Unstructured Uncertainty Based Modeling and Robust Stability Analysis of Textile-Reinforced Composites with Embedded Shape Memory Alloys

Abstract

This paper develops the mathematical modeling and deflection control of a textile-reinforced composite integrated with shape memory actuators. The mathematical model of the system is derived using the identification method and an unstructured uncertainty approach. Based on this model and a robust stability analysis, a robust proportional-integral controller is designed for controlling the deflection of the composite. We showed that the robust controller depends significantly on the modeling of the uncertainty. The performance of the proposed controller is compared with a classical one through experimental analysis. Experimental results show that the proposed controller has a better performance as it reduces the overshoot and provide robustness to uncertainty. Due to the robust design, the controller also has a wide operating range, which is advantageous for practical applications.

Construction, modeling, and control of a three‐beam prototype using interactive fiber rubber composites

“…The mathematical model provides a description of the dynamic behavior of a system, in either the time domain or frequency domain. Various approaches exist to obtain dynamical models [15,16]. One such approach is experimental modeling, also known as system identification, which involves measuring multiple variables of the process and constructing a model that closely matches the measured data.…”

“…These uncertainties may include unknown nonlinearities, parametric variations, additive or multiplicative uncertainties, nonmodel dynamics, and more. Based on [18] and the research conducted in [16], we use a robust stability approach to achieve robust performance for the prototype, even in the presence of uncertainties. In this case, we utilized additive and multiplicative uncertainties, assuming that the nominal transfer function of the plant is represented by G̃(s).…”

“…Mathematical modeling, experimental modeling, or system identification techniques can be employed to derive simplified equations for the system [15,16]. In this study, we follow the approach developed in [16] to represent the relationship between the inputs and outputs of the system using a rational transfer function that incorporates the system's nonlinearities as unstructured uncertainty.…”

Calculation of robustly relatively stabilizing PID controllers for linear time-invariant systems with unstructured uncertainty

“…First, the model with parametric uncertainty (39) has to be replaced by the model with unstructured uncertainty. In fact, the system with parametric uncertainty would not be needed at all here, but it is intentionally used as a preliminary model in this example in order to show the relation with the unstructured uncertainty model, the construction of which resides in the choice of a suitable model type, a nominal system G 0 (s), and a weight function, e.g., W M (s).…”

“…Further, the paper [38] provided a set of simulation results for robust PID control of a hydraulic system with unstructured uncertainty. Recently, in [39], a robust PI controller was designed for a textile-reinforced composite integrated with shape memory actuators, modeled by means of an unstructured uncertainty approach.…”