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In this paper, the problem of hybrid modelling and control of a fixed frequency DC-DC converter, namely the Non-inverting Buck-Boost converter is addressed. The v-resolution method is used to capture the hybrid nature of the system. Two mixed logical dynamical (MLD) models are obtained for the converter using hybrid systems description language (HY...
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... equation is non-linear because of the multiplicative terms of state and duty cycle. In order to determine the dynamic which is in charge of state evolution, we need to define some binary variables first: Figure 5 shows the binary variables for v = 3. Based on obtained binary variables, state update equations can be written as: ...
Citations
... However, they involve solving linear matrix inequalities (LMIs), potentially adding computational complexity. Addressing hybrid modeling and control for fixed-frequency converters like non-inverting buck-boost converters, model predictive control (MPC) solutions were derived, 12 approximating nonlinear terms with piecewise affine approximations, potentially introducing modeling inaccuracies. ...
This paper presents a comprehensive stability analysis of the boundary‐based hybrid control (BBHC) algorithm designed for boost converter. The stability assessment is carried out utilizing multiple Lyapunov functions, addressing both continuous conduction mode (CCM) and discontinuous conduction mode (DCM) operation. The boost converter is modeled as a hybrid automaton to capture its dynamic behavior accurately. Through rigorous Lyapunov stability analysis, this study demonstrates the effectiveness of the BBHC algorithm in ensuring stable operation of the boost converter across various operating modes. Additionally, the proposed control algorithm's validation is conducted using the FPGA‐in‐the‐loop (FIL) technique, highlighting its efficiency and robustness in real‐world applications. This research contributes valuable insights into the design and implementation of stable control strategies for boost converter, emphasizing the practical utility of the BBHC algorithm with FIL for enhanced performance and reliability in power electronics systems.
... Studies and presentations of control techniques for DC-DC converters in the form of SDS and hybrid systems have been focal points for researchers. Mirzaei and Afzalian [12] designed an explicit model predictive controller using current-mode control to regulate the inductor current of a buck-boost converter based on a set of non-linear equations. However, this model required complex and computationally intensive controller design. ...
This paper presents a control scheme for DC-DC buck converters operating in Continuous Conduction Mode (CCM) that achieves fast and accurate regulation of the output voltage while reducing the computational burden on the control system. The study investigates the boundary-based control scheme for a buck converter and models the converter circuit as a Switched Dynamical System (SDS) using hybrid automaton due to its continuous and discrete states. The boundaries of these states are determined to enable the implementation of a fixed-frequency Pulse-Width Modulation (PWM) control scheme. The proposed control scheme was evaluated through simulation with variations in input voltage, load, and reference voltage. It was further analyzed for model mismatch due to parametric variations and parasitic parameters, which demonstrated its effectiveness and robustness under various operating conditions. The SDS approach for controlling the buck converter is simple, requires minimal mathematical calculations, and is free from modeling errors. The output voltage was stable under regulatory and servo problems, as well as sinusoidal input testing. The proposed scheme was compared with other conventional schemes and found superior in terms of steady-state and dynamic response. Additionally, integral compensation was introduced to counter parasitic parameters, which was found to be effective.
... In the last decades, owing to the maturity of hybrid system theory, more and more researchers have used this theory to overcome the problem of model inaccuracy and control limitations previously discussed. The hybrid automaton model was proposed as a natural representation of the power electronic system. it allows describing such a system using the exact model [26,27,28] which depends on the interaction between the continuous dynamics, represented by the differential equation, and the discrete events (ON, OFF) defined by finite-state machines. The use of this modeling technique makes it possible to create an approximation of the system much closer to reality than with other traditional methods. ...
... Except for this change, the rest of the system characteristics are similar as previously under the inductive nonlinear load. The obtained results are illustrated by Figs (24)(25)(26). It is seen that the control performance deterioration remains very limited despite the 50% parameter variation. ...
This paper addresses the problem of controlling a single phase shunt active power filter (SAPF) in presence of nonlinear loads. The considered SAPF is based on a Dual Buck Half Bridge converter (DBHB), which has the ability to eliminate the shoot-through problem arising in the conventional inverter circuit. The aim is to design a controller that is able to achieve the following three control objectives: (i) simple and indirect estimation of harmonic components, (ii) compensating for the harmonic and reactive currents generated by the nonlinear load for assuring a satisfactory power factor correction (PFC) in the grid side, (iii) regulating the DC capacitor voltage of the DBHB converter. In order to meet these control objectives, a new controller based on multi-loop structure is proposed. In the inner loop, a hybrid automaton representation of the DBHB-SAPF is used for the purpose of designing an appropriate control law so that to ensure a unity power factor. In the outer loop, a fuzzy logic controller is developed to guarantee a tight regulation of the converter DC voltage to a desired value. The effectiveness of the proposed controller is verified and validated by numerical simulation using MATLAB/Simulink environment. From the obtained results, the designed controller shows significant performance in terms of robustness and tracking compared to the standard strategy based on PI regulator.
... Another general overview on these devices can be found in [31], even though, more oriented on the dual-active-bridge isolated bidirectional DC-DC converter. One of these approaches is to describe the converter by means of a hybrid system model (see, e.g., [32]). Through this, a highly accurate model can be achieved in which the switching frequency directly indicates the sample time for the solver. ...
DC-DC converters are widely used in a large number of power conversion applications. As in many other systems, they are designed to automatically prevent dangerous failures or control them when they arise; this is called functional safety. Therefore, random hardware failures such as sensor faults have to be detected and handled properly. This proper handling means achieving or maintaining a safe state according to ISO 26262. However, to achieve or maintain a safe state, a fault has to be detected first. Sensor faults within DC-DC converters are generally detected with hardware-redundant sensors, despite all their drawbacks. Within this article, this redundancy is addressed using observer-based techniques utilizing Extended Kalman Filters (EKFs). Moreover, the paper proposes a fault detection and isolation scheme to guarantee functional safety. For this, a cross-EKF structure is implemented to work in cross-parallel to the real sensors and to replace the sensors in case of a fault. This ensures the continuity of the service in case of sensor faults. This idea is based on the concept of the virtual sensor which replaces the sensor in case of fault. Moreover, the concept of the virtual sensor is broader. In fact, if a system is observable, the observer offers a better performance than the sensor. In this context, this paper gives a contribution in this area. The effectiveness of this approach is tested with measurements on a buck converter prototype.
... Dynamical hybrid systems represent a multidisciplinary area which has been developed over the past decade and extend between the limits of computer science, control theory and mathematics. A hybrid system is capable of representing 1 3 complex physical systems with discrete and continuous subsystems that interact with each other [1][2][3][4][5]. Switching circuits in power electronics dedicated to energy conversion are considered as a good example of dynamical hybrid systems, because they are intrinsically hybrid in their nature indeed, power switching devices have discrete inputs, continuous outputs and disturbances that are either continuous, such as parametric variation in a load, or discrete, as in a fault state of a particular switch [6][7][8]. ...
In this paper, a robust loop-shaping control of three-cell inverter is proposed. The hybrid nature of this inverter, represented by the presence of continuous and discrete dynamics, is taken into account in the modeling and control design parts. Firstly, the instantaneous inverter model is derived and the control problem is formulated as a two cascaded current/voltages loops. Then, the hybrid model of the inverter is discussed in details. The continuous dynamics for each mode is developed and the underlying output voltage level is determined. Secondly, the adjacency constraint for the transition between hybrid modes is studied and a new algebraic condition is proposed in order to fulfill this constraint. Furthermore, a hybrid automata defining all possible transitions respecting the adjacency rule is given. Thirdly, the controller synthesis of the current loop is transformed to a robust control problem, and then it is designed offline using loop-shaping method in order to ensure robust stabilization of the load current in the presence of load parametric variations and measurement errors. Fourthly, a new hybrid algorithm is proposed in order to ensure balancing distribution of the flying capacitors voltages. In this algorithm, the states of the inverter are directly controlled through a predefined selection table. The advantages of this hybrid control are the reduction in the execution time by adopting parallel processing and intrinsic robustness properties. Asymptotic stability of the underlying tracking errors is proven using Lyapunov theory. Finally, a virtual experimental setup based on PowerSim software is performed in order to emulate the realistic behavior of the nonlinear inverter elementary elements. The obtained results show that the designed controller meets its objective.
... Hence, abrupt changes on that flow, like the operation of a common switch in hybrid systems, cannot be directly represented without modifications to the method. Systems are defined as hybrid, when they contain both continuous states as well as discrete phenomena (Mirzaei and Afzalian, 2009). Throughout the years, several methods have been suggested and reviewed for representing hybrid systems using bond graphs. ...
In this paper, bond graphs are employed to develop a novel
mathematical model of conventional switched-mode DC-DC converters valid
for both continuous and discontinuous conduction modes. A unique causality
bond graph model of hybrid models is suggested with the operation of the
switch and the diode to be represented by a modulated transformer with a
binary input and a resistor with fixed conductance causality. The operation of
the diode is controlled using an if-then function within the model. The
extracted hybrid model is implemented on a boost and buck converter with
their operations to change from CCM to DCM and to return to CCM. The
vector fields of the models show validity in a wide operational area and
comparison with the simulation of the converters using PSPICE reveals high
accuracy of the proposed model, with the normalised root means square error
and the maximum absolute error remaining adequately low. The model is also
experimentally tested on a buck topology.
In this paper, we proposed a new configuration for a quadruple tanks process which can be modelled as an autonomously switched hybrid system. Then, a hybrid model predictive controller is designed for this plant that guarantees Lyapunov stability and inherent robustness.
Current mode control (CMC) though offers improved line regulation, phase margin and high bandwidth suffers from high output impedance. Although load regulation can be improved by incorporating an integral gain, it reduces the phase margin and increases the overshoot. The objective of this paper is to achieve improved output impedance without using an integral controller. Incorporating a high pass filter in series with the current sensor in CMC, the closed loop DC gain of a CCM buck converter is shown to be almost independent of the load resistance, thus improving load regulation using a proportional controller only. Improved features of CMC are also retained. Following VMC modeling approach, we develop a method to obtain the small signal model of the proposed scheme, and extended to CMC with an accurate low frequency characterisation. The proposed scheme is implemented on a buck converter, and the theoretical results are validated by experiments.
