Adaptive Control for Multi-Shaft with Web Materials Linkage Systems

Abstract

In this paper, a fuzzy disturbance observer and a high-gain disturbance observer based on a variable structure controller are applied to deal with imprecise multi-shaft with web materials linkage systems taking into account the variation of the moment of inertia. Specifically, a high-gain disturbance observer and an adaptive fuzzy algorithm are separately applied to estimate system uncertainties and external disturbances. The high-gain disturbance observer is designed with auxiliary variables to avoid the amplification of the measurement disturbance, and the fuzzy disturbance observer has the advantage that it does not depend on model information. The convergence properties of the tracking error are analytically proven using Lyapunov’s theory. The obtained numerical results demonstrate the validity and the adaptive performance of the proposed control law in case the system is exposed to uncertainties and disturbances. Important remarks on the design process and performance benchmarks of the two observers are also demonstrated.

Model‐free hierarchical control with fractional‐order sliding surface for multisection web machines

“…Based on the previous study of the single-span R2R nonlinear model 30 and the representation of the moment acting on the unwinder roll in Figure 2, we have the following dynamic equations of unwinding roll…”

“…Based on the previous study of the single‐span R2R nonlinear model 30 and the representation of the moment acting on the unwinder roll in Figure 2, we have the following dynamic equations of unwinding roll $$$$ {J}_u\frac{d{v}_u}{R_u dt}={T}_1{R}_u-{M}_u-{b}_{f_u}{\omega}_u-\frac{a{v}_u^2}{2\pi {R}_u}\left(\frac{J_u}{R_u^2}-2\pi w\rho {R}_u^2\right), $$$$ $$$$ {J}_u={J}_{u0}+\pi \rho \omega \frac{\left({R}_u^4-{R}_{u0}^4\right)}{2}, $$$$ $$$$ {R}_u={R}_{u0}-\frac{\theta_ua}{2\pi }, $$$$ where $$$ {J}_u $$$, $$$ {J}_{u0} $$$, …”

“…The architecture proposed in References 28,29 has helped to stabilize the system quickly and achieve proper tension and speed values in the presence of unknown components and external disturbances during transport. Compared with References 28,29 the indicated SMC method has been extended with the addition of a High‐gain Disturbance Observer and a Fuzzy Disturbance Observer on R2R system 30 . The distinguishing features of this structure can be noticed as: reducing dependence on model parameters, ensuring system stability, and solving the dilemma about disturbances and uncertainties.…”

“…[22][23][24][25][26] Apart from that, the use of fractional-order sliding surface plays a vital part in manually optimizing system responses, and hence system performance is improved compared to using traditional sliding surfaces as shown in the works. [27][28][29][30] (3) Instead of just approximating the moment of inertia in the study 45 or calculating uncertainties and disturbances by using fuzzy logic in the study, 30 an RBF neural network-based robust controllers (RBFNN-BRC), which is capable of adapting to uncertainties and disturbances, is implemented to estimate the complete model. Subsequently, the whole system is also easily proven stable by the Lyapunov stability theory.…”

“…Compared with References 28,29 the indicated SMC method has been extended with the addition of a High-gain Disturbance Observer and a Fuzzy Disturbance Observer on R2R system. 30 The distinguishing features of this structure can be noticed as: reducing dependence on model parameters, ensuring system stability, and solving the dilemma about disturbances and uncertainties. Besides, when adopted to a Permanent Magnet Synchronous Motor (PMSM), the recommended Fractional-order Sliding Mode Control (FOSMC) method 31 produces more robustness and effectiveness than the traditional SMC method.…”