Economic Model Predictive Control and Nonlinear Control Actuator Dynamics

Control valves are the most prevalent final control element in the chemical process industries. However, the behavior of valves (i.e., the manner in which the valve output flow rate changes in response to changes in the control signal to the valve) can contribute to a number of negative effects in a control loop, such as set-point tracking issues and sustained closed-loop oscillations. Valve stiction, for example, is a dynamic valve nonlinearity (i.e., the relationship between the valve output flow rate and the control signal to the valve is described by nonlinear differential equations) resulting from friction that is known to be problematic in the process industries. This dissertation describes the impact of valve behavior on process control loops and methods for compensating for the valve behavior through appropriate control designs. It begins by describing how the addition of input rate of change constraints to an optimization-based control design with a general objective function (economic model predictive control (EMPC)) can be performed in a manner that may reduce actuator wear while simultaneously guaranteeing feasibility of the controller and closed-loop stability of a nonlinear process operated under the control design. It then focuses on a specific type of actuator (a valve) and elucidates that coupled, nonlinear interactions between the process and valve model states and any internal states of the controller model create the negative effects that may be observed in control loops containing valves for which the dynamics cannot be neglected (e.g., valves subject to significant stiction). These multivariable interactions illustrate the closed-loop nature of the negative effects observed, and this closed-loop perspective is then used to analyze stiction compensation methods from the literature, to develop a novel stiction compensation scheme for control loops under proportional-integral control, and to demonstrate that incorporating models, both first-principles and empirical, of valve behavior within the model used for making state predictions in a model predictive controller is an effective means for compensating for valve behavior in general. The benefits of adding actuation magnitude and input rate of change constraints within EMPC including a model of stiction dynamics are discussed. Throughout the work, process examples are utilized to illustrate the advanced control-based frameworks for understanding and compensating for valve limitations