Mass flow controller utilizing nonlinearity component functions

1. A method for controlling a mass flow controller, the method comprising:

providing a gas through a thermal mass flow sensor of the mass flow controller;

processing a sensor signal from the thermal mass flow sensor of the mass flow controller to produce a flow signal;

determining a total nonlinearity characteristic function based on nonlinearity effects on the flow signal, wherein the total nonlinearity characteristic function includes, at least, a sensor nonlinearity component function, based on a sensor nonlinearity, and a bypass nonlinearity component function, based on a bypass nonlinearity;

calibrating the total nonlinearity characteristic function;

adjusting the sensor nonlinearity component function responsive to changes in the sensor nonlinearity;

updating the total nonlinearity characteristic function after adjusting the sensor nonlinearity component function;

correcting the flow signal to produce a corrected flow signal using the total nonlinearity characteristic function; and

controlling a valve of the mass flow controller using the corrected flow signal and a setpoint signal.

2. The method of claim 1 , comprising adjusting the bypass nonlinearity component function, independently of the sensor nonlinearity component function, responsive to changes in the bypass nonlinearity, and the updating the total nonlinearity characteristic function includes updating the total nonlinearity characteristic function after adjusting the bypass nonlinearity component function.

3. The method of claim 1 , wherein the adjusting the total nonlinearity characteristic function includes adjusting, dynamically over time, the sensor nonlinearity component function responsive to time-dependent changes in the sensor nonlinearity so that the sensor nonlinearity component function is a sensor time-dependent nonlinearity component function.

4. The method of claim 3 , wherein:

the determining the total nonlinearity characteristic function includes:

determining the sensor nonlinearity component function;

determining the bypass nonlinearity component function; and

the adjusting includes adjusting, dynamically over time, the sensor nonlinearity component function responsive to a flow rate transition of the gas.

5. The method of claim 1 , wherein the determining the total nonlinearity characteristic function includes determining the total nonlinearity characteristic function, F(f)=K*f*C 1 (f)*C 2 (f), where K is a constant, f is a current flow rate of the gas, C 1 (f) is the sensor nonlinearity component function, and C 2 (f) is the bypass nonlinearity component function.

6. The method of claim 3 , wherein:

the adjusting includes:

adjusting, dynamically over time, the bypass nonlinearity component function responsive to time-dependent changes in the bypass nonlinearity so that the bypass nonlinearity component function is a bypass time-dependent nonlinearity component function;

calculating each time-dependent nonlinearity component function, C D (f,t)=C(f2)+[C(f1)−C(f2)]*exp(−t/T), where f1 is an initial flow rate of the gas, f2 is a final flow rate of the gas, C is a nonlinearity component function, t is time, and T is a time constant; and

the updating the total nonlinearity characteristic function includes:

updating the total nonlinearity characteristic function after adjusting the bypass nonlinearity component function; and

calculating the total nonlinearity characteristic function, F(f,t)=K*f*C 1 (f,t)*C 2 (f,t), where f is a flow rate, t is time, K is a constant, C 1 (f,t) is the sensor time-dependent nonlinearity component function, and C 2 (f,t) is the bypass time-dependent nonlinearity component function.

7. A mass flow controller comprising:

a main flow path for a gas;

a control valve to control a flow rate of the gas through the main flow path;

a thermal mass flow sensor coupled to the main flow path to provide a sensor signal indicative of a mass flow rate of the gas;

means for processing the sensor signal from the thermal mass flow sensor of the mass flow controller to produce a flow signal;

means for determining a total nonlinearity characteristic function based on nonlinearity effects on the flow signal, wherein the total nonlinearity characteristic function includes, at least, a sensor nonlinearity component function, based on a sensor nonlinearity, and a bypass nonlinearity component function, based on a bypass nonlinearity;

means for calibrating the total nonlinearity characteristic function;

means for adjusting the sensor nonlinearity component function responsive to changes in the sensor nonlinearity;

means for updating the total nonlinearity characteristic function after adjusting the sensor nonlinearity component function;

means for correcting the flow signal to produce a corrected flow signal using the total nonlinearity characteristic function; and

a control component coupled to the means for correcting and the control valve to control a position of the control valve based upon the corrected flow signal and a setpoint signal.

8. The mass flow controller of claim 7 , wherein the means for adjusting includes means for adjusting the bypass nonlinearity component function, independently of the sensor nonlinearity component function, responsive to changes in the bypass nonlinearity, and the means for updating includes means for updating the total nonlinearity characteristic function after adjusting the bypass nonlinearity component.

9. The mass flow controller of claim 7 , wherein the means for adjusting includes means for adjusting, dynamically over time, the sensor nonlinearity component function responsive to time-dependent changes in the sensor nonlinearity so that the sensor nonlinearity component function is a sensor time-dependent nonlinearity component function.

10. The mass flow controller of claim 9 , wherein:

the means for determining includes:

means for determining the sensor nonlinearity component function;

means for determining the bypass nonlinearity component function; and

the means for adjusting includes means for adjusting, dynamically over time, the sensor nonlinearity component function responsive to a flow rate transition of the gas.

11. The mass flow controller of claim 7 , wherein the means for determining includes means for determining the total nonlinearity characteristic function, F(f)=K*f*C 1 (f)*C 2 (f), where K is a constant, f is a current flow rate of the gas, C 1 (f) is the sensor nonlinearity component function, and C 2 (f) is the bypass nonlinearity component function.

12. The mass flow controller of claim 9 , wherein:

the means for adjusting includes:

means for adjusting, dynamically over time, the bypass nonlinearity component function responsive to time-dependent changes in the bypass nonlinearity so that the bypass nonlinearity component function is a bypass time-dependent nonlinearity component function;

means for calculating each time-dependent nonlinearity component function, C D (f,t)=C(f2)+[C(f1)−C(f2)]*exp(−t/T), where f1 is an initial flow rate of the gas, f2 is a final flow rate of the gas, C is a nonlinearity component function, t is time, and T is a time constant; and

the means for updating includes:

means for updating the total nonlinearity characteristic function after adjusting the bypass nonlinearity component function; and

means for calculating the total nonlinearity characteristic function, F(f,t)=K*f*C 1 (f,t)*C 2 (f,t), where f is a flow rate, t is time, K is a constant, C 1 (f,t) is the sensor time-dependent nonlinearity component function, and C 2 (f,t) is the bypass time-dependent nonlinearity component function.

13. A mass flow controller comprising:

a main flow path for a gas;

a control valve to control a flow rate of the gas though the main flow path;

a thermal mass flow sensor coupled to the main flow path to provide a sensor signal indicative of a mass flow rate of the gas;

a processing portion to receive and process the sensor signal from the thermal mass flow sensor to produce a flow signal; and

a nonlinear compensator including a non-transitory, tangible processor readable storage medium, encoded with processor executable instructions to produce a corrected flow signal, the processor executable instructions comprising instructions to:

determine a total nonlinearity characteristic function based on nonlinearity effects on the flow signal, wherein the total nonlinearity characteristic function includes, at least, a sensor nonlinearity component function, based on a sensor nonlinearity, and a bypass nonlinearity component function, based on a bypass nonlinearity;

calibrate the total nonlinearity characteristic function;

adjust the sensor nonlinearity component function responsive to changes in the sensor nonlinearity;

update the total nonlinearity characteristic function after adjusting the sensor nonlinearity component function;

correct the flow signal to produce the corrected flow signal using the total nonlinearity characteristic function; and

a control component coupled to the nonlinear compensator and the control valve to control a position of the control valve based upon the corrected flow signal and a setpoint signal.

14. The mass flow controller of claim 13 , wherein the instructions to adjust include instructions to adjust the bypass nonlinearity component function, independently of the sensor nonlinearity component function, responsive to changes in the bypass nonlinearity, and the instructions to update include instructions to update the total nonlinearity characteristic function after adjusting the bypass nonlinearity component.

15. The mass flow controller of claim 13 , wherein the instructions to adjust include instructions to adjust, dynamically over time, the sensor nonlinearity component function responsive to time-dependent changes in the sensor nonlinearity so that the sensor nonlinearity component function is a sensor time-dependent nonlinearity component function.

16. The mass flow controller of claim 15 , wherein:

the instructions to determine include instructions to:

determine the sensor nonlinearity component function;

determine the bypass nonlinearity component function; and

the instructions to adjust include instructions to adjust, dynamically over time, the sensor nonlinearity component function responsive to a flow rate transition of the gas.

17. The mass flow controller of claim 13 , wherein the instructions to determine include instructions to determine the total nonlinearity characteristic function, F(f)=K*f*C 1 (f)*C 2 (f), where K is a constant, f is a current flow rate of the gas, C 1 (f) is the sensor nonlinearity component function, and C 2 (f) is the bypass nonlinearity component function.

18. The mass flow controller of claim 15 , wherein:

the instructions to adjust include instructions to:

adjust, dynamically over time, the bypass nonlinearity component function responsive to time-dependent changes in the bypass nonlinearity so that the bypass nonlinearity component function is a bypass time-dependent nonlinearity component function;

calculate each time-dependent nonlinearity component function, C D (f,t)=C(f2)+[C(f1)−C(f2)]*exp(−t/T), where f1 is an initial flow rate of the gas, f2 is a final flow rate of the gas, C is a nonlinearity component function, t is time, and T is a time constant; and the instructions to update include instructions to:

update the total nonlinearity characteristic function after adjusting the bypass nonlinearity component function; and

calculate the total nonlinearity characteristic function, F(f,t)=K*f*C 1 (f,t)*C 2 (f,t), where f is a flow rate, t is time, K is a constant, C 1 (f,t) is the sensor time-dependent nonlinearity component function, and C 2 (f,t) is the bypass time-dependent nonlinearity component function.