Model-based controller design for general nonlinear processes

Non-minimum-phase behavior of a process limits the degree of achievable control quality and complicates the controller design for the process. This behavior can be due to the presence of an unstable mode in the zero dynamics, a time delay, or both. To achieve greater profitability, process designers have been creating designs in regions involving complex nonlinearity where the controllers continue to face stiff challenges. Operation is often more profitable at an unstable steady state or a stable steady state close to an unstable one, sometimes involving non-minimum-phase behavior. This project aims to advance the existing non-minimum-phase control theory and to improve the operation of processes that are unstable and exhibit non-minimum-phase behavior. The research project has two main objectives: (i) the derivation of a general model-based control system and (ii) the development of a software package for modelbased controller design. Two novel nonlinear control laws that are applicable to general multivariable processes, whether non-minimum- or minimum-phase, were developed. The first control law ensures closed-loop stability by forcing all state variables to follow their corresponding linear reference trajectories. The second control law guarantees the closed-loop stability by using a Lyapunov hard constraint that requires all state variables to evolve within a shrinking state 'tube'. A prototype controller design software package was developed to simplify the implementation of differential geometric, model-based controllers. The software package carries out symbolic manipulations to automatically generate the analytical model-based controllers and subsequently test the designed controllers. It has a user-friendly interface that allows the user to enter process model equations and process parameters easily. Using the controller design software, one can design the model-based controllers with much less effort, which is expected to result in more industrial applications of the controllers.