Abstract: A control system is configured to operate a plant to achieve an optimal value for a performance variable of the plant. The system comprise a feedforward controller configured to receive a measurable disturbance to the plant and generate a feedforward contribution to a control input to the plant using the measurable disturbance. The system also comprises an extremum-seeking controller configured to receive the performance variable from the plant and generate an extremum-seeking contribution to the control input to drive the performance variable to the optimal value. The system further comprises a control input element configured to generate the control input by combining the extremum-seeking contribution and the feedforward contribution and provide the control input to the plant.

Abstract: A controller includes a communications interface configured to provide a control input to and receive feedback from a plant. The feedback is representative of a response of the plant to the control input over a response period. The controller further includes a time constant estimator. The time constant estimator calculates a normalized variable based on the feedback, each value of the normalized variable representative of the response of the plant at a different time during the response period. The time constant estimator calculates a plurality of time constant estimates, based on the plurality of values of the normalized variable. The time constant estimator determines a maximum time constant from the time constant estimates. The controller further includes a control input generator that generates the control input for the plant using the maximum time constant. The control input affects a variable state or condition of the plant.

Abstract: A HVAC system for a building includes a plant and a plurality of single-variable extremum-seeking controllers (ESCs). The plant includes HVAC equipment operable to affect an environmental condition in the building. Each of the single-variable ESCs is configured to perturb a different manipulated variable with a different excitation signal and provide the manipulated variables as perturbed inputs to the plant. The plant uses multiple perturbed inputs to concurrently affect a performance variable. The single-variable ESCs are configured to estimate a gradient of the performance variable with respect to the each manipulated variable and independently drive the gradients toward zero by independently modulating the manipulated variables.

Abstract: An extremum-seeking control system for a chilled water plant includes a feedback controller and an extremum-seeking controller. The feedback controller is configured to operate equipment of the chilled water plant to achieve a condenser water temperature setpoint. The equipment include at least one of a chiller compressor, a condenser water pump, and a cooling tower fan. The extremum-seeking controller is configured to provide the condenser water temperature setpoint to the feedback controller.

Abstract: A thermostat is disclosed. The thermostat can include one or more temperature sensors configured to measure one or more temperature values. The thermostat can include a processing circuit. The processing circuit can receive the one or more temperature values from the one or more temperature sensors. The processing circuit can receive one or more central processing unit (CPU) usage values, wherein the one or more CPU usage values indicate computing usage of the processing circuit. The processing circuit can determine, based on an empirical model comprising one or more gain values and one or more filters and based on one or more signals, a temperature of the building. The one or more signals comprise the one or more temperature values and the one or more CPU usage values. The empirical model accounts for dynamics of heat generated by the processing circuit and airflow acting on the thermostat.

Abstract: Disclosed is a system to control a climate of a space via a first control loop and a second control loop interacting with the first control loop. The system includes a first controller of the first control loop to generate a first control signal based on a first modified set point and a first feedback signal. The system further includes a second controller of the second control loop to generate a second control signal based on a second modified set point and a second feedback signal. The system further includes a decoupler configured to predict a first effect of the first control signal on the second control loop and a second effect of the second control signal on the first control loop, and generate the first modified set point and the second modified set point to reduce the first effect and the second effect.

Abstract: A self-configuring extremum-seeking controller includes a dither signal generator, a communications interface, a phase delay estimator, and a bandwidth estimator. The dither signal generator identifies a stored dither frequency, generates a dither signal having the stored dither frequency, and uses the dither signal to perturb a control input for a plant. The communications interface provides the perturbed control input to the plant and receives an output signal from the plant resulting from the perturbed control input. The phase delay estimator estimates a phase delay between the output signal and the dither signal. The bandwidth estimator estimates a bandwidth of the plant based on the estimated phase delay. The dither signal generator updates the stored dither frequency based on the estimated bandwidth.

Abstract: Disclosed is a system to control a climate of a space via a first control loop and a second control loop interacting with the first control loop. The system includes a first controller of the first control loop to generate a first control signal based on a first modified set point and a first feedback signal. The system further includes a second controller of the second control loop to generate a second control signal based on a second modified set point and a second feedback signal. The system further includes a decoupler configured to predict a first effect of the first control signal on the second control loop and a second effect of the second control signal on the first control loop, and generate the first modified set point and the second modified set point to reduce the first effect and the second effect.

Abstract: A self-configuring extremum-seeking controller includes a dither signal generator, a communications interface, a phase delay estimator, and a bandwidth estimator. The dither signal generator identifies a stored dither frequency, generates a dither signal having the stored dither frequency, and uses the dither signal to perturb a control input for a plant. The communications interface provides the perturbed control input to the plant and receives an output signal from the plant resulting from the perturbed control input. The phase delay estimator estimates a phase delay between the output signal and the dither signal. The bandwidth estimator estimates a bandwidth of the plant based on the estimated phase delay. The dither signal generator updates the stored dither frequency based on the estimated bandwidth.

Abstract: A cooperative extremum-seeking control system includes a first controller and a second controller. The first controller is configured to provide a first control input to a first plant and receive a first performance variable as feedback from the first plant. The second controller is configured to provide a second control input to a second plant that interacts with the first plant, receive a second performance variable as feedback from the second plant, and provide the second performance variable to the first controller. The first controller is further configured to aggregate the first performance variable and the second performance variable to determine a total performance variable, calculate a gradient of the total performance variable with respect to the first control input, generate a third control input using the gradient of the total performance variable, and provide the third control input to the first plant.

Abstract: Disclosed is a system to control a climate of a space via a first control loop and a second control loop interacting with the first control loop. The system includes a first controller of the first control loop to generate a first control signal based on a first modified set point and a first feedback signal. The system further includes a second controller of the second control loop to generate a second control signal based on a second modified set point and a second feedback signal. The system further includes a decoupler configured to predict a first effect of the first control signal on the second control loop and a second effect of the second control signal on the first control loop, and generate the first modified set point and the second modified set point to reduce the first effect and the second effect.

Abstract: An extremum-seeking control system includes a plant operable to affect a variable state or condition of a building and an extremum-seeking controller. The extremum-seeking controller is configured to provide a control input to a plant and receive a performance variable as a first feedback from the plant. The plant uses the control input to affect the performance variable. The extremum-seeking controller is configured to receive a constrained variable as a second feedback from the plant and calculate a performance penalty by applying a penalty function to the constrained variable. The extremum-seeking controller is further configured to modify the performance variable with the performance penalty to generate a modified cost function, estimate a gradient of the modified cost function with respect to the control input, and drive the gradient of the modified cost function toward zero by modulating the control input.

Abstract: A control system is configured to operate a multiple-input system to achieve an optimal value for a performance variable of the multiple-input system. The control system includes a mapper configured to generate a mapping from a first number of manipulated variables to a second number of latent variables. The second number is smaller than the first number and each of the latent variables includes a linear combination of the manipulated variables. The control system also includes an extremum-seeking controller configured to receive the performance variable from the multiple-input system as a feedback and modulate values of the second number of latent variables to drive the performance variable to the optimal value. The mapper is further configured to use the mapping to translate modulated values of the second number of latent variables to modulated values of the first number of manipulated variables and provide the modulated values of the first number of manipulated variables to the multiple-input system.

Abstract: A control system is configured to operate a plant to achieve an optimal value for a performance variable of the plant. The system comprise a feedforward controller configured to receive a measurable disturbance to the plant and generate a feedforward contribution to a control input to the plant using the measurable disturbance. The system also comprises an extremum-seeking controller configured to receive the performance variable from the plant and generate an extremum-seeking contribution to the control input to drive the performance variable to the optimal value. The system further comprises a control input element configured to generate the control input by combining the extremum-seeking contribution and the feedforward contribution and provide the control input to the plant.

Abstract: A controller includes a communications interface configured to provide a control input to and receive feedback from a plant. The feedback is representative of a response of the plant to the control input over a response period. The controller further includes a time constant estimator. The time constant estimator calculates a normalized variable based on the feedback, each value of the normalized variable representative of the response of the plant at a different time during the response period. The time constant estimator calculates a plurality of time constant estimates, based on the plurality of values of the normalized variable. The time constant estimator determines a maximum time constant from the time constant estimates. The controller further includes a control input generator that generates the control input for the plant using the maximum time constant. The control input affects a variable state or condition of the plant.

Abstract: A method for controlling an economizer in a building HVAC system includes providing a manipulated variable as an input to a control process, holding the manipulated variable at a first extremum during a first portion of an evaluation period, and applying a dither signal to the manipulated variable during a second portion of the evaluation period. The dither signal causes the manipulated variable to deviate from the extremum. The method further includes monitoring a variable of interest output by the control process during the first and second portions of the evaluation period and switching the manipulated variable to a second extremum opposite the first extremum in response to the variable of interest moving toward an optimal value during the second portion of the evaluation period.

Abstract: A HVAC system for a building includes a plant and a plurality of single-variable extremum-seeking controllers (ESCs). The plant includes HVAC equipment operable to affect an environmental condition in the building. Each of the single-variable ESCs is configured to perturb a different manipulated variable with a different excitation signal and provide the manipulated variables as perturbed inputs to the plant. The plant uses multiple perturbed inputs to concurrently affect a performance variable. The single-variable ESCs are configured to estimate a gradient of the performance variable with respect to the each manipulated variable and independently drive the gradients toward zero by independently modulating the manipulated variables.

Abstract: An extremum-seeking control system for a chilled water plant includes a feedback controller and an extremum-seeking controller. The feedback controller is configured to operate equipment of the chilled water plant to achieve a condenser water temperature setpoint. The equipment include at least one of a chiller compressor, a condenser water pump, and a cooling tower fan. The extremum-seeking controller is configured to provide the condenser water temperature setpoint to the feedback controller.

Abstract: Systems and methods for estimating a time to cool down or warm up a building zone from a temperature setback condition are provided. A described method includes determining, by a controller for the building zone, at least one of a cooling demand for the building zone and a heating demand for the building zone for a time period corresponding to the temperature setback condition. The method further includes estimating a return time using at least one of the cooling demand and the heating demand. The return time is the time to cool down or warm up the building zone from the temperature setback condition.

Abstract: A self-configuring extremum-seeking controller includes a dither signal generator, a communications interface, a phase delay estimator, and a bandwidth estimator. The dither signal generator identifies a stored dither frequency, generates a dither signal having the stored dither frequency, and uses the dither signal to perturb a control input for a plant. The communications interface provides the perturbed control input to the plant and receives an output signal from the plant resulting from the perturbed control input. The phase delay estimator estimates a phase delay between the output signal and the dither signal. The bandwidth estimator estimates a bandwidth of the plant based on the estimated phase delay. The dither signal generator updates the stored dither frequency based on the estimated bandwidth.