Nonlinear Analysis of Hysteretic Modulation-Based Sliding Mode Controlled Quadratic Buck–Boost Converter

2018 ◽  
Vol 28 (02) ◽  
pp. 1950025 ◽  
Author(s):  
Muppala Kumar Kavitha ◽  
Anbukumar Kavitha
Keyword(s):  
Hopf Bifurcation ◽  
Phase Portrait ◽  
Sliding Mode ◽  
Stability Boundary ◽  
Low Frequency ◽  
Nonlinear Behavior ◽  
Input Voltage ◽  
Boost Converter ◽  
Complex Conjugate ◽  
The Stability

In this paper, the dynamics of hysteresis current-controlled quadratic buck-boost converter is investigated in detail. The system model is derived based on the sliding mode approach and also in its dimensionless form for algebraic brevity. The stability of the system is disclosed with the aid of the movement of eigenvalues. Onset of Hopf bifurcation is identified when the complex conjugate eigenvalue pair crosses the imaginary axis of the complex plane. The stability boundary is drawn to benefit the power electronics engineer for a stable and reliable design. The computer simulation of the switched model is performed using MATLAB/Simulink software to uncover the sequential occurrence of nonlinear behavior exhibited due to Hopf bifurcation for variation in control parameters and the input voltage. The phase portrait disclosing the subtle periodicity is plotted at different operating points to elicit that the stable period-1 attractor bifurcates to the quasi-periodic orbit and finally to a limit cycle. The precise dynamic of the phase portrait is also captured using the Poincare section. Experimental outputs are presented for confirming the low-frequency bifurcation scenario witnessed in the simulated and analytical results.

scholarly journals Tracking Nonlinear Oscillations with Time-Delayed Feedback

2006 ◽  
Vol 5-6 ◽  
pp. 417-424
Author(s):  
Jan Sieber ◽  
B. Krauskopf
Keyword(s):  
Dynamical System ◽  
Hopf Bifurcation ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Oscillations ◽  
Stability Boundary ◽  
Nonlinear Dynamical ◽  
Friction Oscillator ◽  
Long Time ◽  
Basic Ideas ◽  
The Stability

We demonstrate a method for tracking the onset of oscillations (Hopf bifurcation) in nonlinear dynamical systems. Our method does not require a mathematical model of the dynamical system but instead relies on feedback controllability. This makes the approach potentially applicable in an experiment. The main advantage of our method is that it allows one to vary parameters directly along the stability boundary. In other words, there is no need to observe the transient oscillations of the dynamical system for a long time to determine their decay or growth. Moreover, the procedure automatically tracks the change of the critical frequency along the boundary and is able to continue the Hopf bifurcation curve into parameter regions where other modes are unstable.We illustrate the basic ideas with a numerical realization of the classical autonomous dry friction oscillator.

Continuous-Time PDC-LMI Fuzzy Applied to 3SSC Boost Converter

2020 ◽  
Author(s):  
Jozias R. L. Neto ◽  
Luis Carvalho ◽  
Jefferson C. Rezende ◽  
Marcus V. S. Costa ◽  
Elenilson De Vargas Fortes
Keyword(s):  
Continuous Time ◽  
Output Voltage ◽  
Input Voltage ◽  
Boost Converter ◽  
Linear Matrix ◽  
External Disturbances ◽  
State Switching ◽  
Integral Action ◽  
Design Characteristics ◽  
The Stability

The application of DC-DC converters is widely approached in several studies to ensure its performance and robustness. This paper proposes the voltage control of a three-state switching cell (3SSC) boost converter in the continuous time. On this occasion, the output voltage is controlled by a Tagaki-Sugeno-Kang (TSK) Fuzzy with integral action, which thegains are obtained using Parallel Distributed Compensation via Linear Matrix Inequalities (PDC-LMI) combined through linear membership functions and activated by the duty cycle and inductor current. This approach aims to reject problems originated by load and input voltage variations and improve the stability response of the converter output voltage. The obtained results of this paper evidences the effectiveness of the proposed controller in the continuoustime, reducing the effects of external disturbances and maintaining the stability of the output voltage conforming to the control design characteristics.

scholarly journals Robust Inverse Optimal Control for a Boost Converter

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2507
Author(s):  
Mario Villegas-Ruvalcaba ◽  
Kelly Joel Gurubel-Tun ◽  
Alberto Coronado-Mendoza
Keyword(s):  
Optimal Control ◽  
Robust Control ◽  
Input Voltage ◽  
Boost Converter ◽  
Voltage Reference ◽  
Inverse Optimal Control ◽  
State Equations ◽  
Control Lyapunov Function ◽  
Operation Conditions ◽  
The Stability

The variability of renewable energies and their integration into the grid via power electronics demands the design of robust control algorithms. This work incorporates two techniques to ensure the stability of a boost converter through its state equations, implementing the inverse optimal control and the gain-scheduling technique for robust control settings. In such a way that, under a single adjustment, it is capable of damping different changes such as changes in the parameters, changes in the load, the input voltage, and the reference voltage. On the other hand, inverse optimal control is based on a discrete-time control Lyapunov function (CLF), and CLF candidate depends on fixed parameters that are selected to obtain the solution for inverse optimal control. Once these parameters have been found through heuristic or artificial intelligence methods, the new proposed methodology is capable of obtaining a robust optimal control scheme, without having to search for new parameters through other methods, since these are sometimes sensitive changes and many times the process of a new search is delayed. The results of the approach are simulated using Matlab, obtaining good performance of the proposed control under different operation conditions. Such simulations yielded errors of less than 1% based on the voltage reference, given the disturbances caused by changes in the input variables, system parameters, and changes in the reference. Thus, applying the new methodology, the stability of our system was preserved in all cases.

Analysis of the Chatter Instability in a Nonlinear Model for Drilling

2006 ◽  
Vol 1 (4) ◽  
pp. 294-306 ◽  
Author(s):  
Sue Ann Campbell ◽  
Emily Stone
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Nonlinear Models ◽  
Stability Boundary ◽  
Vibration Modes ◽  
Loss Of Stability ◽  
Chatter Vibration ◽  
Cutting Depth ◽  
Stability And Bifurcation Analysis ◽  
The Stability

In this paper we present stability analysis of a non-linear model for chatter vibration in a drilling operation. The results build our previous work [Stone, E., and Askari, A., 2002, “Nonlinear Models of Chatter in Drilling Processes,” Dyn. Syst., 17(1), pp. 65–85 and Stone, E., and Campbell, S. A., 2004, “Stability and Bifurcation Analysis of a Nonlinear DDE Model for Drilling,” J. Nonlinear Sci., 14(1), pp. 27–57], where the model was developed and the nonlinear stability of the vibration modes as cutting width is varied was presented. Here we analyze the effect of varying cutting depth. We show that qualitatively different stability lobes are produced in this case. We analyze the criticality of the Hopf bifurcation associated with loss of stability and show that changes in criticality can occur along the stability boundary, resulting in extra periodic solutions.

scholarly journals "Study of effect of the inductor on dynamical behavior for electronic circuit by using nonlinear part from type memductance

2021 ◽  
Vol 8 (1) ◽  
pp. 98-108
Author(s):  
Abo-Talib .Y. Abbas
Keyword(s):  
Hopf Bifurcation ◽  
Phase Portrait ◽  
Bifurcation Diagram ◽  
Electronic Circuit ◽  
Dynamical Behavior ◽  
Stability Zone ◽  
Nonlinear Part ◽  
Bifurcation Line ◽  
Stability Maps ◽  
The Stability

"The effect of the coil on the dynamical behavior of the electronic circuit with nonlinear part memductance was studied, where we studied four coil values: L = 90mH, L = 80mH, L = 70mH and L = 100mH with changing the value of the first capacitance c1. We obtained stability maps consisting of two regions (the dynamical behavior zone and the stability zone), where the dividing line is the Hopf bifurcation line, as well as the bifurcation diagram for each value from the coil and the first capacitance was obtained, as well as the phase portrait diagram in which we obtained the chaotic attractions And the period of the first, second, third, fourth, fifth, sixth and eighth.

scholarly journals Fuzzy Sliding Mode Control of DC-DC Boost Converter

2018 ◽  
Vol 8 (3) ◽  
pp. 3054-3059 ◽  
Author(s):  
Z. B. Duranay ◽  
H. Guldemir ◽  
S. Tuncer
Keyword(s):  
Control System ◽  
Fuzzy Logic Control ◽  
Control Method ◽  
Sliding Mode ◽  
Input Voltage ◽  
Boost Converter ◽  
Fuzzy Sliding Mode Control ◽  
Load Variations ◽  
Logic Control ◽  
Fuzzy Sliding Mode

A sliding mode fuzzy control method which combines sliding mode and fuzzy logic control for DC-DC boost converter is designed to achieve robustness and better performance. A fuzzy sliding mode controller in which sliding surface whose reference is obtained from the output of the outer voltage loop is used to control the inductor current. A linear PI controller is used for the outer voltage loop. The control system is simulated using Matlab/Simulink. The simulation results are presented for input voltage and load variations. Simulated results are given to show the effectiveness of the control system.

scholarly journals Modeling, Control and Design of DC-DC Boost Converter for Grid Connected Photo-Voltaic Applications

2012 ◽  
pp. 260-264
Author(s):  
Suneel Raju Pendem ◽  
Bidyadhar Subudhi
Keyword(s):  
Output Voltage ◽  
Pulse Width Modulation ◽  
Sliding Mode ◽  
Input Voltage ◽  
Boost Converter ◽  
Linear Feedback ◽  
Feedback Controllers ◽  
Control Switch ◽  
Modulation Signal ◽  
Constant Output

This article presents a design and development method of a DC-DC boost converter with constant output voltage. This system has a nonlinear dynamic behavior, as it works in switch-mode. Moreover, it is exposed to significant variations which may take this system away from nominal conditions, due to changes on the load or on the line voltage at the input. From a fluctuating or a variable input voltage, boost converter is able to step up the input voltage to a higher constant dc output voltage using the Non-linear feedback controllers such as PID controller and the Sliding Mode controllers. By this technique, the output of the converter is measured and compared with a reference voltage. The differential of the compared value will be used to produce a pulse width modulation signal to control switch in the boost converter. Simulation results describe the performance of the proposed design.

Sensitivity Analysis of Dissipative Reversible and Hamiltonian Systems: A Survey

2009 ◽  
Author(s):  
Oleg N. Kirillov ◽  
Ferdinand Verhulst
Keyword(s):  
Sensitivity Analysis ◽  
Hopf Bifurcation ◽  
Structural Stability ◽  
Hamiltonian Systems ◽  
Perturbation Analysis ◽  
Stability Boundary ◽  
Conservative System ◽  
Small Dissipation ◽  
Whitney Umbrella ◽  
The Stability

The paradox of destabilization of a conservative or non-conservative system by small dissipation, or Ziegler’s paradox (1952), has stimulated an ever growing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations. Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary. What is less known is that the first complete explanation of Ziegler’s paradox by means of the Whitney umbrella singularity dates back to 1956. We revisit this undeservedly forgotten pioneering result by Oene Bottema that outstripped later findings for about half a century. We discuss subsequent developments of the perturbation analysis of dissipation-induced instabilities and applications over this period, involving structural stability of matrices, Krein collision, Hamilton-Hopf bifurcation and related bifurcations.

Interleaved Double Dual Boost Converter for Renewable Energy System

2014 ◽  
Vol 931-932 ◽  
pp. 904-909 ◽  
Author(s):  
Matheepot Phattanasak ◽  
Wattana Kaewmanee ◽  
Jean Philippe Martin ◽  
Serge Pierfederici ◽  
Bernard Davat
Keyword(s):  
Renewable Energy ◽  
Planning Process ◽  
Sliding Mode ◽  
Energy System ◽  
Input Voltage ◽  
Boost Converter ◽  
Outer Loop ◽  
High Voltage Gain ◽  
Photovoltaic Applications ◽  
Loop 2

This paper presents an interleaved double dual boost converter (IDDB) used in renewable energy application where high voltage gain is required such as fuel cell or photovoltaic applications, etc. Two types of controllers are applied to this converter, 1) a controller based on Flatness properties for regulating the output voltage (outer loop); 2) a sliding mode controller for inductor current (inner loop). The variation of the input voltage is compensated by trajectory planning process. The validation of the proposed system is done through experimental results.

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