Robust Control for Non-Minimum Phase Systems with Actuator Faults: Application to Aircraft Longitudinal Flight Control

This study is concerned with developing a robust tracking control system that merges the optimal control theory with fractional-order-based control and the heuristic optimization algorithms into a single framework for the non-minimum phase pitch angle dynamics of Boeing 747 aircraft. The main control objective is to deal with the non-minimum phase nature of the aircraft pitching-up action, which is used to increase the altitude. The fractional-order integral controller (FIC) is implemented in the control loop as a pre-compensator to compensate for the non-minimum phase effect. Then, the linear quadratic regulator (LQR) is introduced as an optimal feedback controller to this augmented model ensuring the minimum phase to create an efficient, robust, and stable closed-loop control system. The control problem is formulated in a single objective optimization framework and solved for an optimal feedback gain together with pre-compensator parameters according to an error index and heuristic optimization constraints. The fractional-order integral pre-compensator is replaced by a fractional-order derivative pre-compensator in the proposed structure for comparison in terms of handling the non-minimum phase limitations, the magnitude of gain, phase-margin, and time-response specifications. To further verify the effectiveness of the proposed approach, the LQR-FIC controller is compared with the pole placement controller as a full-state feedback controller that has been successfully applied to control aircraft dynamics in terms of time and frequency domains. The performance, robustness, and internal stability characteristics of the proposed control strategy are validated by simulation studies carried out for flight conditions of fault-free, 50%, and 80% losses of actuator effectiveness.

Composition Formulae for the k -Fractional Calculus Operator with the S -Function

In this study, the S-function is applied to Saigo’s k -fractional order integral and derivative operators involving the k -hypergeometric function in the kernel; outcomes are described in terms of the k -Wright function, which is used to represent image formulas of integral transformations such as the beta transform. Several special cases, such as the fractional calculus operator and the S -function, are also listed.

Image Denoising of Adaptive Fractional Operator Based on Atangana–Baleanu Derivatives

A fractional integral operator can preserve an image edge and texture details as a denoising filter. Recently, a newly defined fractional-order integral, Atangana–Baleanu derivatives (ABC), has been used successfully in image denoising. However, determining the appropriate order requires numerous experiments, and different image regions using the same order may cause too much smoothing or insufficient denoising. Thus, we propose an adaptive fractional integral operator based on the Atangana–Baleanu derivatives. Edge intensity, global entropy, local entropy, and local variance weights are used to construct an adaptive order function that can adapt to changes in different regions of an image. Then, we use the adaptive order function to improve the masks based on the Grumwald–Letnikov scheme (GL_ABC) and Toufik–Atangana scheme (TA_ABC), namely, Ada_GL_ABC and Ada_TA_ABC, respectively. Finally, multiple evaluation indicators are used to assess the proposed masks. The experimental results demonstrate that the proposed adaptive operator can better preserve texture details when denoising than other similar operators. Furthermore, the image processed by the Ada_TA_ABC operator has less noise and more detail, which means the proposed adaptive function has universality.

Spatial Path Tracking Controllers for Autonomous Ground Vehicles: Conventional and Nonconventional Schemes

Unlike time-based path tracking controllers, the [Formula: see text]-controller is a spatial path tracking controller. It is a purely geometric path tracking controller and essentially a P-controller to maintain the reasonable spatial distance, [Formula: see text], from the vehicle to the desired path. In this paper, we present some enhancement schemes using the non-conventional PI control laws via optimization. We propose to use a nonlinear term [Formula: see text] for the proportional controller. A fractional-order integral used to achieve a PI[Formula: see text] control. Among the schemes, an optimization search procedure applied to find optimal controller gains by meshing the regions around the values from approximate linear designs. The performance index for parametric optimization is the integration of the absolute purely spatial deviation from the desired path. Three different types of road shape were chosen and the Gazebo-ROS simulation results were presented to show the effectiveness of the proposed enhancement schemes. The results show that in some cases a smaller [Formula: see text] and [Formula: see text] can be achieved by using [Formula: see text] controller, but its disadvantage is there may be some oscillation. For PI[Formula: see text] controller, there is an additional adjustable parameter [Formula: see text], better performance can be achieved without significant disadvantages which is worth in-depth research.