Calculation of steady-state gains for multivariable systems from closed-loop steady-state data

Knowledge of steady-state process gains is required at various stages of control design or implementation. Traditionally, open-loop tests have been used to determine steady-state process gains for multivariable systems. The practical difficulty associated with this approach is that large, complex industrial units take a long time to reach a new steady-state in the open-loop operation. Hence, during the test process outputs drift and the calculation of steady-state gains is very difficult. In addition, the process produces off-spec product. Recently, advanced identification methods (e.g. dynamic matrix identification software, DMI) allow us to identify the dynamic model, including the steady-state gain. Even though DMI software represents a significant advancement in dynamic model identification, the modelling is greatly simplified if a user knows the steady-state gain prior to identifying the dynamic model. This work describes a method to determine steady-state gains from closed-loop data. The method permits calculation of steady-state gains with respect to manipulated and load variables (all system inputs). Process output variables (controlled variables) can be changed from one set of steady-state values to another set of values by changing their setpoints. The existing control system (good or bad) eventually leads the process to a new steady-state. A set of these changes provides sufficient information to calculate open-loop steady-state process gains. Industrial units frequently operate at several distinct states, corresponding to different target product qualities. These distinct operating states (‘modes of operation’) are an excellent basis to apply the proposed methodology. The method has been extended to allow the calculation of steady-state load gains based on data collected under closed-loop conditions. Thus the technique allows the analyst to compute the effect that one or more load variables would have on controlled variables, even though the latter are held constant at their operating targets during the entire test.