Z di ]] d = - R i d + dt Ld [ di q R ] = - L iq q \ dt Lq L d ~i q + Ld L q ~i d + ud Ld uq }m , Lq - Lq ~ Te = 1.5P [}i q + (L d - L q) i d i q], (1) objective function given by (3) has multiple local optima as the reality PMSM is a typical dynamic nonlinear system. (2) Parallel Immune Cooperative Dynamic PSO Learning Algorithm where ~ is the electrical angular velocity, ud, uq, id, and iq are dq-axis stator voltage and current, and P is the number of pole pairs. R, Ld, Lq, and } are the motor winding resistance, dq-axis inductances, and magnet flux, and Te is electromagnetic torque, respectively, while those parameters are needed to be estimated. Optimization-Based Parameter Estimator Modeling The parameter estimation problem can be ascribed to a system optimization problem for a system with known model structure but unknown parameters. The parameter identification problem can be treated as a gray-box modelbased parameter optimization task without needing a lot of prior knowledge of reality systems, and the issue of parameter cross-coupling intersystems can be adaptively decoupled by using a bioinspired optimization algorithm. The idea is to compare the real system output with the ideal mathematical model output through optimization based on an objective function. The schematic can be roughly illustrated as in Figure 1. The problem of parameter identification could be expressed as a minimum optimization problem with some restrictions. Based on (1) and Figure 1, the objective function f (it ) is built and shown as in (3), which follows: n 1 f (it ) = n | w 1 u d0 (k) - ut d0 (k) + w 2 u q0 (k) - ut q0 (k) k=1 + w 3 u d (k) - ut d (k) + w 4 u q (k) - ut q (k) , (3) where n is the length of samples, w1, w2, w3, w4 are the weight coefficients satisfy, 0 < w i < 1 , and the variables with '^' signify that they are calculated voltages through the estimated parameters and measured currents. The ud uq did dt diq dt = - = - R Ld R Lq id + iq - Lq Ld Ld Lq ωiq + ωid + f (θ^ ) ud Ld uq Lq - ψm Lq ω y^ - + ∧ θ Optimization-Based Parameters Estimation Figure 1. a parameter identification model based on PICDPSO-m. 28 Vid (t + 1) = zVid + c 1 * rand 1 () (Pbest id (t) - X id (t)) + c 2 * rand 2 () (gBest d (t) - X id (t)), (4) X id (t + 1) = X id (t) + Vid (t + 1) , (5) where c 1 and c 2 are the acceleration coefficients, z is the inertia weight, rand 1 and rand 2 are two uniformly d istr ibuted ra ndom nu mber s generated w ith i n [0, 1], Pbest id represents the best position found by the ith particle up to now and gBest d is the best position in the entire population, and d represents the dimension of solved problem. The symbol t is the iteration generation. Principle of the PICDPSO-M Algorithm The PICDPSO-M architecture is composed of one memory and several subpopulations, which integrate the cooperative evolution mechanism, immune evolutionary mechanism, and swarms social behavior based on multicore parallel framework. The model of PICDPSO-M is as shown in Figure 2. In Figure 2, the memory conserves searched information selected from the different subpopulation, where PopM (M > 0) represents the Mth normal subpopulation of the whole population. The key operator of PICDPSO-M is shown in the following sections. Dynamic Velocity Modification Strategy for PSO In order to enhance the dynamics of the particles, a dynamic velocity modification strategy is designed for PSO. The details are as follows: y PMSM Basic PSO Algorithm In a d dimensional solution space, each particle i is composed of two vectors, where the velocity vector is Vi = {Vi1, Vi2, f, Vid} and the position vector is X i = {X i1, X i2, f, X id} . The searching procedure can be given as follows: IEEE SyStEmS, man, & CybErnEtICS magazInE Janu ar y 2016 Vid (t + 1) = zVid + c 1 * rand 1 () (Pbest id (t) - X id (t)) + c 2 * rand 2 () (gBest d (t) - X id (t)) min . (7) + (x max id - x id ) Gaussian (0, 1), X id (t + 1) = X id (t) + Vid (t + 1), (8) where Gaussian (0, 1) is a random number of a Gaussian distribution with a 0 mean and a 1 standard deviation, which can provide momentum for particles with few activities. The term will be activated when (growth factors) Gf i < m (m is a n adaptive threshold value as

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