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

Aisha Sir Elkhatem,Mustafa Mutiur Rahman,Subramania Nadaraja Pillai,Seref Naci Engin,Amjad Ali Pasha

doi:10.3390/app112411705

Abstract

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.

Highlights

To verify the effectiveness of the proposed pre-compensator for solving problems related to the non-minimum phase behavior of aircraft pitching up, the augmented dynamics of the open-loop system that produced the step responses with the proposed λ values of 0.1 to 0.9 of fractional integral and with the effects of the integral gain, K I are examined without the impact of the linear quadratic regulator (LQR) controller
It can be concluded that the fractional-order derivative pre-compensator cannot convert the non-minimum phase dynamics to the minimum phase because of the high gains that are multiplied for a finite-dimensional rational filter when a fractional-order derivative is approximated for all μ values as presented in Appendix A, which drive the system to move in the wrong direction initially
It is observed that in all implementations with fractional order compensators (FIC and fractional-order derivative control (FDC)) and full state feedback control systems, the results proved all configurations under examination could ward off the adverse effects of non−minimum phase dynamics when analyzed in the time domain

Summary

Introduction

1958–2020 confirms that loss of flight control in flight (LOC-I) has the largest share of the causes of catastrophic accidents [1,2,3] This motivates researchers to develop effective control systems more in aviation-related studies due to the highly nonlinear nature of the aircraft dynamics and being more prone to perturbation and disturbances, which are among the obstacles that arise when designing robust flight control systems [4]. In this context, it is well known that non-minimum phase (NMP) dynamics are characterized by the right half plane (RHP) zeros that yield undesirable behavior, such as moving in the opposite direction first before correcting its direction. This can be seen in the tracking control problem, where the feedback controller can track the reference signal perfectly, but the system states can become unstable, which is referred to as the internal stability problem generated by non-minimum phase dynamics [6]

Objectives

Results

Conclusion