(322e) Controller Design for Processes with Unmeasured Disturbances Changing the Steady-State Gain Sign

It is well known that no linear controller with integral action can stabilize a plant for which the sign of the steady-state gain may change sign. A nonlinear control scheme must be used, such as nonlinear model-based control or adaptive control. In this work, we focus on an instance of this problem, in which the sign of the steady-state gain may change as a result of large unmeasured external disturbances entering a process with input multiplicities. The study is motivated by a specific gaseous emissions treatment unit in a chemical plant. External disturbances include large changes in the flow rate of hydrogen feed, which itself is combusted, thus potentially changing the air-to-fuel ratio in the process from lean to rich or vice versa. The objective of this paper is to explain the idiosyncracies of the dynamic behavior of the controlled process, suggest potential control system design strategies, and demonstrate some results via computer simulations. In particular, we demonstrate that simple linear control can be effective for a wide range of operating conditions, if designed correctly. The key for linear controller design is that (a) control has to be tight enough (i.e. the controller gain should be large enough) to ensure that the process does not escape far from the desired setpoint trajectory and reversal of the steady-state gain is not realized, and (b) control must not be too tight (i.e the controller gain should not be too high) to avoid potential problems that are well understood in linear control theory (such as instability, noise amplification, or input saturation). Novel theoretical analysis based on nonlinear operator theory is used to provide controller design guidelines and suggest the anticipated closed-loop behavior. Numerical simulations using a dynamic model calibrated on plant data are used to illustrate the proposed controller design approach. Finally, future investigations are suggested for the development of nonlinear and/or adaptive controller design methods.