators are in phase or 180 degrees out of phase with said oscillatory input force waveforms being simultaneously produced by another of said resonators, thereby using destructive interference to minimize the sound projected from the vibratory/oscillatory mixer.