Model Predictive Control Strategies for DC - DC Converters

Abstract

The application of power electronics, including dc-dc converters, is expanding over the last years. However, the control of these devices still remains a challenge that the scientific community has to face. The main objective is to regulate the output voltage to the desired value, while neglecting any input voltage and load variations. Several current and voltage control methods have been developed through the years, but, due to the nonlinear switching characteristics of the dc-dc converters, these methods have still room for improvement. A control algorithm that has been gaining popularity in the past years is model predictive control (MPC). Compared to other control methods, such as the proportional integral derivative (PID) controller with pulse width modulation (PWM), MPC has gained remarkable interest both in academia and industry over the past decades. This is true mainly because MPC can be applied in many different processes, can implement constraints and is easy to be understood, since its basic concept can be explained intuitively. The basic idea of MPC is to predict and optimize the future system behavior using the system model. In this thesis the state-space representation modelling of the MPC is used for the control of an dc-dc buck converter operating in continuous conduction mode (CCM). The formulation of the objective function for the minimization of the voltage error is simple and is achieved by minimizing the output voltage error (difference between output voltage and a reference voltage). Two different implementations of the control problem are presented: a mixed-integer quadratic optimization problem solved with enumeration technique and a quadratic optimization problem solved using the gradient and Newton’s descent methods. In addition, in order to provide offset-free tracking of the output voltage reference, a Kalman filter is used. A voltage MPC algorithm using these three methods (enumeration, gradient and Newton’s) is applied in MATLAB/SIMULINK. Variations in the input voltage, the output voltage and the load are also applied in order to examine the response of the three methods to these. The thesis is divided into two main chapters. In Chapter 1, the theoretical back- ground with regards to the uses of dc-dc converters and their control methods is given. Since MPC is an optimal control scheme, the main aspects of the mathematical optimization theory are also introduced in this chapter. Furthermore, some important classes of optimization problems, namely convex optimization problems, as well as their solving techniques are presented. In Chapter 2, the system modelling for the dc-dc buck converter is presented, the objective function is formulated and the optimization problem is simulated. The results and their comparison for the three solving techniques mentioned above are also presented in Chapter 2.