In this paper, a nonlinear dynamic of permanent magnet synchronous machine scalar drive systems (PMSMSDS) is investigated thoroughly. At first, the mathematical dynamic model of the PMSMSDS is developed and formulated for open-and close-loop cases. Then, constant and periodic load torque are considered for the analysis of the system. The Jacobian matrix and the Poincaré mapping of the system are calculated analytically to study the feasibility of nonlinear phenomena at each point of equilibrium for constant and periodic loads, respectively. Computer simulation is used to obtain bifurcation diagram, time response, and phase plane of the state variables to investigate the complex behavior of the system by changing some parameters. It is shown that by changing the parameters of reference speed command, supply voltage range, and speed controller gain, the response of PMSMSDS state variables will be routed to limit cycle, bifurcated, and chaotic. Numerical analysis is provided to confirm the simulation results.
In this paper, bifurcation diagrams, modified Poincaré map and Lyapunov exponents characteristic are developed for studying non-linear phenomenon in dynamics of permanent-magnet synchronous machine scalar drive systems (PMSMSDS). For this, extended Poincaré model of the system is introduced analytically taking into account voltage saturation effects. Using this proposed discrete map model, chaotic and stable region of the PMSMSDS in voltage frequency plane of the system are determined. Furthermore, bifurcation diagram of the system is derived when reference command speed is considered as a bifurcation parameter. Lyapunov exponents are calculated numerically in order to prove the chaotic response of the system and evaluate the accuracy of simulation and numerical results. Experimental test is implemented to investigate the occurrence of chaotic behaviour in the system. It is shown that the proposed map model of the PMSMSDS is capable to predict the chaotic behaviour of the system at any conditions.
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