Robustness margins for global asymptotic stability in indirect field-oriented control of induction motors

Abstract

The influence of the rotor time constant mismatch on the stability of induction motors under indirect field oriented control is analyzed. The paper focuses on the global asymptotic stability property and extends the results of []. Robustness margins for global asymptotic stability with respect to rotor time constant mismatches are obtained. The effect of the PI settings in such robustness margins is clarified allowing to derive design guidelines. The methodology is applied to two different induction motor drive systems illustrating the stability margin estimates.<br>A estabilidade de acionamentos por orientação de campo indireta de motores de indução quando sujeitos a erros de estimativa da constante de tempo do rotor é analisada. O artigo se concentra na estabilidade global, estendendo os resultados de []. Margens de robustez são determinadas e diretivas para projeto do laço PI de velocidade são obtidas. A metodologia de análise é aplicada a dois sistemas distintos a fim de ilustrar as estimativas de margens de estabilidade

The stochastic stability and H∞‐fuzzy control of stochastic bifurcation of a doubly‐fed induction generator

“…the tuning parameter is defined as k = c ˆ1/c 1 . The physical meaning of the remaining variables can be found in Bazanella et al 25 and Reginatto and Bazanella. Step 5: If ϕ ϕ t = 0, / = 0   , get the center manifold of the system, marked as W c ,…”

“…, x 1 is the stator q-axis magnetic chain, x 2 is the stator d-axis magnetic chain, x 3 is the speed difference, x 4 is the output of indirect magnetic field control, and the physical meaning of the remaining parameters can be found in Yang et al 24 and Bazanella et al, 25 the equilibrium point of the deterministic DFIG is given by Equation (2):…”

“…Equation () was chosen to describe the mathematical model of the doubly‐fed asynchronous power generation system 24 $$$\left\{\begin{array}{c}{\dot{x}}_{1}=-{c}_{1}{x}_{1}+{c}_{2}{u}_{2}^{0}+\frac{k{c}_{1}}{{u}_{2}^{0}}{x}_{4}{x}_{2},\\ {\dot{x}}_{2}=-{c}_{1}{x}_{2}+{c}_{2}{x}_{4}-\frac{k{c}_{1}}{{u}_{2}^{0}}{x}_{4}{x}_{1},\\ {\dot{x}}_{3}=-{c}_{3}{x}_{3}-{c}_{4}[{c}_{5}({x}_{1}{x}_{4}-{u}_{2}^{0}{x}_{2})-{T}_{L}],\\ {\dot{x}}_{4}={k}_{c}{x}_{3}-{k}_{p}{c}_{4}[{c}_{5}({x}_{1}{x}_{4}-{u}_{2}^{0}{x}_{2})-{T}_{L}],\end{array}\right.$$$where $${\dot{x}}_{1}=d{x}_{1}/dt$$, x 1 is the stator q ‐axis magnetic chain, x 2 is the stator d ‐axis magnetic chain, x 3 is the speed difference, x 4 is the output of indirect magnetic field control, and the physical meaning of the remaining parameters can be found in Yang et al 24 and Bazanella et al, 25 the equilibrium point of the deterministic DFIG is given by Equation (): …”

“…Considering that the original determination of the DFIG model on each state space will be disturbed by noise and that the random noise space is complex, 25 therefore, white noise is selected as a random factor to simulate the process of environmental noise.…”