Control Design for Backstepping and Adaptive Backstepping Controllers in MPD
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In the field of oil drilling there is a concept known as Managed Pressure Drilling. In Managed Pressure Drilling one relies on pumps in combination with chokes (valves) in order to maintain a certain pressure at the bottom of the well. It is crucial to maintain this pressure since too low pressure may cause the well to collapse and too high pressure may cause the well to fracture, making it more susceptible for a collapse. The pressure at the bottom of the well is mainly controlled by a choke. In this thesis controllers based on backstepping theory will be developed in order to control the choke pressure. The controllers will be designed such that the choke pressure will track a reference value and the controllers will achieve this by adjusting the choke's angular velocity. It is also common that certain parameters in the well are unknown due to changes that occur in the fluid running through the choke. Because of this, adaptive integrator backstepping controllers will also be developed. The goal for this project is to obtain an understanding of how well controllers based on integrator backstepping and adaptive integrator backstepping can solve this task. Integrator backstepping controllers are useful when designing controllers for systems on cascade form of order 2 or higher, however, the complexity of these controllers increases significantly as the order of the system increases. Because of this, two different design models have been used in this thesis in order to develop controllers based on integrator backstepping. One is of 2nd order and the other is of 3rd order. The 2nd order design model describes how the pressure changes according to the flow in and out of the choke. The flow out of the choke depends on the choke opening and the choke opening changes based on the angular velocity of the choke. The 3rd order design model is an extension of the 2nd order design model. The 3rd order model also describes the actuator dynamics in the choke which will provide a better representation on how the angular velocity affects the choke position. A controller was first developed for the 2nd order system. If the controller behaved well, a new controller would be developed for the 3rd order system. In order to verify the performance of the controllers, they were simulated in common scenarios that occur during drilling. Controllers that performed well during these simulations went through further testing by performing simulations with Straume, a high-end multiphase well simulator. Straume provides a better representation of a real life drilling scenario and serves as a benchmark for the controllers validation. In addition to the common scenarios, the simulations in Straume also cover how wrong parameterization of the often unknown parameters affects the controllers performance. A regular integrator backstepping controller was developed for the 2nd order system. This controller performed well during the simulation and thus a controller for the 3rd order system was developed. The 3rd order controller also performed well during simulations. The adaptive controller developed for the 2nd order system performed badly during simulations and a 3rd order adaptive controller was not developed. The regular integrator backstepping controllers went through further testing by simulating them with Straume. Both controllers performed well, but both experienced a constant offset between the reference value and the choke pressure. The controllers also experienced a drop in performance when the parametrization of the bulk modulus did not match the bulk modulus in Straume. These controllers performed well enough for them to be used further as long as one is aware of their shortcomings.