Chapter 6

Chaos is observed as an unpredictable phenomenon due to its sensitivity to initial states. It is a kind of steady-state but locally unstable behavior, and exhibits irregular properties. Such random-like phenomenon is normally regarded as unstable operation which results in additional loss, and therefore is a harmful behavior. Various control methods have been proposed to stabilize the chaotic behavior, such as the Ott–Grebogi–Yorke (OGY) method (Ott, Grebogi, and Yorke, 1990; Hunt, 1991), the time-delay feedback method (Pyragas, 1992), the non-feedback method (Rajasekar, Murali, and Lakshmanan, 1997; Ramesh and Narayanan, 1999), the proportional feedback method (Jackson and Grosu, 1995; Casas and Grebogi, 1997), the nonlinear control method (Khovanov et al., 2000; Tian, 1999), the adaptive control method (Boccaletti, Farini, and Arecchi, 1997; Liao and Lin, 1999), the neutral networks method (Hirasawa et al., 2000; Poznyak, Yu, and Sanchez, 1999), and the fuzzy control method (Tanaka, Ikeda, and Wang, 1998). Some of them have also been proposed to stabilize the chaotic behavior in electric drive systems.

In this chapter, various control approaches, including the time-delay feedback control, the nonlinear feedback control, the backstepping control, the dynamic surface control and the sliding mode control, are introduced to stabilize the chaos that occurs in both DC and AC drive systems.

6.1 Stabilization of Chaos in DC Drive System

6.1.1 Modeling

As shown in Figure 6.1 ...

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