System and method for output compensation in flow sensors using pulse width modulation

1. A system for monitoring and controlling flow rate of a fluid through a valve, the system comprising:

a flow rate sensor configured to measure the flow rate of the fluid through the valve; and

a controller in communication with the flow rate sensor and configured to:

receive the measured flow rate from the flow rate sensor;

determine if the measured flow rate is equal to a predetermined flow rate value; and

in response to a determination that the measured flow rate is equal to the predetermined flow rate value:

determine a minimum valve position threshold (x min );

determine a minimum flow rate threshold (y min ) corresponding to x min ;

generate a pulse-width modulated (PWM) signal;

calculate a corrected flow rate (ŷ f ) using the PWM signal; and

control a valve operation using the corrected flow rate (ŷ f );

wherein the PWM signal is configured to switch between zero and y min .

2. The system of claim 1 , wherein the PWM signal is equal to zero when a pulse run time (t r ) is between a sum of a beginning of a pulse period (t k ) and a pulse width (T on ) and a sum of the beginning of the pulse period (t k ) and a pulse period (C).

3. The system of claim 1 wherein the PWM signal is equal to y min when a pulse run time (t r ) is between the beginning of a pulse period (t k ) and a sum of the beginning of the pulse period (t k ) and a pulse width (T on ).

4. The system of claim 3 , wherein T on is less than or equal to the pulse period (C).

5. The system of claim 2 , wherein n is a positive integer and τ a is a stroke time corresponding to an actuator, and wherein C is equal to nτ a .

6. The system of claim 5 , wherein n is equal to ten.

7. The system of claim 1 , wherein the controller comprises a position detector configured to determine a position of the valve (x i ).

8. The system of claim 7 , wherein the controller is configured to determine a pulse width (T on ) of the PWM signal, wherein the pulse width (T on ) is equal to

x

i

x

min

⁢

C

and C is a pulse period.

9. The system of claim 1 , wherein the controller comprises a position detector configured to determine a position of the valve (x i ), and

in response to a determination that the measured flow rate is not equal to the predetermined flow rate value, the controller is configured to:

set {circumflex over (x)} min equal to a minimum value of {circumflex over (x)} min and x i ;

set x min equal to {circumflex over (x)} min ; and

in response to a determination that the measured flow rate is equal to the predetermined flow rate value, the controller is configured to:

set {circumflex over (x)} min equal to a maximum value of {circumflex over (x)} min and x i ; and

set x min equal to {circumflex over (x)} min .

10. A system for monitoring and controlling flow rate of a fluid through a valve, the system comprising:

a valve configured to regulate a flow of a fluid through a conduit;

an actuator coupled to the valve and configured to drive the valve between multiple positions;

a flow rate sensor configured to measure the flow rate of the fluid through the valve; and

a controller in communication with the actuator and the flow rate sensor and configured to:

receive the measured flow rate;

determine if the measured flow rate is equal to zero;

in response to a determination that the measured flow rate is equal to zero:

determine a minimum valve position threshold (x min );

determine a minimum flow rate threshold (y min ) using x min ;

generate a pulse-width modulated (PWM) signal that switches between zero and y min ;

calculate a corrected flow rate (ŷ f ) using the PWM signal;

control a valve operation using the corrected flow rate; and

in response to a determination that the measured flow rate is greater than zero:

control the valve operation using the measured flow rate.

11. The system of claim 10 , wherein the controller is further configured to:

determine if t k <t r ≤(t k +T on ) where t k is a beginning of a pulse period, t r is a run time, and T on is a pulse width;

determine if (t k +T on )<t r ≤(t k +C) where C is a pulse period;

in response to a determination that t k <t r ≤(t k +T on ):

set the PWM signal equal to y min ; and

in response to a determination that (t k +T on )<t r ≤(t k +C):

set the PWM signal equal to zero.

12. The system of claim 11 , wherein n is a positive integer and τ a is a stroke time corresponding to the actuator, and wherein C is equal to nτ a .

13. The system of claim 10 , wherein the controller comprises a position detector configured to determine a position of the valve (x i ).

14. The system of claim 13 , wherein a pulse width (T on ) is equal to

x

i

x

min

⁢

C

and C is a pulse period.

15. The system of claim 10 , wherein, in response to a determination that the measured flow rate is not equal to 0, the controller is configured to:

set {circumflex over (x)} min equal to a minimum value of {circumflex over (x)} min and x i ;

set x min equal to {circumflex over (x)} min ; and

in response to a determination that the measured flow rate is equal to 0, the controller is configured to:

set {circumflex over (x)} min equal to a maximum value of {circumflex over (x)} min and x i ; and

set x min equal to {circumflex over (x)} min .

16. A method for monitoring and controlling flow rate of a fluid through a valve, the method comprising:

measuring the flow rate;

determining if the flow rate is equal to zero; and

in response to a determination that the flow rate is equal to zero:

determining a valve opening position (x i );

determining a minimum valve position threshold (x min );

determining a minimum flow rate threshold (y min ) corresponding to x min ;

calculating a corrected flow rate (ŷ f ) using a pulse-width modulated (PWM) signal, wherein the PWM signal is configured to switch between zero and y min ; and

controlling a valve operation using the corrected flow rate (ŷ f ).

17. The method of claim 16 further comprising:

in response to a determination that the flow rate is not equal to zero:

determining an estimated minimum valve position threshold ({circumflex over (x)} min ); and

setting {circumflex over (x)} min equal to a minimum value of {circumflex over (x)} min and x i ;

in response to a determination that the flow rate is equal to zero:

determining the estimated minimum valve position threshold ({circumflex over (x)} min ); and

setting {circumflex over (x)} min equal to a maximum value of {circumflex over (x)} min and x i ;

initializing a filtered estimate ( x min ) to {circumflex over (x)} min ;

filtering {circumflex over (x)} min using a filtering equation comprising

x

_

min

=

x

_

min

+

e

-

h

/

τ

c

⁡

(

x

_

min

-

x

^

min

)

where h is a sample rate and τ c , is a time constant;

setting {circumflex over (x)} min equal to x min ; and

setting x min equal to {circumflex over (x)} min .

18. The method of claim 16 , further comprising generating the PWM signal by:

determining if t k <t r ≤(t k +T on ) where t k is a beginning of a pulse period, t r is a run time, and T on is a pulse width;

determining if (t k +T on )<t r ≤(t k +C) where C is a pulse period;

in response to a determination that t k <t r ≤(t k +T on ):

setting the PWM signal equal to y min ; and

in response to a determination that (t k +T on )<t r ≤(t k +C):

setting the PWM signal equal to zero.

19. The method of claim 18 , wherein the pulse width (T on ) is equal to

x

i

x

min

⁢

C

.

20. The method of claim 18 , wherein n is a positive integer and τ a is a stroke time corresponding to an actuator, and wherein C is equal to nτ a .