Abstract
In this paper, we investigate the control of 4-D nonautonomous fractional-order uncertain model of a PI speed-regulated current-driven induction motor (FOIM) using a fractional-order adaptive sliding mode controller (FOASMC). First, we derive a dimensionless fractional-order model of the induction motor from the well-known integer -model of the induction motor. Various dynamic properties of the fractional-order induction motor, such as stability of the equilibrium points, Lyapunov exponents, bifurcation, and bicoherence, are investigated. An adaptive controller is derived to suppress the chaotic oscillations of the fractional-order model of the induction motor. Numerical simulations of the adaptive chaos suppression methodology are depicted for the fractional-order uncertain model of the induction motor to validate the analytical results of this work. A genetically optimized fractional-order PID (FOPID) controller is also derived to stabilize the states of the FOIM system. FPGA implementation of the proposed FOASMC is also presented to show that the proposed controller is hardware realizable.
Highlights
Electric motors consume approximately % to % of the electric energy [ ]
In Section, we investigate the dynamic properties of the fractional-order induction motor system (FOIMS)
9 Conclusion This paper investigates the control of dimensionless nonautonomous fractional-order uncertain load torque model of an induction motor via an adaptive control technique
Summary
Electric motors consume approximately % to % of the electric energy [ ]. In Section , we derive a fractional-order model of the induction motor system [ , ]. Using ( ) in ( ) with the defined new states and coefficients, the dimensionless integer-order model of a PI speed-regulated current-driven induction motor [ , ] is defined as x. When we wish to numerically calculate or simulate fractional-order equations, we have to use finite-memory principle, where L is the memory length, and h is the time sampling as min{[. Applying these fractional-order approximations of the derivatives in system ( ), we obtain the fractional-order model of the chaotic induction motor given by the following dynamics: Dqt x. Figure shows the -D chaotic phase portraits of the fractional induction motor system ( ) in (x , x ), (x , x ), (x , x ), and (x , x ) planes
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