Control studies on a model evaporation process — constrained state driving with conventional and higher relative degree systems

A number of state driving strategies are investigated for a model evaporation process described by three different sets of state equations. These include optimal and model-based non-linear approaches. A structural analysis shows that with varied mathematical assumptions, the mathematical models of the evaporation process can be classified into different control classes. Conditions for steady state optimality of the systems are firstly determined by employing a standard nonlinear programming technique. Optimal control in the presence of both control and state constraints is then studied by using Pontryagin's maximum principle and a control parameterization approach for obtaining time optimal trajectories. Comprehensive comparative studies are carried out between: (1) optimal control strategies and nonlinear model based control algorithms: (2) constrained and unconstrained GMC algorithms; and (3) different modelling strategies. The development of different models in control studies is significant, due to a variety of important issues including control loop interaction, centralized and decentralized control schemes, relative degree (RD) and output controllability. These issues are investigated by employing concepts from a differential geometrical approach (DGA). Two methods to handle higher RD systems with GMC algorithms are proposed. Physical explanations for the general characteristics of the observed trajectories are presented. It is shown that the evaporator models stated in this work provide good case study examples for investigating the behaviour of control systems with an ill-conditioned decoupling matrix or a higher relative degree. The importance of appreciating optimal control issues in designing and operating evaporation processes is emphasized.