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Nonlinear autopilot control design for a 2-DOF helicopter model
Abstract
Illustrates a robust control scheme for application to helicopters
in vertical flight mode (both take-off and landing) to guarantee
altitude stabilisation. A nonlinear helicopter model is used to derive
the proposed control in which Lyapunov's direct method is used to
establish the overall system stability. A recursive design technique is
applied to design a nonlinear robust controller using the highly coupled
system structure. It is shown that the proposed robust controller
provides semiglobal stabilisation of uniform ultimate boundedness for
achieving the desired altitude. That is, the control design is valid for
all values of the helicopter's collective pitch angle away from zero.
The vertical flight application demonstrates a unique robust control
mechanisation for helicopter and V/STOL autopilot augmentation systems
... The following system model shown in Fig. 1 is taken from [18], Equations (1)(2) show the differential equations model in which vertical altitude and rotational speed of rotors are written as, ...
... Where 1 , 2 are the throttle and collective inputs which is utilized to control the altitude and angle of MH. The marginal values of the system constraints are taken from [17][18][19] are described in Table 1. with angle and at times the gravitational effects in the system in neglected [18]. ...
... Where 1 , 2 are the throttle and collective inputs which is utilized to control the altitude and angle of MH. The marginal values of the system constraints are taken from [17][18][19] are described in Table 1. with angle and at times the gravitational effects in the system in neglected [18]. ...
Many agile software development practices are promoted to improve the quality of software products. In recent years agile software development overlooked the usability features that effected system productivity.Usability is a main feature of interaction. Interaction is a way of a farming relationship between people and designed objects. An interactive model provides the way to band application together to achieve target user’s need. Usability gained attention of researchers and engineers because of its own importance. Agile software methods and usability engineering played a major role for producing better and reliable products, because both of them are concepts of methods as well as practices. The purpose of this research was to highlight the need of usability practices. The proposed model demonstrates that usability heuristics were much compatible with agile methodologies and would help to improve its productivity by reducing time and cost. Action research was applied for the development of framework proposed. The framework was evaluated using case study and further results were compared with existing related work.
... Les auteurs de [29] présentent un modèle non linéaire de l'hélicoptère à 2DDL : Une autre utilisation de la commande par placement de pôles se trouve dans [31]. Dans [32][33], il a été proposé d'utiliser la théorie de la commande µ-Synthèse afin de contrôler un hélicoptère en mode de vol stationnaire. ...
... Les quatre solutions numériques de (4.26) pour le cas de l'hélicoptère VARIO sont : On peut aussi citer les techniques qui se basent sur la commande par la méthode de backstepping comme dans [80]. Dans [29], nous trouvons une application de la méthode directe de Lyapunov pour assurer la stabilité d'un modèle à 2 DDL de l'hélicoptère pour exécuter un vol vertical. ...
... Dans ce chapitre, nous avons développé un modèle non linéaire d'hélicoptère à 3 DDL perturbé par une rafale de vent verticale à partir du modèle non perturbé obtenu au chapitre a été abordé par [56], [78], qui, en utilisant le même modèle dynamique proposé par [55], ont proposé des lois de commande basées sur les techniques robustes du backstepping. Les auteurs dans [29] ont proposé une loi de la commande basée sur la méthode directe de Lyapunov pour commander un hélicoptère à deux degrés de liberté. ...
Ce travail concerne la modélisation et la commande non-linéaire d'un hélicoptère drone à modèle réduit (VARIO Benzin-Trainer) en présence de rafales de vent. En ce qui concerne la modélisation, un modèle général et lagrangien à 7 DDL (degrés de liberté) extrait de [Avila Vilchi, 2001] pour l'hélicoptère en mode de vol libre en basse vitesse est utilisé. Ce système sous-actionné possède 4 entrées de commande. Nous avons développé un modèle lagrangien à 3 DDL de l'hélicoptère perturbé monté sur une plate-forme expérimentale. Le nouveau modèle perturbé présente un grand défi à cause du fort couplage entre les entrées de commande et les états du système, de plus ce modèle est sous-actionné. Différentes stratégies de commande sont utilisées pour commander le modèle réduit de l'hélicoptère perturbé à 3 DDL. Des résultats de simulation montre l'efficacité de la commande backstepping qui stabilise le système en suivant une trajectoire et qui rejete parfaitement la perturbation. Une étude en simulation de la robustesse est faite pour cette commande. Pour le modèle général à 7 DDL, une étude de l'équilibre de l'hélicoptère pendant le vol stationnaire est faite. Nous avons ensuite développé le modèle à 7 DDL de l'hélicoptère perturbé par deux types de rafale de vent, verticale et latérale. Contrairement au modèle à 3 DDL, la dynamique de zéros du modèle à 7 DDL est instable. Toutefois, en négligeant les forces de translation d'amplitude faible et les rafales de vent, on peut obtenir un modèle à minimum de phase. Ce dernier nous permet d'utiliser une loi de commande linéarisante approchée AFLC. Pour améliorer la robustesse et la précision de cette commande linéarisante AFLC, on utilise un observateur non linéaire à état étendu et approché AADRC que nous avons développé en se basant sur la méthode de rejet actif de perturbation ADRC et en utilisant le modèle approché. Plusieurs simulations sur le modèle complet montrent alors que l'ajout de cet observateur permet de compenser l'effet des forces de translation d'amplitude faible et des rafales de vent.
... A two degree freedom helicopter (Kaloust, Ham, & Qu, 1997) is considered. The state variables used to represent this system are given by x = [ hḣ ω θθ ] T , where h is height of helicopter above the ground (meter), ω is the rotational speed of the rotor blades (rad/sec) and θ is the collective pitch angle of rotor blades (rad). ...
Fault Tolerant Control of affine class of MIMO non-linear systems has not received considerable attention of researchers compared to other class of non-linear systems. Therefore, this paper proposes an adaptive passive fault tolerant control method for actuator faults of affine class of MIMO non-linear systems with uncertainties using sliding mode control (SMC). The actuator fault is represented by a multiplicative factor of the control signal which reflects the loss of actuator effectiveness. The design of the controller is based on the assumption that the maximum loss level of the actuator effectiveness is known. Further, since the proposed controller is adaptive, it does not require any a priori knowledge of the uncertainty bounds. The closed loop stability conditions of the controller are derived based on Lyapunov theory. The effectiveness of the proposed controller is demonstrated considering two examples: a two degree of freedom helicopter and a two-link robot manipulator and has been found to be satisfactory.
This study focuses on the novel reinforcement learning control strategy of a nonlinear two-degrees-of-freedom (2-DOF) helicopter system for tracking the desired trajectory while minimizing the tracking error. First, gradient descent algorithm is incorporated in the context of the reinforcement learning control scheme to obtain the adaptive laws. Subsequently, considering the uncertainties in the nonlinear system, radial basis function (RBF) neural networks (NNs) are exploited to approximate the unknown internal dynamics. In contrast to the previous studies, aiming at accelerating the convergence in reinforcement learning control, a barrier Lyapunov function is constructed to constrain the states to ensure that the tracking error rapidly converges to a neighborhood of zero. Under the proposed control strategy, the states of the closed-loop system are proven to be semi-globally uniformly ultimately bounded through rigorous Lyapunov analyses, and the state constraints are satisfied. Furthermore, the simulations and experiments conducted on a Quanser laboratory platform reveal that the proposed control functions are suitable and effective.
Note to Practitioners
—This paper is motivated by designing a reinforcement learning control strategy to enhance online learning capability and control performance of the controller for a nonlinear 2-DOF helicopter system. The control framework is divided into the design of the critic and actor NNs, responsible primarily for evaluating the control performance and approximating uncertainties in the system separately. Unlike the adaptive NN control, the actor NN weights are updated by combining information of states and inputs from the critic NN. In addition, aiming at accelerating the convergence, a barrier Lyapunov function is constructed to constrain the states to ensure that the tracking error rapidly converges to a neighborhood of zero. Finally, the proposed control strategy is validated in simulation and experiment on the Quanser laboratory platform.
Considering the extensive applications of the model predictive control (MPC), this paper investigates the MPC problem with an application to the optimal output consensus of high-order multi-agent systems. A synchronous distributed optimization algorithm for the MPC problem is proposed, and we further devise its asynchronous version. The algorithm allows agents to choose the uncoordinate step-sizes depending on local information, which improves the flexibility of multi-agent systems. The convergence of the proposed algorithm is guaranteed if the positive uncoordinate step-sizes satisfy the explicit conditions. Compared with the synchronous version that needs a global clock to control all agents for communication and update, the asynchronous algorithm does not require each agent in the multi-agent systems to update and communicate simultaneously, and also converges to the optimal global solution to the problem. The numerical simulations demonstrate the availability of the proposed algorithm and the validity of the theoretical results.
This article presents the fuselage/main rotor coupling dynamics under a modal analysis to study the modes of oscillation. The authors provide a rotorcraft simulation model that captures complex dynamics, wherein the validation is done with existing theories. The model has been set up by using VehicleSim, software specialized in modelling mechanical systems composed by rigid bodies. It is presented a helicopter simulation framework, that allows to study the impact of the main rotor varying angular speed on the system. Moreover, the generated heterodyning behaviour and harmonics can be analysed on the fuselage. The detection of this performance is not a simple task, and this helicopter model provides an accurate system for its study using a short-time Fourier transform processing. The coupled dynamics observed between the fuselage and the main rotor indicate that the model can be a suitable tool to detect this type of performance.
This article presents L 1 adaptive control scheme for vertical flight control of helicopter. Linear controller is designed as baseline controller to provide preliminary improvement in performance and robustness. Considering the existence of uncertainties and disturbances, we propose L 1 adaptive controller with modified piecewise constant adaptation law to augment the baseline controllers. Further, the proposed L 1 adaptive controller can be implemented without any modification of the baseline controller. Benefit from this, the design of the entire control system is significantly simplified, and the designed controller is easy to apply to practical engineering. The simulation results indicate that the proposed controllers have good performance for helicopter vertical flight in the presence of uncertainties and disturbances.
This research proposes ASC (Adaptive Synergetic Controller) for the nonlinear model of MH (Mini Helicopter) to stabilize the desired altitude and angle. The model of MH is highly nonlinear, underactuated and multivariable in nature due to its dynamic uncertainties and restrictions of velocities during the flight. ASC can force the tracking errors of the system states converges to zero in a finite interval of time. The MH system requires smooth controller and fast precise transition response from initial state till the desired state, therefore the parametric calculations and simulations can be done by the proposed ASC algorithm. It is validated that the above simulated results of the proposed controller have a better convergence rate and smoother stability response in order to track the desired altitude and angle when compared with SMC (Sliding Mode Controller). Moreover, it does not need any linearization, transformation and variations in the system model.
This paper consider the problem of stabilizing nonlinear uncertain systems. First, we define for nonlinear uncertain systems the generalized matching conditions which encompass a larger class of uncertain systems than the existing matching conditions. Then, a systematic procedure of robust control design is developed for the class of systems satisfying the generalized matching conditions. The procedure is recursive and straightforward, and makes the stability results be easily established. The proposed control is a continuous and bounded function of the system state and requires only nonlinear bounding functions on the size of uncertainties. Global stability in terms of either asymptotic, exponential, or uniform ultimate bounded stability is guaranteed under the proposed control. Extension to tracking problem is shown to be trivial.
A case study in robust control is presented which assesses the
availability of two robust stabilization methods for practical purposes.
The methods considered accomplish H ∞ robust
stabilization and quadratic stabilization, respectively. The system of
concern is a helicopter-like laboratory model with two degrees of
freedom. A comparison of the systems shows the superiority of the
quadratically stabilizing controller. The main reason for this lies in
the fact that uncertainty structure is considered in the Lyapunov-based
design
A systematic procedure for the design of adaptive regulation and
tracking schemes for a class of feedback linearizable nonlinear systems
is developed. The coordinate-free geometric conditions, which
characterize this class of systems, do not constrain the growth of the
nonlinearities. Instead, they require that the nonlinear system be
transformable into the so-called parametric-pure feedback form. When
this form is strict, the proposed scheme guarantees global regulation
and tracking properties, and substantially enlarges the class of
nonlinear systems with unknown parameters for which global stabilization
can be achieved. The main results use simple analytical tools, familiar
to most control engineers