A nonlinear controller design for permanent magnet motors using a synchronization-based technique inspired from the Lorenz system

Abstract

The dynamic behavior of a permanent magnet synchronous machine (PMSM) is analyzed. Nominal and special operating conditions are explored to show that the PMSM can experience chaos. A nonlinear controller is introduced to control these unwanted chaotic oscillations and to bring the PMSM to a stable steady state. The designed controller uses a pole-placement approach to force the closed-loop system to follow the performance of a simple first-order linear system with zero steady-state error to a desired set point. The similarity between the mathematical model of the PMSM and the famous chaotic Lorenz system is utilized to design a synchronization-based state observer using only the angular speed for feedback. Simulation results verify the effectiveness of the proposed controller in eliminating the chaotic oscillations while using a single feedback signal. The superiority of the proposed controller is further demonstrated by comparing it with a conventional PID controller. Finally, a laboratory-based experiment was conducted using the MCK2812 C Pro-MS(BL) motion control kit to confirm the theoretical results and to verify both the causality and versatility of the proposed controller.

Noise considerations and cryptanalysis of chaos-based secure communication systems

“…Utilizing a single scalar time series for the purpose of parameter identification, synchronization, or both usually puts some constraints on the ability to identify all the parameters of the chaotic system. Many techniques were reported in the literature that only deal with partial identification with application to the Lorenz system [22]. Motivated by the requirement to improve the security of the encryption function, the parameter V can be considered as a secret key (cipher).…”

Analysis of torsional stability and the dynamical characteristics of electromechanical systems

“…The projection of equation 2on the plane i d -v 2 can be written as equation (15) in Appendix 1. When the right-hand side of the equations are ordered to be zero, solutions could be obtained that…”

Bounding a domain containing all compact invariant sets of the permanent-magnet motor system

“…A noticeable progress has been achieved in spite of substantial complexity of mathematical models of such systems. In the relation with this we mention papers of [1,[4][5][6]9,13,14,[17][18][19][25][26][27][28]. The paper [9], see also [13], has been devoted to analysis the pitchfork and Hopf bifurcations based on using bifurcations theory and the central manifold theorem, obtaining an approximate stability boundary and some other topics.…”

“…In particular, we mention the two newest papers published to this moment. One of them is the paper [26] containing a controller design for forcing the closed-loop system to follow the performance of a simple first-order linear system with zero steady-state error to a desired set point. In addition, this work contains a construction of a synchronization-based observer using only the angular speed for feedback.…”