Switching LPV Control of an F-16 Aircraft via Controller State Reset

In flight control, the design objective and the aircraft dynamics may be different in low and high angle of attack regions. This paper presents a systematic switching Linear Parameter-varying LPV method to determine if it is practical to use for flight control designs over a wide angle of attack region. The approach is based on multiple parameter-dependent Lyapunov functions a family of LPV controllers are designed, and each of them is suitable for a specific parameter subspace. The state of the controller is reset to guarantee the stability requirement of the Lyapunov function when the switching event occurs. Two parameter-dependent switching logics, hysteresis switching and switching with average dwell times are examined. The proposed switching LPV control scheme is applied to an F-16 aircraft model with different design objectives and aircraft dynamics in low and high angle of attack regions. The nonlinear simulating results using both switching logics are compared

Post-Stall Aerodynamic Modeling and Gain-Scheduled Control Design

A multidisciplinary research e.ort that combines aerodynamic modeling and gain-scheduled control design for aircraft flight at post-stall conditions is described. The aerodynamic modeling uses a decambering approach for rapid prediction of post-stall aerodynamic characteristics of multiple-wing con.gurations using known section data. The approach is successful in bringing to light multiple solutions at post-stall angles of attack right during the iteration process. The predictions agree fairly well with experimental results from wind tunnel tests. The control research was focused on actuator saturation and .ight transition between low and high angles of attack regions for near- and post-stall aircraft using advanced LPV control techniques. The new control approaches maintain adequate control capability to handle high angle of attack aircraft control with stability and performance guarantee

Gain-scheduled H∞ control via parameter-dependent Lyapunov functions

Synthesising a gain-scheduled output feedback H∞ controller via parameter-dependent Lyapunov functions for linear parameter-varying (LPV) plant models involves solving an infinite number of linear matrix inequalities (LMIs). In practice, for affine LPV models, a finite number of LMIs can be achieved using convexifying techniques. This paper proposes an alternative approach to achieve a finite number of LMIs. By simple manipulations on the bounded real lemma inequality, a symmetric matrix polytope inequality can be formed. Hence, the LMIs need only to be evaluated at all vertices of such a symmetric matrix polytope. In addition, a construction technique of the intermediate controller variables is also proposed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameters. Computational results on a numerical example using the approach were compared with those from a multi-convexity approach in order to demonstrate the impacts of the approach on parameter-dependent Lyapunov-based stability and performance analysis. Furthermore, numerical simulation results show the effectiveness of these proposed techniques

비대칭 가변스팬 모핑 무인 항공기의 자체스케줄 파라미터 가변 제어

학위논문(박사) -- 서울대학교대학원 : 공과대학 기계항공공학부, 2023. 2. 김유단.In this dissertation, a novel framework for flight control of a morphing unmanned aerial vehicle (UAV) is proposed. The proposed method uses asymmetric span morphing for lateral-directional motion control considering the dynamic characteristics of the morphing actuators while exploiting the advantages of symmetric span morphing for longitudinal flight performance enhancement. The proposed control system is self-scheduled based on linear parameter-varying (LPV) methods, which guarantees stability and performance for the variations of the morphing configuration and the flight condition. Therefore, the morphing UAV is allowed to swiftly metamorphose into the optimal configuration to maximize the system-level benefit according to the maneuvering command and the flight condition. First, a high-fidelity nonlinear model of an asymmetric variable-span morphing UAV is obtained from the NASA generic transport model. The impacts of morphing on the center of mass, inertia matrix, and aerodynamic coefficients are modeled based on the asymmetrically damaged wing model. The span variation ratios of the left and right wings are decomposed into symmetric and asymmetric morphing parameters, which are considered as the scheduling parameter and the control input, respectively. The nonlinear model is decoupled and linearized to obtain point-wise linear time-invariant (LTI) models for the longitudinal and lateral-directional motions throughout the grid points over the entire rectangularized scheduling parameter domain. The LPV model of the morphing UAV is derived for the longitudinal and lateral-directional motions by associating the family of LTI models through interpolation. Second, the longitudinal and lateral-directional control augmentation systems are designed based on LPV methods to track the normal acceleration command and the angle of sideslip and the roll rate commands, respectively. The inherent dynamic characteristics of the morphing actuator, such as low bandwidth, are considered in the control design procedure through a frequency-dependent weighting filter. The span morphing strategy to assist the intended maneuver is studied considering the impacts of morphing on various aspects. Numerical simulations are performed to demonstrate the effectiveness of the proposed control scheme for pushover-pullup maneuver and high-g turn. Finally, the longitudinal and lateral-directional autopilots are designed based on LPV methods to track the airspeed and altitude commands and the angle of sideslip and roll angle commands, respectively. A nonlinear guidance law is coupled with the autopilots to enable three-dimensional trajectory tracking. Numerical simulation results for the trajectory-tracking flight show that the proposed controller shows satisfactory performance, while the closed-loop system using the conventional gain-scheduled controller may lose stability when the scheduling parameter varies rapidly or widely.본 논문에서는 모핑 무인 항공기(unmanned aerial vehicle: UAV)의 비행 제어를 위한 새로운 프레임워크가 제안된다. 제안된 기법은 모핑 구동기의 동적 특성을 고려한 횡방향축(lateral-directional) 운동 제어를 위해 비대칭 스팬 모핑을 사용하고 종축(longitudinal) 비행 성능 향상을 위해 대칭 스팬 모핑의 이점을 활용한다. 또한 설계된 제어 시스템은 선형 파라미터 가변(linear parameter-varying: LPV) 기법을 기반으로 제어기 이득이 자체적으로 스케줄링 되며 모핑 형상 및 비행 조건의 임의의 변화에 대해 안정성과 성능을 엄밀하게 보장한다. 따라서 모핑 UAV는 기동 명령과 비행 조건에 따라 안정성을 상실할 우려 없이 시스템 수준의 이점을 극대화하는 동시에 내부 루프 안정화를 위한 제어에 기여하도록 최적의 형상으로 신속하게 변형될 수 있다. 첫째, NASA GTM(generic transport model)으로부터 비대칭 가변 스팬 모핑 UAV의 고충실도(high-fidelity) 비선형 모델이 획득된다. 모핑이 질량 중심, 관성 행렬 및 공기역학 계수에 미치는 영향은 날개가 비대칭적으로 손상된 모델을 기반으로 도출된다. 좌우 날개의 스팬 변화율은 대칭 및 비대칭 모핑 파라미터로 분해되며, 두 모핑 파라미터는 각각 스케줄링 파라미터 및 제어 입력으로 간주된다. 비선형 모델을 종축 및 횡방향축 운동으로 분리하고 직사각형 형태의 스케줄링 파라미터 영역의 각 격자점에서 선형화함으로써 각 점에 대한 선형 시불변(linear time-invariant: LTI) 모델이 얻어진다. LTI 모델 집합에 보간(interpolation)을 적용하면 종축 및 횡방향축 운동에 대한 모핑 UAV의 LPV 모델이 얻어진다. 둘째, 수직 가속도(normal acceleration) 명령과 옆미끄럼각(angle of sideslip) 및 롤 각속도 명령 추종을 위해 LPV 기법을 기반으로 종축 및 횡방향축 제어 증강 시스템(control augmentation system)이 설계된다. 이때, 제어 설계 과정에서 주파수종속(frequency-dependent) 가중치 필터를 통해 낮은 대역폭(bandwidth)과 같은 모핑 구동기 고유의 동적 특성이 고려된다. 또한 비행 특성에 대한 모핑의 다양한 영향을 고려하여 실행하고자 하는 기동을 보조하기 위한 스팬 모핑 전략이 논의된다. Pushover-pullup 기동 및 high-g turn에 대한 수치 시뮬레이션 결과를 통해 제안된 기법이 타당함을 확인할 수 있다. 마지막으로, 대기속도(airspeed) 및 고도 명령과 옆미끄럼각 및 롤 각 명령을 추종하기 위해 LPV 기법을 기반으로 종축 및 횡방향축 자동 조종 장치(autopilot)가 설계된다. 이때, 3차원 경로 추종을 위해 비선형 유도 법칙이 자동 조종 장치와 결합된다. 경로 추종 비행에 대한 수치 시뮬레이션 결과를 통해 스케줄링 파라미터의 변화 속도가 빠르거나 변화의 폭이 넓은 경우 일반적인 이득스케줄 제어기는 안정성을 상실할 수 있는 반면 제안된 기법은 만족할 만한 성능을 유지함을 확인할 수 있다.1 Introduction 1 1.1 Background and Motivation 1 1.2 Literature Review 6 1.2.1 Fixed-Wing Aircraft Implementing Morphing Technologies 6 1.2.2 Flight Control of Morphing Aircraft 7 1.2.3 Gain Scheduling Approaches to Controller Design 7 1.3 Objectives and Contributions 9 1.3.1 Objectives 9 1.3.2 Contributions 9 1.4 Dissertation Outline 11 2 Mathematical Preliminaries 13 2.1 LPV Systems 15 2.1.1 Taxonomy of Dynamical Systems 15 2.1.2 Definition of LPV Systems 15 2.1.3 LPV Modeling by Linearization 20 2.2 Gain Self-Scheduled Induced L2-Norm Control of LPV Systems 25 2.2.1 Norms of Signals and Systems 25 2.2.2 Analysis of LPV Systems 26 2.2.3 LPV Controller Design 30 2.2.4 Software for Synthesis and Analysis 30 3 Asymmetric Variable-Span Morphing UAV Model 33 3.1 Nonlinear Model of a Morphing UAV 36 3.1.1 Nominal Model of a Baseline Model 36 3.1.2 Morphing UAV Model 41 3.2 Derivation of an LPV Model of a Morphing UAV 52 3.2.1 Trim Analysis and Scheduling Parameter Selection 52 3.2.2 Pointwise Linearization of a Nonlinear Model 55 3.2.3 Linear Parameter-Varying Modeling and Analysis 58 4 CAS Design Based on LPV Method for Morphing-Assisted Maneuvers 61 4.1 Longitudinal CAS Design for Normal Acceleration Control 65 4.1.1 Performance Specifications 65 4.1.2 Controller Synthesis and Analysis 68 4.2 Lateral-Directional CAS Design for Turn Coordination and Roll Rate Control 73 4.2.1 Performance Specifications 73 4.2.2 Controller Synthesis and Analysis 75 4.3 Span Morphing Strategy 83 4.3.1 Effects of Span Morphing 83 4.3.2 Criteria for Span Variation 85 4.4 Nonlinear Simulation of Morphing-Assisted Maneuvers 86 4.4.1 High-Fidelity Flight Dynamics Simulator 86 4.4.2 Push-over and Pull-up 86 4.4.3 High-g Turn 89 5 Autopilot Design Based on LPV Methods for Morphing-Assisted Flights 109 5.1 Longitudinal Autopilot Design for Airspeed and Altitude Control 111 5.1.1 Performance Specifications 111 5.1.2 Controller Synthesis and Analysis 113 5.2 Lateral-Directional Autopilot Design for Turn Coordination and Roll Angle Control 121 5.2.1 Performance Specifications 121 5.2.2 Controller Synthesis and Analysis 123 5.3 Nonlinear Guidance Law for Trajectory Tracking 131 5.4 Nonlinear Simulation of Morphing-Assisted Flights 132 5.4.1 Waypoint Following at Low Altitude 132 5.4.2 Circular Trajectory Tracking at High Altitude 132 5.4.3 Helical Ascent under Fast Morphing 132 5.4.4 Spiral Descent with Morphing Scheduling 139 6 Conclusion 147 6.1 Concluding Remarks 147 6.2 Future Work 148박

Switching State-Feedback LPV Control with Uncertain Scheduling Parameters

This paper presents a new method to design Robust Switching State-Feedback Gain-Scheduling (RSSFGS) controllers for Linear Parameter Varying (LPV) systems with uncertain scheduling parameters. The domain of scheduling parameters are divided into several overlapped subregions to undergo hysteresis switching among a family of simultaneously designed LPV controllers over the corresponding subregion with the guaranteed H-infinity performance. The synthesis conditions are given in terms of Parameterized Linear Matrix Inequalities that guarantee both stability and performance at each subregion and associated switching surfaces. The switching stability is ensured by descent parameter-dependent Lyapunov function on switching surfaces. By solving the optimization problem, RSSFGS controller can be obtained for each subregion. A numerical example is given to illustrate the effectiveness of the proposed approach over the non-switching controllers

Fuzzy adaptive tracking control within the full envelope for an unmanned aerial vehicle

AbstractMotivated by the autopilot of an unmanned aerial vehicle (UAV) with a wide flight envelope span experiencing large parametric variations in the presence of uncertainties, a fuzzy adaptive tracking controller (FATC) is proposed. The controller consists of a fuzzy baseline controller and an adaptive increment, and the main highlight is that the fuzzy baseline controller and adaptation laws are both based on the fuzzy multiple Lyapunov function approach, which helps to reduce the conservatism for the large envelope and guarantees satisfactory tracking performances with strong robustness simultaneously within the whole envelope. The constraint condition of the fuzzy baseline controller is provided in the form of linear matrix inequality (LMI), and it specifies the satisfactory tracking performances in the absence of uncertainties. The adaptive increment ensures the uniformly ultimately bounded (UUB) predication errors to recover satisfactory responses in the presence of uncertainties. Simulation results show that the proposed controller helps to achieve high-accuracy tracking of airspeed and altitude desirable commands with strong robustness to uncertainties throughout the entire flight envelope

A novel design approach for switched LPV controllers

A novel design procedure for switched linear parameter-varying (LPV) controller is proposed. The new procedure, based on the Youla parameterisation ideas, decomposes the controller design into two steps. One focuses on ensuring global stability and the other on fulfilling the local performance specifications. This scheme allows the design of each local controller independently of each other, which may achieve higher performance without compromising the global stability and also simplifies the synthesis and the implementation of the local controllers. Any standard LPV synthesis procedure can be used to design these controllers. On the other hand, the stability during switching is ensured with convex constraints and no restrictions are imposed on the switching among controllers. The use of the proposed procedure is illustrated with an active magnetic bearing example.Fil: Bianchi, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Politécnica de Catalunya; EspañaFil: Sanchez Peña, Ricardo Salvador. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto Tecnológico de Buenos Aires; Argentin

Filtering for nonlinear genetic regulatory networks with stochastic disturbances

In this paper, the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays, where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition, the stochastic perturbation is in the form of a scalar Brownian motion, and the time delays exist in both the translation process and the feedback regulation process. The purpose of the addressed filtering problem is to estimate the true concentrations of the mRNA and protein. Specifically, we are interested in designing a linear filter such that, in the presence of time delays, stochastic disturbances as well as sector nonlinearities, the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta. By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model, and the filter gain is then characterized in terms of the solution to an LMI, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures

Hypersurface normalised gain-scheduled controller for a non-linear 6-DOF fast jet

This paper describes a novel approach for improving the dynamic response of a bank-to-turn autopilot for a non-linear six degree-of-freedom (6-DoF) aircraft model. The autopilot consists of a series of gain-scheduled (GS) proportional, integral and derivative (PID) controllers that govern the aircraft's angular velocities for roll, pitch and yaw. The controller gains have been optimised for localised trim points and applied continuously to the controllers using linear interpolation to form a hypersurface. Our novel solution has been achieved by implementing a set of scheduled gains for near-zero reference signals and integrating this with a set of gains that are normalised to the reference signal. The proposed approach has been compared to conventional gain scheduling techniques using a series of step input simulated manoeuvres, applied individually to the roll and pitch controllers. The results show improved rise and fall times, steady state errors, as well as reduced controller effor

Robust Adaptive Control of Linear Parameter-Varying Systems with Unmatched Uncertainties

This paper presents a robust adaptive control solution for linear parameter-varying (LPV) systems with unknown input gain and unmatched nonlinear (state- and time-dependent) uncertainties based on the $\mathcal{L}_1$ adaptive control architecture and peak-to-peak gain (PPG) analysis/minimization from robust control. Specifically, we introduce new tools for stability and performance analysis leveraging the PPG bound of an LPV system that is computable using linear matrix inequality (LMI) techniques. A piecewise-constant estimation law is introduced to estimate the lumped uncertainty with quantifiable error bounds, which can be systematically improved by reducing the estimation sampling time. We also present a new approach to attenuate the unmatched uncertainty based on the PPG minimization that is applicable to a broad class of systems with linear nominal dynamics. In addition, we derive transient and steady-state performance bounds in terms of the input and output signals of the actual closed-loop system as compared to the same signals of a virtual reference system that represents the possibly best achievable performance. Under mild assumptions, we prove that the transient performance bounds can be uniformly reduced by decreasing the estimation sampling time, which is subject only to hardware limitations. The theoretical development is validated by extensive simulations on the short-period dynamics of an F-16 aircraft