Design of robust fractional-order controller for 4-leg inverter

This paper proposes design of fractional-order controller for a 4-leg inverter using the concept of Bode's ideal loop transfer function. The 4-leg inverters have been increasingly used to cater nonlinear loads and hence there control is a crucial issue. The linear model of 4-leg inverter has poor phase margin resulting in a highly oscillatory time-domain response. The designed controller makes the closed-loop system robust by maintaining a constant phase with desired phase margin in the selected frequency band. This makes closed-loop system insensitive to system parameters achieving the robustness. The performance of the desired controller is compared with the adaptive pole-placement controller available in the literature. It is shown via simulation studies that the proposed controller results in a better closed-loop performance.

[1]  I. Podlubny.  Fractional differential equations , 1998 .

[2]  Om Prakash Agrawal,et al.  Generalized Variational Problems and Euler-Lagrange equations , 2010, Comput. Math. Appl..

[3]  Ahmad Radan,et al.  Adaptive pole-placement control of 4-leg voltage-source inverters for standalone photovoltaic systems , 2011 .

[4]  G. H. Kim,et al.  Characteristic analysis of three-phase four-leg inverter based load unbalance compensator for stand-alone microgrid , 2015, 2015 9th International Conference on Power Electronics and ECCE Asia (ICPE-ECCE Asia).

[5]  Luigi Fortuna,et al.  Fractional Order Systems: Modeling and Control Applications , 2010 .

[6]  Suttichai Premrudeepreechacharn,et al.  A Carrier-Based Unbalanced PWM Method for Four-Leg Voltage Source Inverter Fed Unsymmetrical Two-Phase Induction Motor , 2013, IEEE Transactions on Industrial Electronics.

[7]  M. Carolin Mabel,et al.  Control methods for four-leg voltage source inverter , 2012 .

[8]  A. Farmanbordar,et al.  Robust control of decoupled 4-leg voltage inverters , 2011, The 2nd International Conference on Control, Instrumentation and Automation.

[9]  Dumitru Baleanu,et al.  Fractional Optimal Control Problems with Several State and Control Variables , 2010 .

[10]  V. Lakshmikantham,et al.  Theory of Fractional Dynamic Systems , 2009 .

[11]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[12]  M. Omizo,et al.  Modeling , 1983, Encyclopedic Dictionary of Archaeology.

[13]  S. Das,et al.  Functional Fractional Calculus for System Identification and Controls , 2007 .

[14]  R.R. Sawant,et al.  A Multifunctional Four-Leg Grid-Connected Compensator , 2009, IEEE Transactions on Industry Applications.

[15]  Ionel Vechiu,et al.  Control of four leg inverter for hybrid power system applications with unbalanced load , 2007 .

[16]  Dushan Boroyevich,et al.  Three-dimensional space vector modulation for four-leg voltage-source converters , 2002 .

[17]  Marie Frei.  Complex Variables And The Laplace Transform For Engineers , 2016 .

[18]  Amin Mohammadbagheri,et al.  Comparison Performance Between PID and LQR Controllers for 4-leg Voltage-Source Inverters , .

[19]  H. Kober.  ON FRACTIONAL INTEGRALS AND DERIVATIVES , 1940 .

[20]  M.K. Mishra,et al.  A Minimally Switched Control Algorithm forThree-Phase Four-Leg VSI Topology toCompensate Unbalanced and Nonlinear Load , 2008, IEEE Transactions on Power Electronics.

[21]  Alain Oustaloup,et al.  Frequency-band complex noninteger differentiator: characterization and synthesis , 2000 .

[22]  Robert D. Lorenz,et al.  Decoupled control of a four-leg inverter via a new 4/spl times/4 transformation matrix , 2001 .

[23]  Dumitru Baleanu,et al.  Generalized variational calculus in terms of multi-parameters fractional derivatives , 2011 .

[24]  Yerramreddy Srinivasa Rao,et al.  Real-Time Electrical Load Emulator Using Optimal Feedback Control Technique , 2010, IEEE Transactions on Industrial Electronics.

[25]  R. Magin.  Fractional Calculus in Bioengineering , 2006 .

[26]  Om P. Agrawal,et al.  A Formulation and Numerical Scheme for Fractional Optimal Control Problems , 2008 .

[27]  Vishwesh A. Vyawahare,et al.  QFT LOOP SHAPING USING A FRACTIONAL INTEGRATOR - REAL-TIME APPLICATION TO A COUPLED-TANK SYSTEM , 2006 .

[28]  D. Vinnikov,et al.  A control strategy for a grid-connected PV system with unbalanced loads compensation , 2015, 2015 9th International Conference on Compatibility and Power Electronics (CPE).

[29]  D. Boroyevich,et al.  Modeling, control and stability analysis of a PEBB based DC DPS , 1999 .

[30]  I. Petráš.  Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation , 2011 .

[31]  Dhanashree Vyawahare,et al.  Power flow analysis in stand-alone 4-wire, 4-leg inverter microgrid with unbalanced loads , 2014, 2014 16th European Conference on Power Electronics and Applications.

[32]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[33]  YangQuan Chen,et al.  Fractional-order systems and control : fundamentals and applications , 2010 .

[34]  K. Diethelm.  The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type , 2010 .