Linear Approximation to Optimal Control Allocation for Rocket Nozzles with Elliptical Constraints

In this paper we present a straightforward technique for assessing and realizing the maximum control moment effectiveness for a launch vehicle with multiple constrained rocket nozzles, where elliptical deflection limits in gimbal axes are expressed as an ensemble of independent quadratic constraints. A direct method of determining an approximating ellipsoid that inscribes the set of attainable angular accelerations is derived. In the case of a parameterized linear generalized inverse, the geometry of the attainable set is computationally expensive to obtain but can be approximated to a high degree of accuracy with the proposed method. A linear inverse can then be optimized to maximize the volume of the true attainable set by maximizing the volume of the approximating ellipsoid. The use of a linear inverse does not preclude the use of linear methods for stability analysis and control design, preferred in practice for assessing the stability characteristics of the inertial and servoelastic coupling appearing in large boosters. The present techniques are demonstrated via application to the control allocation scheme for a concept heavy-lift launch vehicle

Sensitivity Analysis of Linear Programming and Quadratic Programming Algorithms for Control Allocation

The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming

Optimal fault-tolerant flight control for aircraft with actuation impairments

Current trends towards greater complexity and automation are leaving modern technological systems increasingly vulnerable to faults. Without proper action, a minor error may lead to devastating consequences. In flight control, where the controllability and dynamic stability of the aircraft primarily rely on the control surfaces and engine thrust, faults in these effectors result in a higher extent of risk for these aspects. Moreover, the operation of automatic flight control would be suddenly disturbed. To address this problem, different methodologies of designing optimal flight controllers are presented in this thesis. For multiple-input multiple-output (MIMO) systems, the feedback optimal control is a prominent technique that solves a multi-objective cost function, which includes, for instance, tracking requirements and control energy minimisation. The first proposed method is based on a linear quadratic regulator (LQR) control law augmented with a fault-compensation scheme. This fault-tolerant system handles the situation in an adaptive way by solving the optimisation cost function and considering fault information, while assuming an effective fault detection system is available. The developed scheme was tested in a six-degrees-of-freedom nonlinear environment to validate the linear-based controller. Results showed that this fault tolerant control (FTC) strategy managed to handle high magnitudes of the actuator’s loss of effciency faults. Although the rise time of aircraft response became slower, overshoot and settling errors were minimised, and the stability of the aircraft was maintained. Another FTC approach has been developed utilising the features of controller robustness against the system parametric uncertainties, without the need for reconfiguration or adaptation. Two types of control laws were established under this scheme, the H∞ and µ-synthesis controllers. Both were tested in a nonlinear environment for three points in the flight envelope: ascending, cruising, and descending. The H∞ controller maintained the requirements in the intact case; while in fault, it yielded non-robust high-frequency control surface deflections. The µ-synthesis, on the other hand, managed to handle the constraints of the system and accommodate faults reaching 30% loss of effciency in actuation. The final approach is based on the control allocation technique. It considers the tracking requirements and the constraints of the actuators in the design process. To accommodate lock-in-place faults, a new control effort redistribution scheme was proposed using the fuzzy logic technique, assuming faults are provided by a fault detection system. The results of simulation testing on a Boeing 747 multi-effector model showed that the system managed to handle these faults and maintain good tracking and stability performance, with some acceptable degradation in particular fault scenarios. The limitations of the controller to handle a high degree of faults were also presented

An Innovative Control Allocation Scheme to Address Reaction Thruster Interactions on a 3U CubeSat

A wealth of literature exists on control allocation algorithms for over-actuated air vehicles, launch vehicles, and spacecraft's. Most of these algorithms focus primarily on minimizing some objective function such as command tracking error and/or control effector usage. Linear allocators (pseudo inverses) are usually the conventional choice due to their simplicity and the ability to achieve a significant portion of the theoretical moment/impulse space. Generally, it is assumed that there exists minimal interaction effects between control effectors. In fact, very few studies address the problem of control effector interactions in the context of control allocation, especially for small spacecraft's with a reaction control system (RCS). This paper presents a CubeSat RCS design with a four thruster tetrahedral layout such that when two or more thrusters re, the resultant impulse differs noticeably compared to the sum of the contributions from individual thruster rings. This undesirable effect is caused by the design of the propellant tank and regulator. To mitigate this issue, an innovative modified pseudo inverse (MPI) control allocation algorithm was developed that adjusts the pseudo inverse solution based on test data. The algorithm is iteration-free and superior to the standard pseudo inverse in minimizing the command tracking error

A Framework for Optimal Control Allocation with Structural Load Constraints

Conventional aircraft generally employ mixing algorithms or lookup tables to determine control surface deflections needed to achieve moments commanded by the flight control system. Control allocation is the problem of converting desired moments into control effector commands. Next generation aircraft may have many multipurpose, redundant control surfaces, adding considerable complexity to the control allocation problem. These issues can be addressed with optimal control allocation. Most optimal control allocation algorithms have control surface position and rate constraints. However, these constraints are insufficient to ensure that the aircraft's structural load limits will not be exceeded by commanded surface deflections. In this paper, a framework is proposed to enable a flight control system with optimal control allocation to incorporate real-time structural load feedback and structural load constraints. A proof of concept simulation that demonstrates the framework in a simulation of a generic transport aircraft is presented

An investigation of control allocation methods for the ADMIRE simulation model

This paper presents a comparative study of various control allocation methods, using ADMIRE as a benchmark simulation model. The Ganged Pseudo-Inverse, Weighted Pseudo-Inverse, Cascaded Generalized-Inverse, Daisy Chain, and Linear Programming approaches are evaluated and compared against each other using open loop and closed loop analysis with Euclidean-Norm. In open-loop analysis, control allocation methods are analyzed for each approach that can produce an admissible solution and be able to attain commanded moments. Then, in closed-loop analysis, control allocation methods are compared using ADMIRE nonlinear simulation model for predefined maneuvers which are defined by multiple points in the flight envelope

Dynamic Inversion-Based Control Concept for Transformational Tilt-Wing eVTOLs

Transformational electric vertical take-off and landing (eVTOL) vehicles, including tiltwings, have (re)gained popularity over the past decade owing to their advantages of efficient wing-borne cruise flight and reduced requirements on ground-based infrastructure. They promise a new mode of transportation for fast and versatile, short-to-medium-haul on-demand connections. However, they come at the cost of complex mechanics, flight dynamics, and aerodynamics. Among these factors, the different flight regimes and the transition between them make the control system design challenging. Ideally, a flight control system provides means for pilot interaction, autoflight functions, robustness to disturbances, and failure mitigation. The different flight regimes with distinct flight dynamics in a single vehicle motivate a holistic approach. So far, no control approach has prevailed, which raises the question of how to design a control concept that satisfies the above requirements for the full flight envelope. To solve this problem, we derive a generalized representation for transformational eVTOLs and propose a flight control approach for this system, consisting of a dynamic-inversion-based angular rate and velocity control law. Moreover, combining these control functions with optimization-based control allocation is motivated and presented. Finally, the concept is applied to a tandem tilt-wing configuration and analyzed. Results suggest the practicability of the proposed control approach

A Flight Dynamics Model for a Multi-Actuated Flexible Rocket Vehicle

A comprehensive set of motion equations for a multi-actuated flight vehicle is presented. The dynamics are derived from a vector approach that generalizes the classical linear perturbation equations for flexible launch vehicles into a coupled three-dimensional model. The effects of nozzle and aerosurface inertial coupling, sloshing propellant, and elasticity are incorporated without restrictions on the position, orientation, or number of model elements. The present formulation is well suited to matrix implementation for large-scale linear stability and sensitivity analysis and is also shown to be extensible to nonlinear time-domain simulation through the application of a special form of Lagrange s equations in quasi-coordinates. The model is validated through frequency-domain response comparison with a high-fidelity planar implementation

Backstepping-based Super-Twisting Sliding Mode Control for a Quadrotor Manipulator with Tiltable Rotors

Designing a robust controller is very important in the control of outdoor unmanned aerial vehicles. This paper presents the design procedures and implementation of super-twisting sliding mode controller, which is a robust nonlinear controller. The robust controller is applied to an over-actuated quadrotor manipulator with four tiltable rotors. A serial manipulator with two links is mounted on the bottom of the quadrotor. The quadrotor possesses the property of decoupling its position and orientation. The main contribute of this paper is that a super-twisting sliding mode controller in vector form is designed and applied to the control of an over-actuated quadrotor manipulator. Another contribution of this paper is that the stability of the closed-loop system is proved by utilizing the Lyapunov stability theory. It is confirmed that the performance of the super-twisting sliding mode controller is superior to that of the conventional backstepping controller in terms of convergence rate and accuracy by simulations

Flight crew aiding for recovery from subsystem failures

Some of the conceptual issues associated with pilot aiding systems are discussed and an implementation of one component of such an aiding system is described. It is essential that the format and content of the information the aiding system presents to the crew be compatible with the crew's mental models of the task. It is proposed that in order to cooperate effectively, both the aiding system and the flight crew should have consistent information processing models, especially at the point of interface. A general information processing strategy, developed by Rasmussen, was selected to serve as the bridge between the human and aiding system's information processes. The development and implementation of a model-based situation assessment and response generation system for commercial transport aircraft are described. The current implementation is a prototype which concentrates on engine and control surface failure situations and consequent flight emergencies. The aiding system, termed Recovery Recommendation System (RECORS), uses a causal model of the relevant subset of the flight domain to simulate the effects of these failures and to generate appropriate responses, given the current aircraft state and the constraints of the current flight phase. Since detailed information about the aircraft state may not always be available, the model represents the domain at varying levels of abstraction and uses the less detailed abstraction levels to make inferences when exact information is not available. The structure of this model is described in detail