# Publications

Pulse amplitude modulation (PAM) is a widely used power control method of induction heating inverters with resonant load. In this case the inverter switching strategy can focus on the achievment of zero-voltage (ZVS) and zero-current (ZCS) switching modes of the power devices, essential conditions of the high-frequency operation. The optimal switching mode, with minimum switching losses at a given load power, depends on the resonant load topology and is achieved by means of fast phase-locked loops. The aim of this paper is the analysis of a high-frequency PAM voltage inverter, assuming operation with optimal switching defined for a serial resonant load and sinusoidal load current. Presence of lossless snubbers and transistor parasitic capacitors is taken into account and non-linearity of inverter external characteristics is being demonstrated. Describing function and a nonlinear inverter model are derived in order to confirm stability of this operation mode.

Simulation of the closed-loop, large-signal behaviour of resonant converters is a challenge due to high-frequency variation of the state variables, which makes the State Space Averaging method useless. In this paper the d-q modeling technique is proposed and applied in case of a voltage inverter with LLC resonant load. The d-q model is embedded in a closed-loop inverter model with voltage and frequency control.

The frequency-shift method is an attractive choice for power control of induction-heating inverters due to the simplicity of the power circuit. However, frequency-shift control proves to be a challenging task in case of practical resonant loads with high quality factor and uncertain circuit parameters. The paper presents a bilinear large-signal model of the induction-heating inverter with hybrid LLC resonant load. A control law is proposed, which is based on the Lyapunov stability theory. Moreover, an adaptive control method is presented to handle the uncertainty concerning the nominal values of the state variables. The theoretical results are illustrated by numerical simulation.

The paper presents an online approach to the model-predictive control of the boost type PWM rectifier. The optimization is made on a horizon of one switching period for a cost function based on the instantaneous real and imaginary power errors. The control vectors are synthesized by space-vector modulation and are confined to the hexagonal area defined by the possible switching states of the three-phase bridge. The optimal control algorithm is developed in presence of the grid current limitation, introduced as a practical constraint.

The thesis deals with the mathematical modeling and control of the induction heating converters.

Center-aligned and edge-aligned PWM control methods for a voltage-source induction heating inverter are presented. Both phase-shifted mode (PSM) and discontinuous current mode (DCM) are discussed. There are shown power control characteristics and IGBT transistor losses of the inverter with LLC resonant load. Control trajectory for transistor loss minimization is chosen. There are presented PLL and PWM control loop simulation and experimental results.

The aim of the paper is to present further investigation of intelligent control methods that allow increase of operation frequency in case of a voltage source induction heating inverter. Minimization of transistor turn-off current is obtained by means of LLC load resonance, while the two inverter legs are controlled asymmetrically, in discontinuous current mode (ADCM). Simulation and experimental results are presented.

Short-period operation of induction heating resonant inverters is a requirement often met in hardening applications. The high frequency output power has to follow a rectangular reference waveform, well-known ramping procedure for soft-start is therefore not applicable. High control loop gain is desirable in order to have fast response, but its large variation with frequency and with the quality factor of the heating inductor makes stability a delicate problem. The paper directs attention to start-up behavior of a voltage source inverter with LLC resonant load and proposes compensation of the resonance characteristics.

The paper investigates classical and novel power control methods of induction heating converters. The task is reduction of complexity. The practical solutions depend on the frequency and power range and it is emphasized, that power control method and switching strategy can’t be treated independently.

The subject of the thesis is the design and implementation of model predictive control (MPC) algorithms for power electronic converters. Taking into account the hybrid nature of the power electronic converters, the hybrid modeling is a powerful tools for describing the behavior of the system. The thesis deals with the modeling and control of three types of power electronic converters, namely the long-range model predictive control of voltage source inverters for ac drives, the long-range and one sampling period prediction horizon model predictive control of the three-phase boost rectifiers and model predictive control of a voltage source-inverter for induction heating applications.

The paper deals with constrained optimal control of three-phase voltage source converters (VSC), based on a mathematical model developed in the synchronous reference frame. The performance of the current controller determines the overall performance of the system. As a consequence, a well defined control strategy is needed, which must handle the constraints. Taking into account the limits of the d-q currents, an explicit model predictive controller was designed, moving the computation effort off-line. The resulting controller’s online computation needs are reduced. Simulation and experimental results are presented.

The paper presents a DSP-based implementation of the explicit model predictive control of a three-phase PWM boost rectifier. PWM rectifiers are inherently hybrid systems with several constraints which have to be taken into account. This is the reason why predictive control of these converters is a popular research area. Usually unity power factor, sinusoidal line currents and constant DC voltage are of main concern.

The paper presents a novel power control method of the induction-heating inverters with series resonant load. Combining the well-known advantages of the frequency-shift control with the model predictive control approach, a predictive frequency-shift control method is proposed, where the classical PI controller has been replaced with a constrained finite-time optimal (model predictive) controller. With this approach the control signal (the operating frequency in case of the frequency-shift control) optimizes the predicted cost function at the end of the current switching cycle, taking into account the constraints imposed by the frequency characteristics of the load circuit – i.e. the minimum and the maximum value of the working frequency. The prediction has been performed based on the large-signal d-q model of the inverter with series resonant load. The cost function defined for the control problem consist of the sum of the quadratic errors of the controlled variables at the end of the switching cycle. The results obtained with the new control algorithm are superior compared to the PI controller. However, the parameter variations of the model must be considered, and therefore a parameter estimator is needed.

The paper presents the large-signal model of the induction-heating inverter with series resonant load, the principle of frequency-shift control and the design of the predictive frequency-shift controller. The theoretical results are illustrated by numerical simulations.

Predictive algorithms are present in drive applications implicitly by means of well- known control structures like Direct Torque Control (DTC), Direct Self Control (DSC), etc.,or as a predictive control technique for a given control task. The paper presents briefly the existing predictive structures and focuses on two main algorithms, namely the use of explicit model predictive control in the field oriented vector control algorithm and the long-range model predictive direct torque control.

Switch-mode rectifiers are front-end converters able to solve the power quality requirements which are more and more restrictive. Usually unity power factor, sinusoidal line currents and constant DC voltage are of main concern. PWM rectifiers are inherently hybrid systems with several constraints which have to be taken into account. This is the reason why predictive control of these converters is a popular research area.

The solution to constraint optimal control problems is the modell predictive controller, where the constraints on the states, input and output variables are considered at the controller design. Limitation of computing effort is one of the main targets in order to make model predictive control of PWM rectifiers feasible. An important step in this direction has been the development of the explicit model-predictive control method. The explicit solution to the MPC problem makes this control technique applicable for systems with high dynamics, the implementation of the control law being reduced to a simple search in a table with the parameters of the optimal control law.

This paper presents the real time implementation of the explicit model predictive control algorithm on a Siemens S7 industrial programmable logic controller. The explicit solution of constrained linear MPC problems can be obtained by solving multi-parametric quadratic programs(mp-QP) where the parameters are the components of the state vector, so the real time implementation of the algorithm is possible on industrial programmable controllers, which have less memory and relative small processing capabilities. In this paper we focus on controller design and simulations with Matlab MPT Toolbox, and the real time implementation and real life tests with a second order system in order to validate the implementation procedure.

The PWM voltage source rectifier analyzed in this paper exhibits both continuous and discrete dynamic behavior and therefore represents a hybrid dynamic system. The jump condition between switching states is defined by the control space vector. Direct Power Control (DPC) is a control method tailored to such hybrid systems, and its optimization has been considered by several authors. However, the constraints are usually disregarded, leading to unrealistic results. The paper presents the constant frequency Model Predictive Direct Power Control (MP-DPC) of the PWM voltage source rectifier using two types of symmetrical switching patterns. The control algorithms are validated by Matlab Simulink modeling and simulation.