Design a variable stability systems with nonlinear and linear approaches for a continuous flight envelope

Abstract

In this thesis, control architectures for a Variable Stability System (VSS) or Variable Stability Aircraft are studied for an open-source jet aircraft. As a nonlinear control approach, nonlinear dynamic inversion is employed, while linear control techniques are applied in the form of pole placement for the longitudinal axis and eigenstructure assignment for the lateral/directional axes. In addition, model stitching and gain scheduling techniques are implemented for the guest aircraft by utilizing linearized systems across the flight envelope. Finally, a mode transition switch is designed in order to provide flight safety requirements. In the first chapter, a comprehensive review of the scientific literature related to Variable Stability Systems (VSS) is presented. The motivation behind the emergence of variable stability systems, their adaptation to aircraft, and the historical development of adaptation methodologies are discussed in chronological order. The primary objective became the improvement of pilot-perceived dynamics by directly feeding back selected flight responses of the aircraft known as response feedback. As a result, it became possible to obtain the guest aircraft responses rather than the inherent dynamics of the host aircraft. However, this approach was found to be insufficient due to several factors. With the mathematical maturation of the state-space framework, implicit model-following control methods were introduced. Although implicit model-following methods provided higher accuracy compared to response feedback in multivariable systems, they were considered inadequate in eliminating the effects of nonlinearities on flight responses and in accurately reproducing the guest aircraft behavior. Subsequently, with the advancement of nonlinear dynamic inversion and feedback linearization theories, explicit model-following control approaches were adopted for aircraft equipped with variable stability systems. In this thesis, a variable stability aircraft is developed using both linear and nonlinear control laws, and its capability to replicate the responses of the guest aircraft is investigated through various flight test methodologies. In the second chapter, an open-source jet aircraft is introduced. This aircraft is designated as the host aircraft. The modeled aircrafts include the leading-edge flap, coordinate reference frames, actuator model, equations of motion, atmospheric model, aerodynamic model, and the propulsion model. The atmospheric model comprises the fundamental equations used to determine dynamic pressure, speed of sound, and atmospheric gravitational acceleration. The propulsion system is simplified to represent military and maximum thrust levels. Actuator dynamics are modeled using first-order transfer functions. The leading-edge flap is incorporated into the integrated model in order to represent the aircraft with higher fidelity under varying flight conditions. At this stage, the aerodynamic model is formulated based on a wind tunnel report published by NASA. The aerodynamic model is constructed without manipulations to accurately represent the host aircraft. To obtain the guest aircraft model, several manipulations are applied into the aerodynamic data. Through these manipulations, the dynamic behavior of the guest aircraft is intentionally differentiated from that of the host aircraft in both the time and frequency domains. The expected differences are validated in the third chapter. Following the introduction of these differences, the aircraft equipped with the variable stability system is defined as the host aircraft, while the aircraft with manipulated aerodynamic data is defined as the guest aircraft. Finally, a three-axis control architecture for the jet aircraft is developed as presented in the NASA report. The third chapter addresses trim point and linearization techniques. The equilibrium point search is restricted only to straight and steady state level flight conditions. To find the trim, Newton–Raphson algorithm is employed. The methodology is verified through time-domain responses. For linearization, small perturbation theory is applied individually to the input and state variables about the selected equilibrium point at a fixed altitude and airspeed. For control system design purposes, the state variables in each channel are identified and decomposed into longitudinal and lateral–directional channels. The time and frequency domain responses of the trimmed and linearized models for the different channels are presented. Subsequently, the trim and linearization procedures are applied separately to both the host and guest aircraft models at the same trim condition, and the corresponding responses are analyzed in the time and frequency domains. In this manner, the distinct dynamic behaviors targeted in the second chapter are observed to be achieved. Finally, the accuracy of the linearization approach is validated by comparing the time-domain responses of the nonlinear and linearized model. In the first part of the fourth chapter, nonlinear control design technique is introduced for the development of a variable stability system both guest and host aircrafts. The scope of thesis, the model stitching approach is selected to represent guest aircraft dynamics over a wide and continuous flight envelope. Initially, the model stitching approach is designed in a one-dimensional structure at a single altitude as a function of airspeed across the flight envelope. To achieve a continuous flight envelope representation, the model stitching approach is subsequently extended to a two-dimensional formulation dependent on both altitude and airspeed. Finally, the nonlinear controller developed in the second chapter is integrated into the stitched model structure, enabling closed-loop model stitching. As a result, closed-loop stitched guest model is accurately represented the nonlinear guest aircraft. For the host aircraft, nonlinear control methods are presented and NDI is selected as the primary approach. The NDI methodology applied by following several steps: control variables selection, onboard model, and outer-loop controller. The mathematical foundation of the NDI method is presented to establish the theoretical basis of the study. Body-axis angular rate variables are chosen as a control variables for this study. The derivation of the onboard model, which represents the most critical step for achieving effective dynamic inversion, is explained in detail. The corresponding mathematical expressions are derived for the host aircraft, and the performance of the NDI scheme is evaluated. For validation purposes, the desired angular rate commands are applied to the system. The required control surface deflections are obtained through the NDI to achieve the desired angular rates. As a result, the inherent dynamics of the host aircraft are effectively canceled, and achieved the desired angular rates. An outer-loop controller architecture is introduced to mitigate errors and uncertainties arising from onboard model. A proportional–integral (PI) control strategy is adopted for the outer loop. The inclusion of the outer-loop controller is shown to improve the performance of NDI in the presence of system uncertainties. Subsequently, the guest aircraft model generated via model stitching and the host aircraft controlled via NDI architectures are combined. It is demonstrated that, the host aircraft successfully follows the dynamic responses of the guest aircraft. In the second part of the fourth chapter, a linear control approach is presented which is, also referred to as an implicit model-following (IMF) control method. The IMF is implemented using pole placement in the longitudinal axis. In the first step, the guest aircraft model is linearized in the longitudinal channel with respect to the body-axis variables. Subsequently, using the rotational matrices, a linearized structure expressed in terms of angle of attack and true airspeed is obtained due to practical application considerations. The same procedure is repeated for the host aircraft. The derived systems for the host aircraft have a single control input corresponding to the horizontal tail deflection. The method is used to assign the eigenvalues of the host aircraft to those of the guest aircraft. Guest aircraft dynamic behaviors are successfully reflected by the closed-loop structure the host aircraft under linearized conditions by computed gains. When the same approach is applied to the lateral–directional axis, which has two control inputs corresponding to the aileron and rudder, the limitations of the pole placement method are revealed. Although, eigenvalues are assigned correctly, it is shown that the methodology is insufficient for controlling all four state variables using only eigenvalue matching with two control inputs since the system is MIMO. This observation leads to the requirement of assigning not only eigenvalues but also eigenvectors of the host aircraft to those of the guest aircraft. Consequently, the eigenstructure assignment method is adopted, and it is demonstrated that the host aircraft successfully tracks the guest aircraft responses in the lateral–directional channel. Moreover, since linear controller design is performed at a single operating point, it is insufficient to represent a continuous flight envelope. Therefore, gain scheduling is employed to extend the applicability of the linear control approach. The resulting gain values are presented as functions of altitude and airspeed. As the final study in the fourth chapter, a mode transition switching algorithm is detailed. The algorithm is widely used in industrial applications and defined as a flight-safety-enhancing function. Mode transitions are demonstrated by switching between two predefined modes, verifying the suitability of the proposed algorithm. The switching strategy is incorporated into both variable stability system architectures developed in this study. The objective is safe transitions between the baseline operational mode namely, nominal mode and the variable stability controller referred as VSS mode for the host aircraft. In the final chapter, two different variable stability controller architectures are evaluated through a set of defined flight maneuvers, and the corresponding simulation results are presented. These test cases include mode transition switching, doublet inputs, frequency sweep, tracking tasks, and carefree handling qualities evaluations. These test cases are applied to both variable stability system configurations. The resulting responses are discussed. Finally, the thesis is concluded with a section that outlines recommendations for future work. In this study, AI tools are used to assist the research process.