3-DOF Helicopter Research Articles

Adaptive sliding mode attitude control of 2-degrees-of-freedom helicopter system with actuator saturation and disturbances

The modelling uncertainties, external disturbance and actuator saturation issues will degrade the performance and even the safety of flight. To improve control performance, this study proposes an adaptive U-model based double sliding control (UDSMC) algorithm combined with a radial basis function neural network (RBFNN) for a nonlinear two-degrees-of-freedom (2-DOF) helicopter system. Firstly, the adaptive RBFNN is designed to approximate the system dynamics with unknown uncertainties. Furthermore, two adaptive laws are designed to deal with unknown external disturbances and actuator saturation errors. The global stability of the proposed helicopter control system is rigorously guaranteed by the Lyapunov stability analysis, realizing precise attitude tracking control. Finally, the comparative experiments with conventional SMC and adaptive SMC algorithms conducted on the Quanser Aero2 platform demonstrate the effectiveness and feasibility of the proposed 2-DOF helicopter control algorithm.

Pitch and yaw motion control of 2 DoF helicopter subjected to faults using sliding-mode control

Pitch and yaw motion control of 2 DoF helicopter subjected to faults using sliding-mode control

Prescribed-Time Adaptive Backstepping Control of an Uncertain Nonlinear 2-DOF Helicopter

This paper addresses the prescribed-time attitude tracking issue for an uncertain nonlinear 2-Degree of Freedom (DOF) helicopter. Based on the Euler-Lagrange equations, a nonlinear model is developed for the 2-DOF helicopter, where the system parameters and control input constant coefficients are unknown. The proposed prescribed-time control is based on adaptive backstepping and utilized to track the desired pitch and yaw positions separately. Using the theory of Lyapunov stability, we show that the proposed prescribed-time control and adaptive law ensure the boundedness of all the closed-loop signals of the system for all future time. A noticeable advantage of the proposed method is that the upper bound of the settling time can be specified in advance. Finally, to verify the efficacy and control capabilities of the proposed scheme, simulations are conducted on the Quanser 2-DOF helicopter system.

Deterministic Learning From Adaptive Neural Network Control for a 2-DOF Helicopter System With Unknown Backlash and Model Uncertainty

In this study, we develop a deterministic learning control approach using adaptive neural network (NN) for a two-degrees-of-freedom helicopter nonlinear system subject to unknown backlash and model uncertainty. First, by combining the backstepping and direct Lyapunov approaches, a novel adaptive NN control scheme with an inverse compensation method is proposed to address the input backlash nonlinearity, track specified trajectories, and stabilize the closed-loop system. Simultaneously, uncertain system dynamics are accurately identified and stored as learned knowledge in constant radial basis function NN weights, while satisfying partial persistent excitation. Subsequently, by extracting the learned knowledge, a learning-based controller is constructed to operate the same control tasks to achieve a superior control performance, less backlash nonlinearity, and minimal computational burden. Finally, the validity and efficacy of the proposed scheme are demonstrated through numerical examples and experiments.

Vector Control Lyapunov Function Based Stabilization of Nonlinear Systems in Predefined Time

Predefined-time stability is the stability of dynamical systems whose solutions approach the equilibrium point within a pre-decided time duration. In this technical note, we develop general results of predefined-time stability of nonlinear systems using vector Lyapunov functions. A vector comparison system, which is predefined time convergent, is constructed, and after that the stability of the original dynamical system is proved using differential inequalities and comparison principles. Moreover, we design predefined-time controllers for large-scale systems using vector control Lyapunov functions (VCLFs). Sliding mode control is introduced in the design approach to mitigate matched bounded disturbances/uncertainties. Also, we aggregate comparison systems to reduce their dimensionality in order to effectively apply the derived results on practical systems. The theoretical results are implemented on a 2 DOF Helicopter model.

LQR-based attitude controllers design for a 3-DOF helicopter system with comparative experimental tests

LQR-based attitude controllers design for a 3-DOF helicopter system with comparative experimental tests

Event-triggered nonlinear information fusion preview control of a two-degree-of-freedom helicopter system

This research presents a novel nonlinear information fusion preview control (NIFPC) method for the flight control problem of two-degree-of freedom (2-DOF) helicopter system. First, according to the information fusion optimal estimation methodology, the system performance index and the system dynamic equation are converted to several information equations about the control input, and then the control input is directly derived by fusing these information equations via the centralized information fusion optimal estimation. In the limited bandwidth, transmitting a large number of sampled data through the network will increase the computational and communication burden of the system. In order to overcome this difficulty, event triggering mechanism is introduced. The asymptotic convergence of system performance index is guaranteed by Lyapunov stability theory. Numerical simulation and experiment results have been provided to demonstrate the effectiveness of the proposed control scheme.

Type-2 evolving fuzzy Kalman filter design based on unobservable spectral components space for interval tracking of non-stationary experimental data

In this paper, an interval type-2 evolving fuzzy Kalman filter is designed for processing of unobservable spectral components of uncertain experimental data. The adopted methodology consider the following steps: an initial model of the interval type-2 fuzzy Kalman filter, which is off-line identified from an initial window of the experimental data; the updating of antecedent proposition of interval type-2 fuzzy Kalman filter by using an interval type-2 formulation of evolving Takagi-Sugeno (eTS) clustering algorithm and the updating of consequent proposition by using a type-2 fuzzy formulation of Observer/Kalman Filter Identification (OKID) algorithm, taking into account the multivariable recursive Singular Spectral Analysis of the experimental data. The computational results for tracking the Mackey-Glass chaotic time series illustrate the efficiency of proposed methodology as compared to relevant approaches from literature, and the experimental results for tracking a 2DoF helicopter demonstrate its applicability.

Event-Triggered Control Strategy for 2-DoF Helicopter System Under DoS Attacks

This paper focuses on the event-triggered strategy design of a two-degree-of-freedom (DoF) helicopter system (HS) with denial-of-service (DoS) attacks, which has essential applications in traffic information security and military information security. First, the attack characteristics of DoS are introduced from the cloud servers and converters at the physical layer. Then, hackers launching a DoS attack on HS also are considered. Second, a new first-order weight sampling (FOWS) control method is developed, fully considering sampling intervals resource consumption. Meanwhile, novel looped-functionals are constructed, which contain more sampling time information and sampling interval weight information. In addition, quadratic scaling is used to process the integral terms to obtain a tighter upper limit, which helps optimize the two control algorithms (TCAs). Furthermore, TCAs are obtained using the linear convex combination method (LCCM). Then, a new event-triggered controller under DoS attacks is designed to ensure the 2-DoF HS is asymptotically stable. Finally, the feasibility and superiority of our designed approach are verified through an experimental simulation.

Computationally Efficient Continuous-Time Model Predictive Control of a 2-DOF Helicopter via B-Spline Parameterization.

This paper investigates one way to reduce the computational burden of continuous-time model predictive control (MPC) laws by representing the input/output signals and related models using B-spline functions. Such an approximation allows to implement the resulting feedback control law more efficiently, requiring less online computational effort. As a result, the proposed controller formulates the control signals as continuous polynomial spline functions. All constraints assumed over the prediction horizon are then expressed as constraints acting on the B-splines control polygon vertices. The performance of the proposed theoretical framework has been demonstrated with several real-time experiments using the well-known 2-DOF laboratory helicopter setup. The aim of the presented experiments was to track given step-like reference trajectories for pitch and yaw angles under notable parameter uncertainties. In order to suppress the influence of uncertainties, the control algorithm is implemented in an adaptive mode, equipped with the recursive least squares (RLS) estimation of model parameters and with the adaptation of stabilizing terminal set and terminal cost calculations. Thanks to the presented framework, it is possible to significantly reduce the computational burden, measured by the number of decision variables and input constrains, indicating the potential of the proposed concept for real-time applications, even when using embedded control hardware.

Sliding-mode observer–based active fault-tolerance control for a two-degree-of-freedom helicopter system with sensor faults

In this paper, an active fault-tolerance controller is proposed for a two-degree-of-freedom (2-DOF) helicopter model with different types of sensor faults. The proposed controller is designed by combining an interval type-2 fuzzy logic control approach with a sliding-mode control technique. In addition, the controller is compensated by a sliding-mode observer used to estimate faults in real-time. For the proposed control scheme, the overall stability of the closed-loop system is proven using the Lyapunov stability theory. Finally, numerical simulations and experiments verify that the proposed scheme achieves superior control performance in the case of sensor failure.

Robust Attitude Control of Helicopters with Three-Degree Freedom Based on Intermittent Event-Triggered Mechanism

In the field of the widely used helicopter, this paper studies whether the helicopters with three-degree freedom (3DOF helicopters) have a new control method of stable attitude. Therefore, two research methods are adopted. One is to use intermittent control, so as to achieve control stability in a short time without its inputting. The other is to find and update the time needed to meet the next control through the event-triggered mechanism. A theorem is given to prove the feasibility of these methods, and Lyapunov’s second law is also applied in this paper to analyze the stability of the model designed for robust attitude control. Besides, we use the linear matrix inequality solver to solve the feedback gain of the controller in the theorem. Finally, through MATLAB simulation, the system error state of helicopters tends to zero under intermittent control, which highlights the advantages of short communication time and few times of simulation, thus achieving the simulation goal.

Robust Control Based on a Time-varying UDE for an Under-actuated 3-DOF Helicopter

The UDE (uncertainty and disturbance estimator) based control approach has received increasing attention in recent years due to its simplicity and effectiveness to attenuate the influence of uncertainties and disturbances. Despite this fact, the trade-off issue of its steady-state performance and transient performance has not been addressed explicitly. A novel time-varying UDE (TV-UDE) is proposed to resolve the trade-off issue in this paper. The main idea behind the design is to use a differential equation with a time-varying parameter, rather than a transfer function, to represent the underlying filtering relationship. By changing the UDE gain smoothly, the performance limitations of a fixed-gain UDE are avoided. Moreover, the TV-UDE is reduced to a classic UDE when its parameter value is finally frozen. Two design specifications are provided to guide the design of the time-varying parameter. We then apply this design to the angular trajectory tracking problem of a 3-DOF helicopter model, and reveal the four time-scales property of the closed-loop dynamics. The advantages of the proposed approach are shown by simulation comparisons.

Prescribed-time adaptive constraint control of an uncertain nonlinear 2-DOF helicopter

This paper addresses the problem of attitude tracking for a 2-Degree of Freedom (DOF) helicopter system with uncertainties. Euler-Lagrange equations are utilized to develop a nonlinear model for the helicopter, considering the control input constant coefficients and system parameters as unknown. The prescribed-time control approach is proposed using adaptive backstepping to track the desired pitch and yaw positions separately. In Addition, a constrained function is also used to avoid the risk of a larger signal when time gets closer to the appointed settling time. Through the application of the theory of Lyapunov stability, it is shown that the proposed strategy ensures that all closed-loop signals are bounded, and all the states converge within the prescribed time. A significant advantage of this approach is the ability to pre-specify the upper bound of the settling time. Finally, the efficacy and control capabilities of the proposed scheme are verified by obtaining the simulation results on the Quanser 2-DOF helicopter.

Adaptive quantized fault-tolerant control of a 2-DOF helicopter system with actuator fault and unknown dead zone

This study proposes an adaptive quantized fault-tolerant control for a nonlinear two-degree of freedom (2-DOF) helicopter system with an unknown dead zone and actuator failures. First, a hysteresis quantizer is employed to reduce the jittering during signal quantization. Second, a radial basis function neural network is adopted to address the uncertainty in the nonlinear helicopter system. Bounded estimates, smoothing functions, and adaptive parameters are used to compensate for the effects of unknown dead zones, actuator faults, and quantization inputs. Subsequently, an adaptive neural network quantized fault-tolerant control strategy is developed for the nonlinear 2-DOF helicopter system using a backstepping technique. In addition, the closed-loop system is proved to be semi-globally uniformly bounded using rigorous Lyapunov stability analysis. Finally, the effectiveness of the derived control strategy is demonstrated through simulation and experimental results.

Optimizing an adaptive fuzzy logic controller of a 3-DOF helicopter with a modified PSO algorithm

This paper investigates the controller optimization for a helicopter system with three degrees of freedom (3-DOF). The system is extensively nonlinear and highly sensitive to the controller’s parameters, making it a real challenge to study these parameters’ effects on the controller’s performance. We combined fuzzy logic with adaptive control theory to control the system and used metaheuristic algorithms to determine these parameters. Then, we compare the results with the controller optimized through the standard PSO and PID controller. The results indicate the high ability of MPSO to perform the global search and to find a reasonable search space. The proposed method’s effectiveness and robustness properties are shown through computer simulations, while the system is subject to uncertainties and disturbance. We also prove the efficiency of the MPSO algorithm by comparing it with the standard PSO and six other well-known metaheuristic algorithms and analyzing the results by statistical tests.

On the exact linearisation and control of flat discrete-time systems

The paper addresses the exact linearisation of flat nonlinear discrete-time systems by generalised static or dynamic feedbacks which may also depend on forward-shifts of the new input. We first investigate the question which forward-shifts of a given flat output can be chosen in principle as a new input, and subsequently how to actually introduce the new input by a suitable feedback. With respect to the choice of a feasible input, easily verifiable conditions are derived. Introducing such a new input requires a feedback which may in general depend not only on this new input itself but also on its forward-shifts. This is similar to the continuous-time case, where feedbacks which depend on time derivatives of the closed-loop input – and in particular quasi-static ones – have already been used successfully for the exact linearisation of flat systems since the nineties of the last century. For systems with a flat output that does not depend on forward-shifts of the input, it is shown how to systematically construct a new input such that the total number of the corresponding forward-shifts of the flat output is minimal. Furthermore, it is shown that in this case the calculation of a linearising feedback is particularly simple, and the subsequent design of a discrete-time flatness-based tracking control is discussed. The presented theory is illustrated by the discretised models of a wheeled mobile robot and a 3DOF helicopter.

Stealthy replay attack detection of 3-DOF helicopter benchmark system using dynamic watermarking approach

Cyber security for unmanned systems has drawn tremendous research attention in recent years owing to its priority in ensuring system performance and safety. This paper presents a dynamic watermarking-based active detection approach for unmanned helicopter system under stealthy replay attacks. First, the dynamic model of the 3-DOF helicopter and the replay attack model are constructed, respectively. Statistical analysis is conducted using Kalman filter residuals to interpret the concealment of stealthy replay attacks for a system under intrusion. Then, as traditional chi-square detector is unable to detect stealthy replay attacks, an active detector by incorporating dynamic watermarking with the chi-square detector is explored. Finally, by conducting simulations of the detection procedures under different test scenarios comparatively using traditional chi-square detector and the proposed approach, the effectiveness and merits of the watermarking approach is verified sufficiently. The watermarking-based approach is promising in comprehensive detections against stealthy replay attacks for enhancing system security.

Adaptive Neural Control of a 2DOF Helicopter with Input Saturation and Time-Varying Output Constraint

An adaptive neural control for uncertain 2DOF helicopter systems with input saturation and time-varying output constraints is provided. A radial basis function neural network is used to estimate the uncertainty terms present in the system. The saturation error and the external disturbance are considered as a composite disturbance, and an adaptive auxiliary parameter is introduced to compensate it. An asymmetric barrier Lyapunov function is employed to address the constraint violation of the system output. The closed-loop stability of the system is then demonstrated by Lyapunov theory analysis. Simulation results demonstrate the effectiveness of the control strategy.

Adaptive Neural Control for an Uncertain 2-DOF Helicopter System with Unknown Control Direction and Actuator Faults

In accordance with the rapid development of smart devices and technology, unmanned aerial vehicles (UAVs) have been developed rapidly. The two-degree-of-freedom helicopter system is a typical UAV that is susceptible to uncertainty, unknown control direction and actuator faults. Hence, a novel adaptive neural network (NN), fault-tolerant control scheme is proposed in this paper. Firstly, to compensate for the uncertainty, a radial-basis NN was developed to approximate the uncertain, unknown continuous function in the controlled system, and a novel weight-adaptive approach is proposed to save on computational cost. Secondly, a class of Nussbaum functions was chosen to solve the unknown-control-direction issue to prevent the effect of an unknown sign for the control coefficient. Subsequently, in response to the actuator faults, an adaptive parameter was designed to compensate for the performance loss of the actuators. Through rigorous Lyapunov analyses, the designed control scheme was proven to enable the states of the closed-loop system to be semi-globally uniformly bounded and the controlled system to be stable. Finally, we conducted a numerical simulation on Matlab to further verify the validity of the proposed scheme.