Autonomous Aircraft

Autonomous functioning via real-time monitoring and information management is an attractive ingredient in the design of any complex system. The inevitable presence of uncertainties due to malfunctions, environmental variations, ageing, and modeling errors, requires this management to be adaptive. Several projects are ongoing in the area of autonomous flight platforms and analysis, and are listed below.

Hypersonics

Current hypersonic control and modeling research efforts are being conducted between the Air Force Research lab (AFRL), the University of Michigan and the Massachusetts Institute of Technology (MIT) under the Michigan/AFRL Collaborative Center in Control Science (MACCCS, or MAX) program. MIT will focus on exploring technologies for flight control of highly uncertain air breathing hypersonic vehicles performing complex maneuvers using a 6-DOF simulation.

MAX at MIT

ghv Control of Hypersonic vehicles is an extremely challenging task due to the largely varying operating conditions taking place during flight envelope. Due to the significant changes that occur in the aerodynamics, propulsion, and environmental conditions, and due to the fact that both physics-based models and data-driven models are either inaccurate or too complex, any feedback controller that is introduced in the vehicle has to be suitably advanced. The sophistication in this controller has to be two-fold: first, it has to accommodate the large changes that occur in the vehicle dynamics by incorporating self-adaptive components that have the ability to make on-line changes based on the newly available system measurements. Second, it should possess the ability to ascertain the dynamics that exists at a given operating point and provide a robust compensatory action that ensures safe realization of desired Figures of Merit.

Current hypersonic control and modeling research efforts are being conducted between the Air Force Research lab (AFRL), the University of Michigan and the Massachusetts Institute of Technology (MIT) under the Michigan/AFRL Collaborative Center in Control Science (MACCCS, or MAX) program. MIT will focus on exploring technologies for flight control of highly uncertain air breathing hypersonic vehicles performing complex maneuvers using a 6-DOF simulation.

MIMO Output Feedback Adaptive Control for Hypersonic Vehicles

A state feedback LQR baseline controller with integral action and augmented with an adaptive component has proven to be an effective choice for accommodating the parametric uncertainties present in flight control applications, and ensuring satisfactory reference tracking. However, such a controller requires that the state is measurable, which is not always possible. Also, inaccuracies in the system output measurements may render state feedback controllers sensitive and thus not applicable. For these reasons there has been an increasing drive to develop an adaptive output feedback extension of the robust integral-augmented LQR baseline plus adaptive controller.

Existing classical methods of multi-input multi-output adaptive control are applicable for plants that are square. An m x m transfer matrix is used to represent the dynamic behavior of the plant, and the existence of a stable adaptive solution depends on the available prior information about this plant transfer matrix. The solution relies on non-minimal controller representations to dynamically decouple the plant, and the controller structure consists of a feedforward gain and two filters in the feedback path, the order of which depends on m and an upper bound on the observability index of the plant, v. The resulting classical MIMO adaptive solution will introduce 2mv controller states and 2m^2v adjustable parameters.

More recent methods of MIMO output feedback adaptive control have adopted a Luenberger observer-based approach in which a minimal observer is used to generate a state estimate to use for feedback control. This observer also serves as the reference model which is used by the adaptive controller, and the presence of the observer feedback gain L provides the structure known as the closed-loop reference model, or CRM. These CRM based approaches have relied on the so-called squaring-up procedure to add fictitious inputs to a tall system, making it square and ensuring any transmission zeros are stable. These fictitious inputs are used only to synthesize a postcompensator S1 and the CRM gain L which ultimately render a set of underlying error dynamics strictly positive real (SPR). These SPR error dynamics allowed stable update laws to be chosen to guarantee system stability. We note that systems with transmission zeros cannot be squared up using the existing method, which has led to a recent modification to overcome this limitation and allow the design of output feedback controllers for systems with stable transmission zeros.

Our recent work on output feedback adaptive control has taken alternative approach to synthesizing S1 and L which does not require the system first be squared-up. Instead, the postcompensator S1 is determined as a generalized inverse of the system matrices, and a state feedback approach is used to stabilize a related lower order plant subsystem resulting in a feasible LMI which is solved to yield L. We consider in this work the case of tall systems, but the case of wide systems holds by duality. Furthermore, because L is a component of both the baseline and adaptive controllers, it is crucial that it be selected to provide good frequency domain properties for the baseline control system, as well as desirable adaptive control performance. This procedure is able to exploit the structure of the given system to obtain a large amount of freedom in the selection of L in order to achieve a robust baseline control design and the desired adaptive performance.


Very Flexible Aircraft

Vulture

vulture High-altitude long-endurance flight (HALE) challenge is first proposed in 1950s for the purpose of military surveil- lance. Special aircraft such as SR-71 in 1970s and Global Hawk in more recent date were developed to meet the chal- lenge1. Those aircraft run on conventional fossil oil and cannot achieve real long-endurance flight. In the last decade, HALE challenge evolves into a scientific research program, and platforms with renewable power source, such as solar energy, was investigated. Possible platform features a huge wingspan to host a large amount of solar panels. Daedalus and Helios are two successful attempts in this category and both were able to climb to a record-breaking altitude with stretched operation hours2,3. For this kind of aircraft, power limited energy source only allows small propellers as thrust, which in turn results into low cruise speed (less than 50mph). As a result, payload is limited. Very light material, such as epoxy and carbon fiber, has to be used on wings. Long slender wing with low-yield material results into a flexible structure. In fact, the flexible effect on the wing is so significant that the wing is visibly deforming when load varies. Figure 1a shows that the wing of Helios deforms into a ā€œVā€ shape when the aircraft is climbing.

Helios is an example of aerial platforms denoted as Very Flexible Aircraft (VFA) which corresponds to those whose trim critically depends on flexible modes4,5. One of the challenges that VFA introduces is a significant change in the rigid-body dynamics as the wing morphs. For example, the pitch (short period) mode of VFA can become unstable when wing dihedral is trimmed at a high value4. As a consequence, control designs based on rigid-body dynamics only may face unexpected adversities. An example of this adversity occurred in 2003 during the second test flight of Helios when a sequence of events took place: the wind turbulence drove the wing to a high dihedral position; flexible effects of wing fought against control and sustains the high dihedral for a long period of time; unstable pitch mode eventually grew unbounded, which causes airspeed exceeding design limit and structure disintegration. The lesson that was learned from the mishap is that the model for control design has to include body flexible effects4.

Recently, a VFA platform, denoted as Vulture, has been under development to meet the goals of HALE maneu- vers6. Vulture is an experimental aircraft with a huge wingspan of 400ft. The wing body consists of four slender wing segments and four booms. A high-fidelity 707 state model has been derived at a single trim point, with a large amount of body flexible modes6. The goal of this paper is to develop an adaptive controller using this model, accommodate uncertainties that typically occur in a VFA, and carry out desired maneuvers despite the large flexible modes present.

Helios

Analysis on the VFA model show that there are two dominant types of uncertainties that can affect the flight dynamics significantly. The first type of uncertainty is the additive control effectiveness change caused by morphing wing (trim drift). The second type of uncertainty is the multiplicative control effectiveness change caused by actuator anomalies. Both effects can be modeled as parametric uncertainties in the underlying plant model.

Adaptive control outline

Figure: The challenge of VFA control design, a state-inaccessible plant with a large amount of uncertainties (as represented by Λ and Ψ*)

Presence of large parametric plant uncertainties motivates an adaptive control solution.

Adaptive control outline

Figure: The classical LQG Controller is not able to accomodate unknown uncertainties (Λ and Ψ*) that are commonly seen in a VFA model

The theory developed in my recent research provides a decent adaptive control solution to a general multi-input-multi-output system, and therefore can be applied on VFA.



Theoretical Development of Adaptive Output-Feedback Control

Adaptive controller was renowned to handle parametric plant uncertainties. The idea of adaptive control is to compare system's real performance with an ideal reference performance and adjust the control action until the two coincide. It detects any performance-compromising faults right from the beginning of the action and reacts in a way such that the effect of faults are guaranteed to be compensated. However, current adaptive controller requires all plant states (x) are measurable, which is not the case for many plant models, especially VFA (only y available). These wing modes cannot be ignored either because of their significant effects on flight dynamics (as in Helios). Current adaptive control theory needs to be extended to be applicable on a state-inaccessible plant model. To this end, we propose a new model-reference-adaptive-control solution designated as, adaptive output-feedback control.

Adaptive control state-feedback

Figure: A new adaptive output-feedback controller is developed by introducing an additional parameter adaptation module on top of a LQG controller; the adaptive design can provably accomodate model uncertainties

The goal is to develop an adaptive controller for a general MIMO plant model. Innovatively, we proposed an observer-based method that generates state estimate (as a surrogate of states) for parameter adaptation, and achieves esitmate convergence and parameter adaptation simultaneously. In this way, we are able to overcome the inaccessibility of state measurements from the plant.

Unlike previous attempts to the problem, we provided a systematic way to design the controller in a step-by-step fashion, and also gave a rigorous proof for its stability and tracking performance. The overall method is simple, straightforward, instructive and self-contained.

To implement our method, one can keep the LQG controller structure and just add the adaptive component on top of it to perform adaptation. The major change is that the feedback gain L of the observer has to be redesigned as Lρ to satisfy an underlying strict-positive-real condition, for which we provided a closed-form analytical solution. By our design, the Lρ also has the robust property that a classical L has in a LQG controller (known as loop-transfer-recovery). As a result, our controller integrats two excellent controllers together and combine their benefits.

The resulting adaptive controller has two modes: When the adaptive module is off, the controller is a conventional linear controller (LQG-like with LTR properties); when the adatpive module is on, the controller becomes adaptive and robust to model uncertainties. The controller can switch between these two modes in real time seamlessly.


Flight Control Applications

Climb Control of 3-Wing VFA

2015 AIAA JGCD pre-print

The most important feature of a VFA is that its wing structure is so flexible that it cannot be considered as a rigid body. The most simplified illustration of the flexible wing is that three rigid wing sections with elastic pivot connections adjoining them. This wing model introduce an additional degree of freedom: the outer wings can rotate with respect to the center wing about longitudinal axis. The angle of such rotation is denoted as dihedral angle, and its dynamics is denoted as dihedral dynamics. The longitudinal and vertical acceleration dynamics of the 3-wing VFA is coupled with the dihedral dynamics.

3-W_VFA_Model

Figure: 3-Wing VFA model represents the essense of VFA dynamics, and can be viewed as building blocks of large VFA

The model represents a typical MIMO plant with limited measurements and actuation. It captures the essence of VFA dynamics and can be viewed as building blocks of large VFA model. The goal is to make the VFA to climb and dive (BTT), i.e. following a vertical acceleration command, while keeping the VFA oriented. The simulation results validate the performance of the adaptive system when the vehicle was subject to a large magnitude of actuator anomaly and plant uncertainties (6 deg dihderal change and 90% actuator effectivenss reduction).

Both baseline linear controllers suffer and lose stability in the middle of the simulation. Only adaptive controller is able to ensure stability and achieve command tracking.


Bank-to-Turn Control of Vulture VFA

2015 AIAA JGCD pre-print

This section describe the application of our adaptive output-feedback theory on a high-fidelity VFA model. Recently, a VFA platform, denoted as Vulture, has been under development to meet the goals of HALE maneuvers.

Vulture_Model

Figure: Vulture VFA model can be considered as hundreds of 3-wing VFA adjoining together

The VFA model represents a typical MIMO plant with limited measurements and actuation, and can be viewed as hundreds of 3-wing VFA adjoined together. The goal is to make the VFA bank to turn (BTT), i.e. tracking a roll angle command, while keeping the VFA oriented. The details of problem statement can be found here. The simulation results validate the performance of the adaptive system when the vehicle was subject to a large magnitude of actuator anomaly and plant uncertainty (10ft dihderal change and 50% actuator magnitude surge).

The figure below presents a segement of the simulation to illustrate the mechanism of the adaptive controller. It clearly shows that the adaptive controller not only stabilize the system but also achieve ideal performance, while LQR controller suffers in performance and LQG controller suffers in stability. The success of adaptive controller roots from its underlying principle: compare system's real performance with ideal reference performance from the very beginning and adjust control action accordingly until the two become same.

Adaptive control outline

Figure: The underline principle of the adaptive controller: compare actual performance with an ideal reference performance and actively tune the control gain until the two become identical