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Extra resources for Control and Mechatronics (The Industrial Electronics Handbook)

Sample text

It was developed originally as a demography model. It is a very simple system, but its response can be surprisingly colorful. 10 shows. We cannot uniquely determine xn from xn+1. As we see later, an invertible map can be chaotic only if its dimension is two or more (Henon map). , the logistic map. 6). The system stays in steady state at FP where xn+1 = xn = x*. 25) is nonlinear, it can have more than one FP. 1 One-Dimensional Iterated Maps For the sake of simplicity, the one-dimensional maps are discussed from now on.

The three-phase AC terminals of the VSC are tied through series L–R components to voltage space vector e–s rotating with angular speed ω. This simple circuit can approximately model either the AC mains or an induction motor. Space vectors with suffix s are written in stationary reference frame (SRF). There are some benefits by using rotating reference frame (RRF) fixed to voltage space vector e–s over SRF. Space vectors without suffix s are in RRF. 34 Condenser voltage in period-9 operation. 2).

The derivative λ = df/dx has to be evaluated at x*. λ is the eigenvalue of f(x) at x*. 31) It is obvious that x* is stable FP if | df / dx |x * < 1 and x* is unstable FP if | df / dx |x * > 1. In general, when the dimension is more than one, λ must be within the unit circle drawn around the origin of the complex plane for stable FP. The nonlinear f(x) has multiple FPs. The initial conditions leading to a particular x* constitute the basin of attraction of x*. As there are more basins of attraction, none of FPs can be globally stable.

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