Helicopter Dynamics Research Articles

Model predictive control of a 3-DOF helicopter system using successive linearization

Helicopter dynamics are in general nonlinear, time-varying, and may be highly uncertain. Traditional control schemes such as proportional–integral–derivative (PID) control, linear quadratic regulator (LQR), and eigen-structure assignment are usually not effective when a linearized model is used and the helicopter moves away from the design trim point. This paper presents a nonlinear model predictive control (NMPC) method to control the elevation and travel of a three degree of freedom (DOF) laboratory helicopter using successive linearization to approximate the internal model of the system. The developed algorithm is evaluated by simulation, and its performance is compared with that achieved by linear model predictive control (LMPC). Keywords : nonlinear systems, helicopter dynamics, MIMO systems, model predictive control, successive linearization International Journal of Engineering, Science and Technology , Vol. 2, No. 10, 2010, pp. 9-19

Adaptive fuzzy control for a quadrotor helicopter robust to wind buffeting

The nonlinear and open-loop unstable dynamics of a quadrotor helicopter makes a control system design non-trivial. However, even more difficulty lies in adapting to an uncertain dynamic model and unknown payloads while remaining robust to significant buffeting wind disturbances. Fuzzy-adaptive or neural-adaptive control offer possible solutions, exhibiting computational efficiency and adaptation to arbitrary nonlinearities. A common method for making these adaptive controls robust to disturbances, e-modification, is found to be unsuitable when applied to the quadrotor in simulation. The adaptive parameters tend to drift to large values in the presence of a sinusoidal disturbance. In this work, we propose a method that uses alternate adaptive parameters in the adaptation scheme. The proposed method successfully controls the quadrotor in simulation, with realistic control signals and computational effort. The adaptive parameter drift and control chatter present with e-modification both vanish. Moreover, performance improves dramatically in the presence of disturbances.

Identification of Lateral/Directional Model for a UAV Helicopter in Forward Flight

A lateral/directional state-space model of the Raptor 50 helicopter is identified in forward flight condition. A frequency sweep test is properly designed and executed to collect a well-suited time-history database. The measured accelerometers are transferred from the sensor location to the gravity, then, a complete set of non-parametric input-to-output frequency responses that fully characterizes the coupled helicopter dynamics are extracted from the frequency sweep test data. With the help of small perturbation theory, a linearized dynamic model for the stability and control derivative is extracted from linearization of a nonlinear mathematical model. A nonlinear search based on secant method is conducted for the linear lateral/directional state-space model that matches the frequency-response data set. The identified model is verified in the time domain, which indicates that the model matches the flight data well.

Simulation system design of a small-scale unmanned helicopter

This paper investigates the simulation design of unmanned helicopter with MATLAB, and completes the development of modelling, control system, navigation system, device input system and virtual reality system, eventually accomplishes the simulation system which can alternate between manned mode and unmanned mode freely. According to the flight test, the simulation and test fit well, this indicates the simulation system accurately describes the characteristics of helicopter dynamics and control system.

Robust attitude control of helicopters with actuator dynamics using neural networks

In this study, attitude control is proposed for helicopters with actuator dynamics. For the nominal helicopter dynamics, model-based control is firstly presented to keep the desired helicopter attitude. To handle the model uncertainty and the external disturbance, radial basis function neural networks are adopted in the attitude control design. Using neural network approximation and the backstepping technique, robust attitude control is proposed with full state feedback. Considering unknown moment coefficients and the mass of helicopters, approximation-based attitude control is developed for the helicopter dynamics. In all proposed attitude control techniques, multi-input and multi-output non-linear dynamics are considered and the stability of the closed-loop system is proved via rigorous Lyapunov analysis. Extensive numerical simulation studies are given to illustrate the effectiveness of the proposed attitude control.

Nonlinear adaptive aggressive control using recurrent neural networks for a small scale helicopter

This paper presents a nonlinear adaptive aggressive controller to provide the small scale helicopter with full authority of a variety of flight conditions. Adaptive backstepping technique is employed to systematically synthesize the proposed controller with the online parameter adaptation rule to the vehicle mass variations and with the recurrent neural network (RNN) approximation to the coupling effect between the force and moment controls. This single and systematic design methodology is shown to achieve the semi-global ultimate boundedness of the closed-loop helicopter dynamics and accommodate the aggressive control of flight maneuvers from hovering to trajectory tracking. The high-fidelity and well-validated nonlinear model of a small scale helicopter incorporating with unmodeled dynamics and measurement uncertainties is adopted in the numerical simulations. The performance and merits of the proposed controller are exemplified by conducting three simulation scenarios including the slalom maneuver described in the ADS33.

Embedded UAV model and LASER aiding techniques for inertial navigation systems

This work proposes the integration of two aiding information sources to enhance the performance of inertial navigation systems (INS), for precise maneuvering of uninhabited air vehicles (UAVs). A new methodology is derived to exploit vehicle dynamics (VD) information by embeding the VD equations directly in an extended Kalman filter architecture. In this technique, the INS estimates are propagated simultaneously using the VD and the INS differential equations, allowing for the estimation of the INS errors. The proposed technique reduces the computational load associated with classical VD aiding, while retaining the same accuracy enhancements. A LASER range finder sensor is also integrated for precise landing and takeoff maneuvers. Simulation results for the nonlinear dynamics of a Vario X-Treme model-scale helicopter are presented, illustrating the contributions of the proposed aiding techniques for precise UAV navigation.

《航空・宇宙機制御の基礎理論》第2回: ヘリコプターのダイナミクスと制御

《航空・宇宙機制御の基礎理論》第2回: ヘリコプターのダイナミクスと制御

A robust guidance and control scheme of an autonomous scale helicopter in presence of wind gusts

This article deals with the problem of robust trajectory tracking for a scale model autonomous helicopter. A large class of uncertainties/disturbance is addressed, namely uncertain parameters and uniform time-varying tridimensional wind gusts occurring in the vicinity of the aircraft. Using an unknown input observer technique, it is shown that disturbances/uncertainties effects on the autonomous helicopter can be accurately reconstructed online. The analysis further extends to the design of a control law whose methodology takes the disturbance estimation procedure into account. Regarding passivity feature of the resulting model, a control law was designed using robust backstepping techniques. The approach proposed here significantly improves the performance of the control and the flight security by counteracting wind gusts in any flight phases. The framework proposed is applied to a non-linear six degree-of-freedom helicopter model. Consequently, a non-linear dynamic model of miniature helicopter is proposed, which focuses on the key effects in the dynamics of a miniature helicopter. Lyapunov stability analysis is then performed to keep the balance between robustness, short response time and large stability domain with a given security margin to guarantee obstacle avoidance during the tracking trajectory process. Simulations results are presented at the end of the article.

Robust multi-mode flight control design for an unmanned helicopter based on multi-loop structure

In this paper, a novel multi-mode flight control strategy for unmanned helicopter, in presence of model uncertainty, atmospheric disturbances and handling qualities specification requirements (as in ADS-33E), based on multi-loop control structure combining robust H-infinity and PI control is presented. In inner loop H-infinity optimal control technique is utilized ensuring the stability of flight control system in case of change of helicopter dynamics, model uncertainties and eliminates effect of gust disturbance on helicopter states and collective/cyclic inputs. PI control in outer loop is used to improve the dynamic and static operation characteristics. Attitude control and attitude holding flight mode with satisfactory command response and decoupling characteristics is designed using the proposed control strategy. Analysis and simulation results show that Level 1 handling requirements as defined in ADS-33E are accomplished even when helicopter is under constant wind circumstance.

Control of uncertain systems by feedback linearization with neural networks augmentation. Part I. Controller design

The paper highlights the main steps of adaptive output feedback control for non-affine uncertain systems – both in parameters and dynamics – having a known relative degree. Given a reference model, the objective is to design a controller that forces the measured system output to track the reference model output with bounded errors. A single hidden layer neural network is used to counteract feedback linearization error. A dynamic observer of tracking error is added. The treatment of control saturation is also sketched. The mathematical model for the longitudinal dynamics of an experimental helicopter is used as framework.

Approximation-based control of uncertain helicopter dynamics

In this study, the altitude and yaw angle tracking is considered for a scale model helicopter, mounted on an experimental platform, in the presence of model uncertainties, which may be caused by unmodelled dynamics, or aerodynamical disturbances from the environment. To deal with the uncertainties, approximation-based techniques using neural network (NN) are proposed. In particular, two different types of NN, namely multilayer neural network and radial basis function neural network are adopted in control design and stability analysis. Based on Lyapunov synthesis, the proposed adaptive NN control ensures that both the altitude and the yaw angle track the given bounded reference signals to a small neighbourhood of zero, and guarantees semiglobal uniform ultimate boundedness of all the closed-loop signals at the same time. The effectiveness of the proposed control is illustrated through extensive simulations. Compared with the model-based control, approximation-based control yields better tracking performance in the presence of model uncertainties.

Potential Panel and Time-Marching Free-Wake-Coupling Analysis for Helicopter Rotor

A potential-based panel method coupled with advanced time-marching free-wake techniques is developed to achieve fast and accurate prediction for unsteady aerodynamics and wake dynamics of helicopter rotating blades. This coupling analysis is enabled by using the equivalence of the doublet-wake panels and the vortex filaments. The coupled panel method allows the inclusion of the self-induced velocity of curved vortex filaments and high-order time integration for the computation of wake convection. A parallel computation is applied to the wake convection for fast numerical calculation. The computation of the induced velocity from each vortex filament is parallelized and computed separately. The velocity-field integration technique is used to avoid numerical singularity during the interaction between the wake and blades. It is found that blade-pressure predictions and the wake roll-up agree well with the measured data for helicopter rotors, both in hover and forward flight. Tip-vortex pairing phenomena are also predicted and compared with the measured data.

Backstepping Approach for Controlling a Quadrotor Using Lagrange Form Dynamics

The dynamics of a quadrotor are a simplified form of helicopter dynamics that exhibit the same basic problems of underactuation, strong coupling, multi-input/multi-output design, and unknown nonlinearities. Control design for the quadrotor is more tractable yet reveals corresponding approaches for helicopter and UAV control design. In this paper, a backstepping approach is used for quadrotor controller design. In contrast to most other approaches, we apply backstepping on the Lagrangian form of the dynamics, not the state space form. This is complicated by the fact that the Lagrangian form for the position dynamics is bilinear in the controls. We confront this problem by using an inverse kinematics solution akin to that used in robotics. In addition, two neural nets are introduced to estimate the aerodynamic components, one for aerodynamic forces and one for aerodynamic moments. The result is a controller of intuitively appealing structure having an outer kinematics loop for position control and an inner dynamics loop for attitude control. The control approach described in this paper is robust since it explicitly deals with unmodeled state-dependent disturbances and forces without needing any prior knowledge of the same. A simulation study validates the results obtained in the paper.

H-Infinity Static Output-feedback Control for Rotorcraft

The problem of stabilization of an autonomous rotorcraft platform in a hover configuration subject to external disturbances is addressed. Necessary and sufficient conditions are presented for static output-feedback control of linear time-invariant systems using the H-Infinity approach. Simplified conditions are given which only require the solution of two coupled matrix design equations. This paper also proposes a numerically efficient solution algorithm for the coupled design equations to determine the output-feedback gain. A major contribution is that an initial stabilizing gain is not needed. The efficacy of the control law and the disturbance accommodation properties are shown on a rotorcraft design example. The helicopter dynamics do not decouple as in the fixed-wing aircraft case, so that the design of helicopter flight controllers with a desirable intuitive structure is not straightforward. In this paper an output feedback approach is given that allows one to selectively close prescribed multivariable feedback loops using a reduced set of the states. Shaping filters are added that improve performance and yield guaranteed robustness and speed of response. This gives direct control over the design procedure and performance. Accurate identification of the System parameters is a challenging task for rotorcraft control, addition of loop shaping facilitates implementation engineers to counteract unmodeled high frequency dynamics. The net result yields control structures that have been historically accepted in the flight control community.

From the Test Benches to the First Prototype of the muFly Micro Helicopter

The goal of the European project muFly is to build a fully autonomous micro helicopter, which is comparable to a small bird in size and mass. The rigorous size and mass constraints infer various problems related to energy efficiency, flight stability and overall system design. In this research, aerodynamics and flight dynamics are investigated experimentally to gather information for the design of the helicopter's propulsion group and steering system. Several test benches are designed and built for these investigations. A coaxial rotor test bench is used to measure the thrust and drag torque of different rotor blade designs. The effects of cyclic pitching of the swash plate and the passive stabilizer bar are studied on a test bench measuring rotor forces and moments with a 6---axis force sensor. The gathered knowledge is used to design a first prototype of the muFly helicopter. The prototype is described in terms of rotor configuration, structure, actuator and sensor selection according to the project demands, and a first version of the helicopter is shown. As a safety measure for the flight tests and to analyze the helicopter dynamics, a 6DoF vehicle test bench for tethered helicopter flight is used.

Neural Network Based System Identification for Autonomous Flight of an Eagle Helicopter

Abstract Neural Network Identification (NNID) for modeling the dynamics of a miniature Eagle helicopter is presented in this paper. Off-line and on-line identification is carried out for both coupled and decoupled dynamics of the helicopter from the flight test data. For both the cases, identification results and the error statistics are provided. The off-line identification performs better due to sufficient training time and data. Results indicate neural network based black-box method is suitable for modeling the nonlinear dynamics of the helicopter. This can be further applied for the design of Automatic Flight Control System (AFCS).

Robust Autonomous Flight Control of an UAV by Use of Neural Networks

Abstract This paper describes a method to develop robust flight control systems for UAVs. It was difficult to develop flight control systems, because the helicopter dynamics is nonlinear. Moreover the flight environment is not fixed because of the atmospheric changes, such as the wind. The wind affects the attitude or velocities of the UAV, but the wind speed or direction is hard to predict, so the wind is usually categorized into stochastic uncertainties. An efficient method to design robust controllers by training neural networks is proposed in this paper. Neural networks trained by the proposed method are robust against stochastic uncertainties. In this paper, the small unmanned helicopter is focused on, and numerical results of altitude control are shown to demonstrate the effectiveness of our approach.

Distributed Rate-Dependent Elastoslide Model for Elastomeric Lag Dampers

To describe the nonlinear behavior of elastomeric dampers, a distributed rate-dependent elastoslide model is developed based on physically motivated damping mechanisms of a filled elastomer. Mathematically, the forced response of an elastomeric damper under a harmonic displacement excitation is developed from a summation of an integral of distributed yield force and a linear-spring force. This physically motivated model consists of rate-dependent elastoslide elements, using a distribution law to account for the yield force, and a parallel polymer residual stiffness. The selection of a yield-distribution function is based on an initial loading curve determined from force vs displacement hysteresis cycles over a broad amplitude range. The fidelity of this five-parameter time-domain model is justified by comparing measured and reconstructed damper responses, that is, steady-state hysteresis cycles, as well as by comparing complex modulus. The elastoslide model is formulated in the state space to improve ease of implementation into helicopter dynamics analyses.

Modelling the interaction of helicopter main rotor and tail rotor wakes

AbstractThe mutual interaction between the main rotor and tail rotor wakes is central to some of the most problematic dynamic phenomena experienced by helicopters. Yet achieving the ability to model the growth and propagation of helicopter rotor wakes with sufficient realism to capture the details of this interaction has been a significant challenge to rotorcraft aerodynamicists for many decades. A novel computational fluid dynamics code tailored specifically for rotorcraft applications, the vorticity transport model, has been used to simulate the interaction of the rotors of a helicopter with a single main rotor and tail rotor in both hover and low-speed quartering flight, and with the tail rotor rotating both top-forward and top-aft. The simulations indicate a significant level of unsteadiness in the performance of both main and tail rotors, especially in quartering flight, and a sensitivity to the direction of rotation of the tail rotor. Although the model thus captures behaviour that is similar to that observed in practice, the challenge still remains to integrate the information from high fidelity simulations such as these into routine calculations of the flight dynamics of helicopters.