Feedback control system with normalized performance indices for setpoint alarming

1. A feedback control system comprising:

a plant comprising:

building equipment operable to affect a variable state or condition within a building; and

one or more measurement devices operable to measure a process variable indicating a value of the variable state or condition within the building and generate a feedback signal comprising the process variable;

a feedback controller that monitors the process variable provided via the feedback signal from the plant and uses an error signal representing a difference between the process variable and a setpoint to generate a control signal for the plant, wherein the plant uses the control signal to affect the process variable by operating the building equipment;

an exponentially-weighted moving average (EWMA) calculator that generates EWMA values based on the error signal as new values of the process variable are received;

a normalized index generator that uses the EWMA values to calculate a normalized performance index;

a threshold generator that uses predetermined values for a first alarm parameter κ and a second alarm parameter η to generate a threshold without requiring knowledge of any variables or parameters that are specific to the feedback control system, the first alarm parameter κ representing a ratio of a magnitude of a persistent setpoint error to a standard deviation of the error signal, the second alarm parameter η representing a ratio of a duration for which the setpoint error has persisted to a time constant of the EWMA values; and

an alarm manager that compares the normalized performance index to the threshold and generates an alarm in response to the normalized performance index dropping below the threshold.

2. The feedback control system of claim 1 , wherein the threshold is control loop agnostic and does not depend on any variables or parameters that are specific to the feedback control system.

3. The feedback control system of claim 1 , wherein the threshold represents an expected value of the normalized performance index when a setpoint error of a predetermined magnitude has persisted for a predetermined duration.

4. The feedback control system of claim 3 , wherein:

the predetermined magnitude is specified as a multiple of a standard deviation of the error signal without requiring knowledge of the standard deviation; and

the predetermined duration is specified as a multiple of a time constant of the EWMA values without requiring knowledge of the time constant.

5. The feedback control system of claim 1 , further comprising an expected value estimator that estimates a value of the normalized performance index expected to occur when a setpoint error of a predetermined magnitude has persisted for a predetermined duration;

wherein the threshold is based on the expected value of the normalized performance index.

6. The feedback control system of claim 1 , further comprising an error calculator that receives the process variable from the plant and compares the process variable with a setpoint to generate the error signal.

7. A method for using a normalized performance index for setpoint alarming in a feedback control system, the method comprising:

operating building equipment of a plant to affect a variable state or condition within a building;

operating one or more measurement devices of the plant to measure a process variable indicating a value of the variable state or condition within the building and generate a feedback signal comprising the process variable;

monitoring the process variable provided via the feedback signal from the plant;

using an error signal representing a difference between the process variable and a setpoint to generate a control signal for the plant, wherein the plant uses the control signal to affect the process variable by operating the building equipment;

generating exponentially-weighted moving average (EWMA) values based on the error signal as new values of the process variable are received;

calculating a normalized performance index based on the EWMA values;

using predetermined values for a first alarm parameter κ and a second alarm parameter η to generate a threshold without requiring knowledge of any variables or parameters that are specific to the feedback control system, the first alarm parameter κ representing a ratio of a magnitude of a persistent setpoint error to a standard deviation of the error signal, the second alarm parameter η representing a ratio of a duration for which the setpoint error has persisted to a time constant of the EWMA values;

comparing the normalized performance index to the threshold; and

generating an alarm in response to the normalized performance index dropping below the threshold.

8. The method of claim 7 , wherein the threshold is control loop agnostic and does not depend on any variables or parameters that are specific to the feedback control system.

9. The method of claim 7 , wherein the threshold represents an expected value of the normalized performance index when a setpoint error of a predetermined magnitude has persisted for a predetermined duration.

10. The method of claim 9 , wherein:

the predetermined magnitude is specified as a multiple of a standard deviation of the error signal without requiring knowledge of the standard deviation; and

the predetermined duration is specified as a multiple of a time constant of the EWMA values without requiring knowledge of the time constant.

11. The method of claim 7 , further comprising:

estimating a value of the normalized performance index expected to occur when a setpoint error of a predetermined magnitude has persisted for a predetermined duration; and

generating the threshold based on the expected value of the normalized performance index.

12. The method of claim 7 , further comprising:

receiving the process variable from the plant; and

comparing the process variable with a setpoint to generate the error signal.

13. A setpoint alarming system comprising:

a plant comprising:

building equipment operable to affect a variable state or condition within a building; and

one or more measurement devices operable to measure a process variable indicating a value of the variable state or condition within the building and generate a feedback signal comprising the process variable;

a feedback controller that monitors the process variable provided via the feedback signal from the plant and uses an error signal representing a difference between the process variable and a setpoint to generate a control signal for the plant, wherein the plant uses the control signal to affect the process variable by operating the building equipment;

a normalized index generator that uses the error signal to generate a normalized performance index for the plant;

an expected value estimator that estimates an expected value of the normalized performance index expected to occur when a setpoint error of a predetermined magnitude has persisted for a predetermined duration, wherein the expected value of the normalized performance index is a function of:

a first alarm parameter κ representing a ratio of a magnitude of a persistent setpoint error to a standard deviation of the error signal; and

a second alarm parameter η representing a ratio of a duration for which the setpoint error has persisted to a time constant of the error signal; and

an alarm manager that compares the normalized performance index to the expected value and generates an alarm in response to the normalized performance index dropping below the expected value.

14. The setpoint alarming system of claim 13 , wherein the expected value of the normalized performance index is control loop agnostic and does not depend on any variables or parameters that are specific to the plant.

15. The setpoint alarming system of claim 13 , wherein:

the predetermined magnitude is specified as a multiple of a standard deviation of the error signal without requiring knowledge of the standard deviation; and

the predetermined duration is specified as a multiple of a time constant of the error signal without requiring knowledge of the time constant.