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This article studies identification problems of multiple linear regression models, which may be described a class of multi-input multi-output systems (i.e. multivariable systems). Based on the coupling identification concept, a novel coupled-least-squares (C-LS) parameter identification algorithm is introduced for the purpose of avoiding the matrix inversion in the multivariable recursive least-squares (RLS) algorithm for estimating the parameters of the multiple linear regression models. The analysis indicates that the C-LS algorithm does not involve the matrix inversion and requires less computationally efforts than the multivariable RLS algorithm, and that the parameter estimates given by the C-LS algorithm converge to their true values. Simulation results confirm the presented convergence theorems.

Nuclear fusion is one of the newest and most promising clean and safe energies hence, it imposes a new research area of control. In this paper, the design of a multivariable adaptive proportional-integral-derivative (PID) controller for the control of the plasma current, shape and position to ensure the safe operation of the fusion reactor is successfully developed. The recursive least square algorithm is used in an alternative way as an adaptation mechanism for tuning PID controller gains. Since stability is a vital issue in the evaluation of control systems, therefore stability analysis of the proposed controller is developed using the Lyapunov stability theory. The main objective of plasma current, shape and position controller in fusion reactors is to improve the stability and the performance of tokamak magnetic systems without contravening the limits imposed by the actuating coils voltages physical limitations. The proposed APID (adaptive PID) controller tunes online its parameters to cope with the presence of the disturbance or any parameters changes occur during the operation. The results of the proposed APID on a simulation code of a tokamak show a noteworthy improvement with respect to those obtained with other control techniques in the cases of changing the initial controller gains, adding disturbance signal and variation in the reactor model parameters.

We propose in the present paper a lower gain adaptive Sliding Mode Control (SMC) method, of Doubly Fed Induction Generator (DFIG) stator powers. This allows eliminating some problems caused by high gain SMC. The main idea is to put the DFIG model under state space presentation using as states the stator and rotor currents with rotor speed. Using Euler method, the DFIG model can be rewritten as ARMA model, which used to online identification of DFIG resistances and inductances based on Recursive Least Square (RLS) algorithm and Low-Pass Filter (LPF). These identified parameters are used to calculate the stator power control law. In this case, we demonstrated using Lyapunov function that a lower gain satisfied to achieve the control objectives. The viability of our approach is verified by simulation results in the case of DFIG rating at 1.5 MW.