1
Introduction

1.1 General Remarks

Power electronics converters are widely utilized in almost every aspect of todays' modernized world including computers, smart home systems, electric vehicles (EVs), trains, marine, aircrafts, microgrids, robots, renewable energy conversion and integration, and many industrial applications. The main function of a power converter is to convert the electrical power from one form to the other [1]. In general, there are four different categories of power converters: DC-DC, AC-DC, DC-AC, and AC-AC. In each category, various converter topologies have been developed to meet the desired conversion and application objectives. For instance, when the photovoltaic (PV) energy is to be converted and injected into the grid, a DC-DC boost converter is connected between the PV panel and DC-AC inverter to ensure a constant inverter input voltage and to possibly track the panel's maximum power point. The necessity of DC-DC boost converter in such application arises due to the buck operation of the inverter (i.e. DC input voltage is greater than the amplitude of its AC voltage). On the other hand, an AC-DC converter (usually referred to as rectifier) is used in an electric vehicle (EV) charging system to convert the grid's AC voltage to DC such that the battery can be charged. Another example is the use of series active filter (usually referred to as dynamic voltage restorer) in the protection of sensitive loads (i.e. medical equipment in the hospitals, data centers, and so on) against voltage sags, and voltage swells in the grid voltage. When such voltage variations occur in the grid, the series active filter, which is built using a DC-AC inverter, generates and injects the required compensation voltage to the point of common coupling such that the sensitive load voltage is always kept at the desired value. Similar examples can be given for the other converter categories.

Thus, considering the importance of today's energy demand and the need for clean and reliable resources, the use of power electronics has increased tremendously. As such, the performance of the power converters used in these applications has gained utmost importance. In most of the power electronics-related applications, closed-loop control is essential to keep the voltage or current at reference values under various conditions, which include load changes, grid voltage deterioration (voltage sags, voltage swells, and distorted grid voltages), and parameter variations, which occur because of aging and operating conditions. More importantly, the stability of closed-loop system should not be jeopardized under these situations. For this reason, the design of a closed-loop system that responds to these challenges is an essential and difficult task. First of all, it should be noted that the design of closed-loop control for power electronics converters requires a deep knowledge in many areas such as circuit analysis, advanced mathematics, modeling, control systems, and power electronics. In this regard, this chapter starts with the introduction of simplest closed-loop control for power converters. Then, mathematical modeling, basic control objectives, and performance evaluation are explained briefly. Hence, the reader is urged to refresh or gain further basic information in the areas of control theory and power electronics converters from the literature.

This book is primarily concerned with advanced nonlinear control of power converters. A closed-loop control is referred to as nonlinear control if it contains at least one nonlinear component. Nonlinear control of power converters received attention of many researchers in the last two decades. The main reason of this popularity comes from the advantages over linear control methods, which lack guaranteed stability in large operation range of the converters; facing hard nonlinearities (saturation, dead-zone, backlash, and hysteresis), which cannot be approximated linearly; and having model uncertainties, which are assumed to be known when designing the linear controller. Whereas the nonlinear control is able to cope with the problems mentioned above. In this book, sliding mode control, Lyapunov function-based control, and model predictive control methodologies are explained for power converters. Although these nonlinear control methods are not new, their application in power converter control was limited in the past due to the required extensive computations. Since last decade, the advent of fast implementation platforms such as digital signal processors and field programmable gate arrays (FPGAs) relieved the computation burden issue. Therefore, compiling the design and application of the nonlinear control methods mentioned above in a single book is very beneficial for the interested readers.

1.2 Basic Closed-Loop Control for Power Converters

A basic single input single output (SISO) closed-loop power converter control system is illustrated in Figure 1.1. Here, the main aim is to control the power converter in order to accomplish specific desired control objectives (see Section 1.4). Clearly, the output signal (i.e. voltage or current) is measured and compared with the reference one to produce an error signal. This error signal is applied to the controller. Then, the controller generates modulation signal from which the pulse width modulation (PWM) signals are generated. These signals are applied to the gates of switching devices (i.e. insulated gate bipolar transistors [IGBTs], metal oxide semiconductor field effect transistors [MOSFETs], etc.) in the power converter. Upon the application of PWM signals, the switching devices are turned on and off. The value of voltage (or current) in the converter is changed by these switching actions. If the controller is well designed, the error signal is continually reduced until the output signal tracks the reference signal in the steady state. On the other hand, the number of loops in a control system may be more than one depending on the converter topology and the application area.

Figure 1.1 Basic closed-loop power converter control system. (a) With modulation, (b) without modulation.

Numerous control approaches have been developed for the power converters. Each control approach has its own advantages and disadvantages concerning with the controller complexity and cost, dynamic response, steady-state error, robustness to parameter variations, and closed-loop stability. It is worth to mention that the discussion in this book is based on the introduction, design and application of sliding mode control, Lyapunov function-based control, and model predictive control methods used in various power converters. While the sliding mode control and Lyapunov function-based control methods require a modulation block as shown in Figure 1.1a, the finite control set model predictive control (FCS-MPC) method does not require a modulation as shown in Figure 1.1b. The design of sliding mode control, Lyapunov function-based control, and model predictive control are explained in Chapters 3, 4, and 5, respectively. The following sections intend to present background information regarding the steps that should be taken into consideration when designing a controller. Even though these steps are well known in the modern control systems area, the readers, who are not fully familiar with these, will gain a knowledge before learning each of these control methods.

1.3 Mathematical Modeling of Power Converters

Usually, an accurate mathematical model of the converter is necessary when there is a need to design its controller. As it will be discussed in Chapter 3, the sliding mode control does not require mathematical modeling of the converter. Whereas the Lyapunov function-based control and model predictive control approaches rely on the mathematical model of the power converter as will be explained in Chapters 4 and 5, respectively. However, a perfect mathematical model, which represents all dynamics of the converter, is not possible in practice due to the certain noises (i.e. measurement noise) and possible failure conditions. There are two types of mathematical models in the continuous time: linear models and nonlinear models. The behavior of a linear converter system is usually described by linear differential equations written in the state-space form as follows:

where x represents the state vector, u represents the input vector, y represents the output vector, and A, B, C, and D represent the matrices with appropriate dimension. Such models are suitable to be used with the root-locus method, state-space method, and frequency domain design methods such as Bode plot and Nyquist method. As will be discussed in Chapter 4, the Lyapunov function-based control method uses the linear converter system model in (1.1). On the other hand, the model predictive control method (see Chapters 5 and 9) uses discrete-time version of the continuous-time model in (1.1) as given below:

where Ad, Bd, Cd, and Dd are discretized matrices of A, B, C, and D, respectively. The sampling instants are represented by k and k?+?1. It is worth to mention...