Abstract: A method and system for modelling industrial processes, including closed loop feedback processes. The system includes a sensor for measuring an input for the industrial process; and a processor configured to receive a measurement of the input from the sensor at an input time. The processor is also configured to implement a hybrid neural network model to output a derivative of the output at the input time, wherein the neural network model incorporates at least one neural network block and a first-principle block incorporating dynamic model having an ordinary differential equation defining the rate of change over time of the output as a function of the or each associated input; to input the derivative to an ordinary differential equation solver to predict the output at a subsequent time; and to output the prediction of the output at the subsequent time using the measured input.

Abstract: A method is described for acquiring data for relay-based controller tuning of a controller controlling a system. The method includes determining, based on controller output constraint, a relay amplitude representing an amplitude of a relay signal to be added to steady state controller output to obtain a sum signal to be fed to the system as system input during the acquiring data for relay-based controller tuning; and starting acquiring controller output data and system output data when detecting a steady state of system output while controller output is fed to the system as system input.

Abstract: A method is described for acquiring data for relay-based controller tuning of a controller controlling a system. The method includes determining, based on controller output constraint, a relay amplitude representing an amplitude of a relay signal to be added to steady state controller output to obtain a sum signal to be fed to the system as system input during the acquiring data for relay-based controller tuning; and starting acquiring controller output data and system output data when detecting a steady state of system output while controller output is fed to the system as system input.

Abstract: A method for detecting a steady-state in a process plant, the method includes: receiving a process value of the process plant, determining a recursive mean of the process value, calculating an arithmetic mean of the process value within a pre-determined window, determining a standard deviation of the process value within the pre-determined window and based on the calculated arithmetic mean, determining an upper limit and a lower limit of the process value based on the recursive mean of the process value and on the determined standard deviation, determining whether the calculated arithmetic mean is between the determined upper limit and the determined lower limit, and if the calculated arithmetic mean is between the determined upper limit and the determined lower limit, generating a first index indicating that the calculated arithmetic mean is between the determined upper limit and the determined lower limit.