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: A controller for HVAC equipment of a plant includes a processing circuit configured to predict an impact of a time delay of the plant on a performance variable received as feedback from the plant. The processing circuit is configured to artificially increase or decrease a value of the performance variable using an adjustable time delay parameter to at least partially negate the impact of the time delay on the performance variable. The processing circuit is configured to use the artificially increased or decreased value of the performance variable in on-off feedback control to operate the HVAC equipment.

Abstract: A self-optimizing controller for equipment of a plant provides a manipulated variable as an input to the plant and receives an output variable as feedback. The controller generates a performance variable model defining the performance variable as a function of the manipulated variable and an output variable model defining the output variable as a function of the manipulated variable. The controller uses the performance variable model to determine a gradient of the performance variable, uses the output variable model to determine a gradient of the output variable, and generates a self-optimizing variable based on the gradient of the performance variable model and the gradient of the output variable model. The controller operates the equipment of the plant to affect a variable state or condition of the building based on the value of the self-optimizing variable from the self-optimizing variable model.

Abstract: A variable refrigerant flow (VRF) system for a building includes a plurality of outdoor VRF units configured to heat or cool a refrigerant for use in heating or cooling the building and an extremum-seeking controller. The extremum-seeking controller is configured to determine a total power consumption of the plurality of outdoor VRF units, generate a pressure setpoint for the plurality of outdoor VRF units using an extremum-seeking control technique that drives the total power consumption toward an extremum, and use the pressure setpoint to operate the plurality of outdoor VRF units.

Abstract: A method for controlling flow in a heating, ventilation, and air conditioning (HVAC) system that imposes an upper limit on the flow of fluid through a heating or cooling coil. Imposing this limit on the flow rate ensures that a temperature change across the coil remains above a minimum threshold and can significantly reduce energy waste. The method includes receiving a first temperature measurement associated with an inlet of the coil, receiving a second temperature measurement associated with an outlet of the coil, and receiving a flow measurement associated with the valve, applying the first temperature measurement, the second temperature measurement, and the flow measurement as input to a model, determining a maximum flow rate that ensures that a difference between the first temperature measurement and the second temperature measurement is above a threshold using the model, and operating the valve in accordance with the maximum flow rate.

Abstract: An extremum-seeking control system for a plant includes a feedback controller for operating the plant to achieve a value of a manipulated variable, and an extremum-seeking controller. The extremum-seeking controller is configured to provide the value of the manipulated variable to the feedback controller and to determine a value for the manipulated variable. The extremum-seeking controller determines the value for the manipulated variable by perturbing the manipulated variable with an excitation signal and monitoring a performance variable of the plant resulting from the perturbed manipulated variable, estimating a normalized correlation coefficient relating the performance variable to the manipulated variable, and modulating the manipulated variable to drive the normalized correlation coefficient toward zero using a general set of tuning parameters. The general set of tuning parameters are adapted for use with the normalized correlation coefficient, independent of a scale of the performance variable.

Abstract: Systems and methods for monitoring and controlling a plant using extremum-seeking control. The method includes perturbing a setpoint for a controller by applying a dither signal to the setpoint. The controller uses a perturbed setpoint to generate one or more control inputs for the building equipment. Receiving, from the building equipment, an output signal and obtaining values of a performance variable based on the output signal, the values of the performance variable resulting from operating the building equipment based on the perturbed setpoint. The method includes determining a gradient of the performance variable with respect to the perturbed setpoint and a Hessian of the performance variable affected by the building equipment with respect to the setpoint. The method includes determining an adjustment to the setpoint predicted to drive the performance variable to an extremum based on the gradient and the Hessian of the performance variable.

Abstract: Systems and methods for monitoring and controlling a plant using extremum-seeking control. The method includes perturbing a setpoint for a controller by applying a dither signal to the setpoint. The controller uses a perturbed setpoint to generate one or more control inputs for the building equipment. Receiving, from the building equipment, an output signal and obtaining values of a performance variable based on the output signal, the values of the performance variable resulting from operating the building equipment based on the perturbed setpoint. The method includes determining a gradient of the performance variable with respect to the perturbed setpoint and a Hessian of the performance variable affected by the building equipment with respect to the setpoint. The method includes determining an adjustment to the setpoint predicted to drive the performance variable to an extremum based on the gradient and the Hessian of the performance variable.

Abstract: A self-configuring controller includes one or more processors and one or more non-transitory machine readable media storing instructions. When executed by the one or more processors, the instructions cause the one or more processors to receive an output signal from a controlled system or device representative of an operation of the controlled system or device in response to a first perturbed control input perturbed using a first dither signal, estimate a bandwidth of the controlled system or device based on the output signal and the first dither signal, perturb a second control input using a second dither signal based on the bandwidth of the controlled system or device to generate a second perturbed control input, and transmit the second perturbed control input to the controlled system or device.

Abstract: A building management system includes building equipment configured to operate in accordance with an input to alter a variable state or condition of a building, a feedback controller configured to generate the input as a function of a measured state of the building equipment, and an analytics circuit. The analytics circuit is configured to obtain and store a dataset comprising the measured state and the input for a plurality of time steps, determine, based on at least a portion of the dataset, a self-optimizing control function that defines a self-optimizing control variable as a function of the measured state, calculate a value of the self-optimizing control variable using the self-optimizing control function and the measured state, monitor the value of the self-optimizing control variable over time, and generate an indication of performance of the building equipment relative to optimal performance based on the value of the self-optimizing control variable.

Abstract: A self-optimizing controller for equipment of a plant provides a manipulated variable as an input to the plant and receives an output variable as feedback. The controller generates a performance variable model defining the performance variable as a function of the manipulated variable and an output variable model defining the output variable as a function of the manipulated variable. The controller uses the performance variable model to determine a gradient of the performance variable, uses the output variable model to determine a gradient of the output variable, and generates a self-optimizing variable based on the gradient of the performance variable model and the gradient of the output variable model. The controller operates the equipment of the plant to affect a variable state or condition of the building based on the value of the self-optimizing variable from the self-optimizing variable model.

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: An on-off control system includes on-off equipment configured to operate in either an on state or an off state, an on-off controller configured to cause the equipment to transition between the on state and the off state based on a setpoint value and a deadband value to drive a control variable toward the setpoint value, and a deadband controller, according to some embodiments. In some embodiments, the deadband controller is configured to generate the deadband value used by the on-off controller. In some embodiments, the deadband controller is configured to generate the deadband value by obtaining a cost function that defines a cost based on at least a set of control values and the deadband value and selecting the deadband value that results in an optimal value of the cost function over a range of possible deadband values, the selected deadband value defining an optimal deadband value.

Abstract: A method for performing extremum-seeking control of a plant includes determining multiple values of a correlation coefficient that relates a control input provided as an input to the plant to a performance variable that characterizes a performance of the plant in response to the control input. The performance variable includes a noise-free portion and an amount of noise. The method includes determining an adjusted correlation coefficient by scaling a first value of the correlation coefficient selected from the multiple values relative to a second value of the correlation coefficient selected from the multiple values. The adjusted correlation coefficient relates the noise-free portion of the performance variable to the control input. The method includes using the adjusted correlation coefficient to modulate the control input provided as an input to the plant.

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 building management system includes building equipment configured to operate in accordance with an input to alter a variable state or condition of a building as a process function of the input while incurring a cost of operating the equipment as a cost function of the input. The building management system also includes a controller configured to calculate a value of a self-optimizing control variable as a function of a measured state of the building equipment and drive the value of the self-optimizing control variable towards a setpoint value by generating the input based on the self-optimizing control variable and providing the input to the building equipment. The function comprises multiplying the measured state by a matrix and adding an offset vector. Values of elements of the matrix and the offset vector are determined using a non-optimal reference.

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 space controller and method for determining energy savings of the space controller are provided. The method includes estimating, by one or more processing circuits, a steady state gain of a controlled variable of a heating, ventilation, and air conditioning (HVAC) system; determining, by the one or more processing circuits, an actual runtime that HVAC equipment of the HVAC system is in an on state based on a first setpoint or schedule; predicting, by the one or more processing circuits, a reduction of runtime that the HVAC equipment is in the on state for a second setpoint or schedule based on the actual runtime and the steady state gain; and adjusting, by the one or more processing circuits, the first setpoint or schedule to the second setpoint or schedule based on the reduction of runtime.

Abstract: A variable refrigerant flow (VRF) system for a building includes a plurality of outdoor VRF units configured to heat or cool a refrigerant for use in heating or cooling the building and an extremum-seeking controller. The extremum-seeking controller is configured to determine a total power consumption of the plurality of outdoor VRF units, generate a pressure setpoint for the plurality of outdoor VRF units using an extremum-seeking control technique that drives the total power consumption toward an extremum, and use the pressure setpoint to operate the plurality of outdoor VRF units.

Abstract: An extremum-seeking control system for a plant includes a feedback controller for operating the plant to achieve a value of a manipulated variable, and an extremum-seeking controller. The extremum-seeking controller is configured to provide the value of the manipulated variable to the feedback controller and to determine a value for the manipulated variable. The extremum-seeking controller determines the value for the manipulated variable by perturbing the manipulated variable with an excitation signal and monitoring a performance variable of the plant resulting from the perturbed manipulated variable, estimating a normalized correlation coefficient relating the performance variable to the manipulated variable, and modulating the manipulated variable to drive the normalized correlation coefficient toward zero using a general set of tuning parameters. The general set of tuning parameters are adapted for use with the normalized correlation coefficient, independent of a scale of the performance variable.