Model-Based Ambient Temperature Estimation for Control of an HVAC System

Abstract

A method is provided for controlling an HVAC system. The method includes obtaining observations of a measured temperature by at least one temperature sensor, and accessing a lumped-element model of the at least one temperature sensor in which a change in the measured temperature is expressed as a function of one or more independent variables including the measured temperature, and unknown parameter(s) including an ambient temperature of the conditioned space. A regression analysis of the lumped-element model is performed using observations of the one or more independent variables including the observations of the measured temperature, and estimates of the unknown parameter(s), to determine updated estimates of the unknown parameter(s) including an updated estimate of the ambient temperature. A value of the ambient temperature is determined from the updated estimate of the ambient temperature, and HVAC equipment is controlled using the value of the ambient temperature.

1 . A heating, ventilation, and air conditioning (HVAC) system comprising:
 HVAC equipment configured to provide conditioned air to a conditioned space;   a temperature sensor for the conditioned space; and   control circuitry operably coupled to the HVAC equipment and the temperature sensor, the control circuitry configured to:
 obtain observations of a measured temperature by the temperature sensor; 
 access a lumped-element model of the temperature sensor where a change in the measured temperature is expressed as a function of an independent variables comprising:
 the measured temperature; and 
 an unknown parameters including an ambient temperature of the conditioned space; 
 
 perform a regression analysis of the lumped-element model using observations of the independent variables comprising:
 the observations of the measured temperature; and 
 an estimates of the one or more unknown parameters; 
 
 determine an updated estimates of the unknown parameters including an updated estimate of the ambient temperature based on the performed regression analysis; 
 determine a value of the ambient temperature from the updated estimate of the ambient temperature; and 
 control the HVAC equipment based, at least in part, on the value of the ambient temperature. 
   
     
     
         2 . The HVAC system of  claim 1 , wherein the control circuitry configured to perform the regression analysis includes the control circuitry configured to:
 apply an observation of the measured temperature and the estimates of the unknown parameters to the lumped-element model to determine a predicted change in the measured temperature;   determine an observed change in the measured temperature from the observations of the measured temperature;   determine an error between the predicted change and the observed change in the measured temperature; and   perform the regression analysis to update the estimates of the unknown parameter to the updated estimates of the unknown parameter that cause the predicted change in the measured temperature to be closer to the observed change in the measured temperature, and thereby reduce the error.   
     
     
         3 . The HVAC system of  claim 1 , wherein the temperature sensor includes a conditioned air temperature sensor for the conditioned space, the independent variables include the measured temperature from the conditioned air temperature sensor, and the unknown parameter further include a thermal parameter of the conditioned air temperature sensor. 
     
     
         4 . The HVAC system of  claim 1 , wherein the HVAC equipment is operably coupleable with a return air duct, the temperature sensor includes a return air temperature sensor for return air from the return air duct, the independent variables include the measured temperature from the return air temperature sensor, and the unknown parameters further include a temperature around the return air duct and thermal parameter of the return air temperature sensor. 
     
     
         5 . The HVAC system of  claim 1 , wherein the HVAC equipment is operably coupleable with a return air duct, the temperature sensor includes a conditioned air temperature sensor for the conditioned space, and a return air temperature sensor for return air from the return air duct,
 wherein the control circuitry configured to access the lumped-element model includes the control circuitry configured to access lumped-element models of the conditioned air temperature sensor and the return air temperature sensor,   wherein the control circuitry configured to perform the regression analysis includes the control circuitry configured to perform regression analyses of the lumped-element models to determine respective updated estimates of the ambient temperature, and   wherein the control circuitry is configured to determine the value of the ambient temperature from the respective updated estimates of the ambient temperature.   
     
     
         6 . The HVAC system of  claim 1 , wherein the control circuitry is further configured to:
 obtain observations of the ambient temperature from the lumped-element model of the temperature sensor;   access a lumped-element model of the conditioned space in which a change in the ambient temperature is expressed as a function of one or more respective independent variables including the ambient temperature, an outdoor temperature, and an output capacity of the HVAC system, and respective one or more unknown parameters including thermal parameters of the conditioned space;   perform a regression analysis of the lumped-element model of the conditioned space using observations of the respective independent variables including the observations of the ambient temperature, and an estimate of the respective unknown parameters, to determine updated estimates of the respective unknown parameter; and   apply the observations of the respective independent variables and the updated estimates of the respective unknown parameter to the lumped-element model of the conditioned space to determine a second updated estimate of the ambient temperature, and   wherein the control circuitry is configured to determine the value of the ambient temperature from the updated estimate of the ambient temperature and the second updated estimate of the ambient temperature.   
     
     
         7 . The HVAC system of  claim 6 , wherein the control circuitry configured to perform the regression analysis of the lumped-element model of the conditioned space includes the control circuitry configured to:
 apply observations of the respective independent variables and the estimates of the respective unknown parameter\ to the lumped-element model of the conditioned space to determine a predicted change in the ambient temperature;   determine an observed change in the ambient temperature from the observations of the ambient temperature;   determine an error between the predicted change and the observed change in the ambient temperature; and   perform the regression analysis to update the estimate of the unknown parameter to the updated estimate of unknown parameter that causes the predicted change in the ambient temperature to be closer to the observed change in the ambient temperature, and thereby reduce the error.   
     
     
         8 . The HVAC system of  claim 1 , wherein the HVAC system further comprises a humidity sensor, and the control circuitry is further configured to:
 obtain an observation of measured dew point by the humidity sensor and the temperature sensor;   access a relative humidity model in which dew point is expressed as function of respective an unknown parameter that includes the ambient temperature and a relative humidity fraction; and   perform a regression analysis of the relative humidity model using the observation of the measured dew point and the estimate of the respective unknown parameter to determine an updated estimate of the respective unknown parameter including a second updated estimate of the ambient temperature, and   wherein the control circuitry is configured to determine the value of the ambient temperature from the updated estimate of the ambient temperature and the second updated estimate of the ambient temperature.   
     
     
         9 . The HVAC system of  claim 8 , wherein the control circuitry configured to perform the regression analysis of the relative humidity model includes the control circuitry configured to:
 apply the estimate of the respective unknown parameter to the relative humidity model to determine a predicted dew point;   determine an error between the predicted dew point and the observation of the measured dew point; and   perform the regression analysis to update the estimate of the respective unknown parameter to the updated estimate of the respective unknown parameter that cause the predicted dew point to be closer to the observation of the measured dew point, and thereby reduce the error.   
     
     
         10 . The HVAC system of  claim 1 , wherein there is a plurality of temperature sensors that include a conditioned air temperature sensor for the conditioned space and a return air temperature sensor for return air from a return air duct, and the HVAC system further comprises a humidity sensor,
 wherein the control circuitry configured to access the lumped-element model includes the control circuitry configured to access lumped-element models of the conditioned air temperature sensor, the return air temperature sensor and the conditioned space, and further includes the control circuitry configured to access a relative humidity model,   wherein the control circuitry configured to perform the regression analysis includes the control circuitry configured to perform regression analyses of the lumped-element models and the relative humidity model using observations of respective independent variables including measured temperature from the conditioned air temperature sensor and the return air temperature sensor, an output capacity of the HVAC system, and measured dew point from the humidity sensor and the conditioned air temperature sensor, the regression analyses performed to determine respective updated estimates of the ambient temperature, and   wherein the control circuitry is configured to determine the value of the ambient temperature from the respective updated estimates of the ambient temperature.   
     
     
         11 . A method of controlling a heating, ventilation, and air conditioning (HVAC) system that includes HVAC equipment configured to provide conditioned air to a conditioned space, and that includes at least one temperature sensor for the conditioned space, the method comprising:
 obtaining observations of a measured temperature by the at least one temperature sensor;   accessing a lumped-element model of the at least one temperature sensor in which a change in the measured temperature is expressed as a function of an independent variable comprising:
 the measured temperature; and 
 an unknown parameter including an ambient temperature of the conditioned space; 
   performing a regression analysis of the lumped-element model using an observation of the independent variable comprising:
 the observation of the measured temperature; and 
 estimates of the unknown parameter; 
   determine updated estimates of the unknown parameter including an updated estimate of the ambient temperature based on the performed regression analysis;   determining a value of the ambient temperature from the updated estimate of the ambient temperature; and   controlling the HVAC equipment based, at least in part, on the value of the ambient temperature.   
     
     
         12 . The method of  claim 11 , wherein performing the regression analysis comprises:
 applying an observation of the measured temperature and the estimate of the unknown parameter to the lumped-element model to determine a predicted change in the measured temperature;   determining an observed change in the measured temperature from the observation of the measured temperature;   determining an error between the predicted change and the observed change in the measured temperature; and   performing the regression analysis to update the estimates of the unknown parameter to the updated estimates of the unknown parameter that cause the predicted change in the measured temperature to be closer to the observed change in the measured temperature, and thereby reduce the error.   
     
     
         13 . The method of  claim 11 , wherein the temperature sensor includes a conditioned air temperature sensor for the conditioned space, the independent variables include the measured temperature from the conditioned air temperature sensor, and the unknown parameter further includes a thermal parameter of the conditioned air temperature sensor. 
     
     
         14 . The method of  claim 11 , wherein the HVAC system further includes a return air duct, the temperature sensor includes a return air temperature sensor for return air from the return air duct, the independent variable include the measured temperature from the return air temperature sensor, and the unknown parameter further include a temperature around the return air duct and a thermal parameter of the return air temperature sensor. 
     
     
         15 . The method of  claim 11 , wherein the HVAC system further includes a return air duct, and the temperature sensor includes a conditioned air temperature sensor for the conditioned space and a return air temperature sensor for return air from the return air duct,
 wherein accessing the lumped-element model includes accessing lumped-element models of the conditioned air temperature sensor and the return air temperature sensor,   wherein performing the regression analysis includes performing a regression analysis of the lumped-element models to determine a respective updated estimate of the ambient temperature, and   wherein the value of the ambient temperature is determined from the respective updated estimate of the ambient temperature.   
     
     
         16 . The method of  claim 11  further comprising:
 obtaining observations of the ambient temperature from the lumped-element model of the temperature sensor; 
 accessing a lumped-element model of the conditioned space in which a change in the ambient temperature is expressed as a function of respective independent variables including the ambient temperature, an outdoor temperature, and an output capacity of the HVAC system, and respective one or more unknown parameters including thermal parameters of the conditioned space; 
 performing a regression analysis of the lumped-element model of the conditioned space using an observation of the respective independent variables including the observation of the ambient temperature and estimates of the respective one or more unknown parameters to determine updated estimates of the respective unknown parameter; and 
 applying the observation of the respective independent variable and the updated estimate of the respective unknown parameter to the lumped-element model of the conditioned space to determine a second updated estimate of the ambient temperature, and 
 wherein the value of the ambient temperature is determined from the updated estimate of the ambient temperature and the second updated estimate of the ambient temperature. 
 
     
     
         17 . The method of  claim 16 , wherein performing the regression analysis of the lumped-element model of the conditioned space comprises:
 applying an observation of the respective independent variable and the estimate of the respective an unknown parameter to the lumped-element model of the conditioned space to determine a predicted change in the ambient temperature;   determining an observed change in the ambient temperature from the observation of the ambient temperature;   determining an error between the predicted change and the observed change in the ambient temperature; and   performing the regression analysis to update the estimates of the unknown parameter to the updated estimate of the unknown parameters that cause the predicted change in the ambient temperature to be closer to the observed change in the ambient temperature, and thereby reduce the error.   
     
     
         18 . The method of  claim 11 , wherein the HVAC system further includes a humidity sensor, and the method further comprises:
 obtaining an observation of measured dew point by the humidity sensor and the temperature sensor;   accessing a relative humidity model in which dew point is expressed as function of respective an unknown parameter including the ambient temperature and a relative humidity fraction; and   performing a regression analysis of the relative humidity model using the observation of the measured dew point and an estimate of the respective unknown parameter to determine an updated estimate of the respective unknown parameter including a second updated estimate of the ambient temperature, and   wherein the value of the ambient temperature is determined from the updated estimate of the ambient temperature and the second updated estimate of the ambient temperature.   
     
     
         19 . The method of  claim 18 , wherein performing the regression analysis of the relative humidity model comprises:
 applying the estimate of the respective unknown parameters to the relative humidity model to determine a predicted dew point;   determining an error between the predicted dew point and the observation of the measured dew point; and   performing the regression analysis to update the estimates of the respective unknown parameter to the updated estimates of the respective unknown parameter that cause the predicted dew point to be closer to the observation of the measured dew point, and thereby reduce the error.   
     
     
         20 . The method of  claim 11 , wherein there is a plurality of temperature sensors includes a conditioned air temperature sensor for the conditioned space, and a return air temperature sensor for return air from a return air duct, and the HVAC system further includes a humidity sensor,
 wherein accessing the lumped-element model includes accessing lumped-element models of the conditioned air temperature sensor, the return air temperature sensor and the conditioned space, and further includes accessing a relative humidity model,   wherein performing the regression analysis includes performing regression analyses of the lumped-element models and the relative humidity model using observations of respective independent variables including measured temperature from the conditioned air temperature sensor and the return air temperature sensor, an output capacity of the HVAC system, and measured dew point from the humidity sensor and the conditioned air temperature sensor, the regression analyses performed to determine respective updated estimates of the ambient temperature, and   wherein the value of the ambient temperature is determined from the respective updated estimates of the ambient temperature.