State Space Realization of Model Predictive Controllers Without Active Constraints

To enable the use of traditional tools for analysis of multivariable controllers such as model predictive control (MPC), we develop a state space formulation for the resulting controller for MPC without constraints or assuming that the constraints are not active. Such a derivation was not found in the literature. The formulation includes a state estimator. The MPC algorithm used is a receding horizon controller with infinite horizon based on a state space process model. When no constraints are active, we obtain a state feedback controller, which is modified to achieve either output tracking, or a combination of input and output tracking. When the states are not available, they need to be estimated from the measurements. It is often recommended to achieve integral action in a MPC by estimating input disturbances and include their effect in the model. We show that to obtain offset free steady state the number of estimated disturbances must equal the number of measurements. The estimator is included in the controller equation, and we obtain a formulation of the overall controller with the set-points and measurements as inputs, and the manipulated variables as outputs. One application of the state space formulation is in combination with the process model to obtain a closed loop model. This can for example be used to check the steady-state solution and see whether integral action is obtained or not

Controllability analysis for process and control system design

Controllability is the ability of a process to achieve acceptable performance, and in this thesis we use controllability analysis in the design of buffer tanks, feedforward controllers, and multivariable controllers such as model predictive control (MPC). There is still an increasing pressure on the process industry, both from competitors (prize and quality) and the society (safety and pollution), and one important contribution is a smooth and stable production. Thus, it is important to dampen the effect of uncontrolled variations (disturbances) that the process may experience. The process itself often dampens high-frequency disturbances, and feedback controllers are installed to handle the low-frequency part of the disturbances, including at steady state if integral action is applied. However, there may be an intermediate frequency range where neither of these two dampens the disturbances sufficiently. In the first part of this thesis we present methods for the design of buffer tanks based on this idea. Both mixing tanks for quality disturbances and surge tanks with “slow” level control for flow-rate variations are addressed. Neutralization is usually performed in one or several mixing tanks, and we give recommendations for tank sizes and the number of tanks. With local PI or PID control, we recommend equal tanks, and give a simple formula for the total volume. We also give recommendations for design of buffer tanks for other types of processes. We propose first to determine the required transfer function to achieve the required performance, and thereafter to find a physical realization of this transfer function. Alternatively, if measurements of the disturbances are available, one may apply feedforward control to handle the intermediate frequency range. Feedforward control is based mainly on a model, and we study the effect of model errors on the performance. We define feedforward sensitivities. For some model classes we provide rules for when the feedforward controller is effective, and we also design robust controllers such as μ -optimal feedforward controllers. Multivariable controllers, such as model predictive control (MPC), may use both feedforward and feedback control, and the differences between these two also manifest themselves in a multivariable controller. We use the class of serial processes to gain insight into how a multivariable controller works. For one specific MPC we develop a state space formulation of the controller and its state estimator under the assumption that no constraints are active. Thus, for example the gains of each channel of the MPC (from measurements to the control inputs) can be found, which gives further insight into to the controller. Both a neutralization process example and an experiment are used to illustrate the ideas.Paper 4 reprinted with kind permission of the Research Council of Norway Paper 8 reprinted with kind permission of Elsevier Publishing, http://www.sciencedirect.co

Subsea field layout optimization (part II)–the location-allocation problem of manifolds

The location-allocation problem of manifolds, which is a part of subsea field layout optimization, directly affects the flowline cost. This problem has always been studied as a mixed-integer nonlinear programming (MINLP) problem, or an integer linear programming (ILP) problem when there are location options for the facilities. Making a MINLP model is surely convenient to interpret the optimization problem. However, finding the global optimum of the MINLP model is very hard. Hence, practically, engineers use approximation algorithms to search a good local optimum or give several good location options based on their experience and knowledge to reduce the MINLP model into an ILP model. Nevertheless, the global optimum of the original MINLP model is no longer guaranteed. In this study, enlightened by the graphic theories, we propose a new method in which we reduce the MINLP model into an ILP model---more precisely, a binary linear programming (BLP) model---without compromise of achieving global optimum, but also with extremely high efficiency. The breakthrough in both efficiency and accuracy of our method for the location-allocation problem of manifolds and wellheads is well demonstrated in various cases with comparison to the published methods and the commercial MINLP solver from LINDO. Besides, we also provide our results for larger-scale problems which were considered infeasible for the commercial MINLP solver. More generally, our method can be regarded as a specific MINLP/NIP (nonlinear integer programming) solver which can be used for many other applications. This work is the second of a series of papers which systematically introduce an efficient method for subsea field layout optimization to minimize the development cost

Subsea field layout optimization (Part I) – directional well trajectory planning based on 3D Dubins Curve

Directional well trajectory planning, which includes the optimization of the drilling site location and the trajectory between the drilling site to the completion interval, plays an important role in reducing subsea field development cost. The traditional well trajectory planning methods are based on the projected 2D profile of the wellbore trajectory with empirical knowledge or trial-and-error method to select a proper drilling site. In this study, we propose a new efficient optimization method based on the 3D Dubins curve, which has been widely used in autopilot for path planning but has never been mentioned in drilling industry. In short, we use gradient descent method to find the best drilling site location while adopting the 3D Dubins curve as the optimal wellbore trajectory to reach each completion interval so that the “-site--wells” problem can be easily solved. Abundant case studies including both mathematically representative cases and the real practical field cases are conducted to demonstrate the feasibility and efficiency of our method. Wider application of our method for more complex situations are also discussed. This work is the first of a series of papers which systematically introduce an efficient method for subsea field layout optimization to minimize the development cost

Subsea field layout optimization (part III) --- the location-allocation problem of drilling sites

This study proposes an efficient method to optimize the subsea field layout with the aim of minimizing the subsea field development cost, based on the two methods introduced in Part I and Part II for solving the well trajectory planning problem and the location-allocation problem, i.e., 3D Dubins Curve method and Binary Linear Programming (BLP) method, respectively. The most complex part in subsea field layout optimization is essentially a location-allocation problem of drilling sites embedded with the well trajectory optimization. The full process of our method is clearly summarized in a flowchart. Abundant case studies with comparison to the existing results demonstrate the optimality and the flexibility of our method to solve practical subsea field layout optimization problems. In the cases studies, we also reveal how different user-defined cost items affect the optimal field layout. Details of implementing our method for a better performance is also discussed. This work is the third of a series of papers which systematically introduce an efficient method for subsea field layout optimization to minimize the development cost