Fuzzy adaptive observer‐based fault estimation design with adjustable parameter for satellite under unknown actuator faults and perturbations

Abstract

This study considers the problem of fault estimation for rigid satellite in the presence of external disturbances, parameter perturbations, and actuator time‐varying faults. Firstly, a Takagi‐Sugeno (T‐S) fuzzy model with interval matrix for satellite attitude system under large attitude angle scope is established, along with a detailed analysis of actuator faults in terms of additive and multiplicative descriptions. Then, a novel fuzzy adaptive observer with adjustable parameter is proposed to estimate both system states and actuator faults. The estimated errors are proved to be uniformly ultimately bounded, based on descriptor augmentation technique and Lyapunov stability theory. The proposed observer realizes a lower estimation performance index in terms of quantitative assessment compared to existing observer methods. Furthermore, an auxiliary optimization variable and the elimination method are applied to decrease the conservatism of the proposed design. And an intuitive quantitative performance index of fault estimation is introduced to obtain reliable evaluation and decision. Finally, numerical simulations and analyses of rigid satellite illustrate the effectiveness and benefit of the proposed strategy.

Fuzzy model based fault estimation and fault tolerant control for flexible spacecraft with unmeasurable vibration modes

“…In this example, according to the general working situation of the flexible spacecraft, the operating regions of premise variables are set as $${{\omega }_{j}}(t)\in [ \begin{matrix} -0.7 & 0.7 \end{matrix} ]{\text{rad}}/{\text{s}}\;,j=1,2,3$$. Based on eight operating points [42], which are (0.7, 0.7, 0.7), (0.7, 0.7, −0.7), (0.7, −0.7, 0.7), (0.7, −0.7, −0.7), ( − 0.7, 0.7, 0.7), $$(-0.7,0.7,-0.7 )$$, $$(-0.7,-0.7,0.7 )$$, $$(-0.7,-0.7,-0.7 )$$, the membership functions of T–S fuzzy sets $$M_{j}^{i}(i=1,2,\ldots ,8,j=1,2,3 )$$ are illustrated in Figure 2. The T–S fuzzy model of the flexible spacecraft is expressed as follows: …”

“…In this example, according to the general working situation of the flexible spacecraft, the operating regions of premise variables are set as 𝜔 j (t ) ∈ [−0.7 0.7]rad∕s , j = 1, 2, 3. Based on eight operating points [42], which are (0.7, 0.7, 0.7), (0.7, 0.7, −0.7), (0.7, −0.7, 0.7), (0.7, −0.7, −0.7), (−0.7, 0.7, 0.7), (−0.7, 0.7, −0.7), (−0.7, −0.7, 0.7), (−0.7, −0.7, −0.7), the membership functions of T-S fuzzy sets M i j (i = 1, 2, … , 8, j = 1, 2, 3) are illustrated in Figure 2. The T-S fuzzy model of the flexible spacecraft is expressed as follows:…”