Chaos Control in Fractional Order Smart Grid with Adaptive Sliding Mode Control and Genetically Optimized PID Control and Its FPGA Implementation

Abstract

We investigate a specific smart grid system and its nonlinear properties. Lyapunov exponents are derived to prove the existence of chaos and bifurcation and bicoherence contours are investigated to show the parameter dependence and existence of quadratic nonlinearities, respectively. A fractional order model of the smart grid system (FOSG) is then derived and bifurcation of the FOSG system with variation in the commensurate fractional order of the system is investigated to show that largest Lyapunov exponent of the system exists in fractional order. Hence we proposed two different control methods to suppress the chaotic oscillations. In the first method we derive fractional order adaptive sliding mode control (FOASMC) algorithm to control chaotic oscillations and in the second method we used genetically optimized fractional order PID controllers (GAFOPID) for chaos control. Numerical simulations are conducted to show the effectiveness of the controllers and also to prove that GAFOPID controllers are more effective than FOASMC controllers for fractional order systems. The GAFOPID controllers are then realized in FPGA to show that the proposed methodology is hardware realizable.

No Chattering and Adaptive Sliding Mode Control of a Fractional‐Order Phase Converter with Disturbances and Parameter Uncertainties

“…Chaos control methodologies have been of greater interest in nonlinearity suppression of power systems. Chaos control problems in fractional-order complex systems with higher harmonics like the induction motor drive system and smart grid systems are discussed where the control objective is achieved with a genetically optimized fractional-order PID controller [3,8].…”

“…To be specific, three cases, (i) high-frequency, time-sharing inverter, (ii) hysteresis current-controlled three-phase voltage source converter, and (iii) dual-channel resonant converter, were studied for existence and effectiveness of chaotic behavior in power electronics [2]. Nonlinear behaviors, especially chaotic phenomena of the three-phase voltage source inverter (VSI) with hysteresis current comparator, are studied [3]. Chaotic behavior of various types of switching converters is discussed in [2,[4][5][6][7]; the analytical model of switching converters with piecewise switched circuits is developed during the 1970s.…”

Two Novel Approaches of NTSMC and ANTSMC Synchronization for Smart Grid Chaotic Systems

“…In (H. [31]), Steer-by-Wire Equipped Road Vehicle has been controlled by using adaptive control concept within a finite time. A fractional order adaptive sliding mode controllers (FOASMC) has been proposed in [14] for a fractional order smart grid chaotic system.…”

“…To make a comprehensive comparison, three well-known performance criteria are used including integral of the absolute value of the error (IAE), integral of the time multiplied by the absolute value of the error (ITAE), and integral of the square value (ISV) of the control input. Furthermore, the numerical simulation of the FOASMC is done by applying the control input presented in [14] to the proposed smart grid chaotic system. Note that the numerical simulation of FOASMC has been done to calculate the numerical values of the performance criteria and to show the effectiveness of our proposed controllers compared to the FOASMC controller.…”

Model-free Adaptive Sliding Mode Control for Continuous Stirred Tank Reactor

“…However, for discrete time systems, the reaching law based sliding mode control may only achieve quasi-sliding motion [21][22][23]. The adaptive discrete time sliding mode control approach [24][25][26] can ensure the system exhibits good performance without large chattering. This paper proposes an adaptive model-free control algorithm by combining discrete time sliding mode control and the partial form dynamic linearization method.…”