This thesis is focused on developing a framework for achieving constrained optimal control of phase-change time varying heating process taking place in an electrically heated tank/pipe. The problem of developing a heat transfer model, which captures the dynamics of heating process, is addressed by formulating differential equations using basic laws of thermodynamics and applied physics. In the control design part, adaptive control based on MPC is employed as it offers optimal control performance while enforcing constraints on inputs, outputs, and their rates of change. To capture uncertain and/or varying dynamics, data driven system identification is utilized where system parameters are estimated in real time using input-output measurement data. In order to reduce online computations, process parameters are updated only when the control performance degrades and current process parameters fail to capture time varying system dynamics. To lessen strain on resistive heating element and avoid overheating, constraints are incorporated into the optimization problem which is solved online;​ moreover, constraints softening is employed to avoid infeasibility.

This thesis also provides an optimal control strategy to control the heating process in a novel and advanced EOR technique named as In-situ reflux (ISR) proposed in [1], in which water at room temperature is injected and vaporized using resistive heating elements. Generated high temperature steam is then utilized to reduce bitumen viscosity, which is extracted out of ground through production well. However, while implementing ISR, the challenging problem faced is the burnout of equipment including thermocouples and heating elements due to uncertain and time varying dynamics leading to severely high temperature inside injection well. Data driven system identification is employed to develop and update the plant model for ISR heating process.

Simulation results illustrate the effectiveness of proposed control strategy as offset free tracking is achieved for heating element temperature inside an (1) electrically heated pipe, and (2) injection well used in ISR.