3-DOF Helicopter Research Articles

Adjusted linear quadratic regulator-proportional-derivative control of Quanser’s three degrees of freedom helicopter based on flower pollination algorithm under external disturbances

External disturbances, saturation of actuator motors, and limits of certain angular movements are commonly encountered in robotic systems, particularly those involving flight, and they present the most common and influential factors affecting the stability and performance of these systems. In this paper, a hybrid controller for a three-degree-of-freedom (3-DoF) helicopter is designed and applied to this flying robot system, taking into account the previously mentioned constraints. The proposed hybrid controller integrates proportional-derivative (PD) control with an adjusted linear quadratic regulator (ALQR) using the flower pollination algorithm (FPA) optimization method. Simulation results of travel (λ), elevation (ε), and pitch (ρ) responses, as well as experimental results of elevation and travel tracking responses under external disturbances using the bench-top Quanser’s (3-DoF) helicopter, demonstrate the robustness and good performance of the controlled system using the proposed method. The effectiveness of the proposed method is compared to several methods in the literature.

Dynamic Surface Tracking Control for Nonlinear Constraints

Abstract An adaptive control scheme based on dynamic surface control (DSC), and intelligent control techniques is developed for a 3-DOF helicopter with unknown disturbance and asymmetric saturation. The reconstructed dynamic neural network (NN) is established to compensate for nonlinear terms in real-time. A designed smooth nonlinear sigmoid function is used to model saturation nonlinearity. The combination of dynamic surface control with adaptive intelligent control techniques resolves and improves the tracking and robust performance of the system. The stability and ultimately bound of all signals of the controlled system are demonstrated by theoretical analysis. Numerical results prove the feasibility of the presented control scheme.

Neural Network-based Adaptive Finite-time Control for 2-DOF Helicopter Systems with Prescribed Performance and Input Saturation

In this study, we propose an adaptive neural network (NN) control approach for a 2-DOF helicopter system characterized by finite-time prescribed performance and input saturation. Initially, the NN is utilized to estimate the system’s uncertainty. Subsequently, a novel performance function with finite-time attributes is formulated to ensure that the system’s tracking error converges to a narrow margin within a predefined time span. Furthermore, adaptive parameters are integrated to address the inherent input saturation within the system. The boundedness of the system is then demonstrated through stability analysis employing the Lyapunov function. Finally, the effectiveness of the control strategy delineated in this investigation is validated through simulations and experiments.

Synthesis of an Orbit Tracking Controller for a 2DOF Helicopter based on Sequential Manifolds with Stabilization Time in the Presence of Disturbances

Synthesis of an Orbit Tracking Controller for a 2DOF Helicopter based on Sequential Manifolds with Stabilization Time in the Presence of Disturbances

Output Feedback Active Fault Tolerant Control for a 3-DOF Laboratory Helicopter With Sensor Fault

In this paper, an output feedback-based active fault tolerant control (FTC) scheme is proposed for an unstable three degree-of-freedom (3-DOF) helicopter equipped only with angular position sensors, of which a single sensor can be faulty. Limited by the available outputs, existing fault estimation (FE) and FTC schemes cannot be applied to this helicopter because when the sensor measuring the elevation or travel angle is faulty, it does not satisfy the minimum-phase and matching conditions required by standard observers. To circumvent this problem, an adaptive interval observer is firstly designed as a fault detection and isolation (FDI) unit to indicate the occurrence and location of a fault, in contrast to the existing FDI methods that require a bank of observers and incur a high computational cost. Then a high-gain observer is combined with a sliding mode observer to form an FE unit that does not require the matching and minimum-phase conditions. Based on the estimate of the fault, an FTC scheme is constructed to ensure an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal{H}_{\infty}$</tex-math> </inline-formula> performance of the faulty system. Finally, physical experiments on the 3-DOF helicopter verify the effectiveness of the proposed scheme. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The 3-DOF lab helicopter serves as an ideal experimental platform for control strategies. In this paper, an active fault tolerant control (FTC) scheme is developed for a 3-DOF lab helicopter when any single sensor can be faulty. The helicopter is nonlinear and subject to external disturbances. There are only encoders measuring the attitude angles and no sensors for angular velocities. In this paper, we firstly design a fault detection and isolation (FDI) unit based on an adaptive interval observer to detect the fault and identify its location; it incurs a lower computational cost compared to existing methods that use a bank of observers. Then a high-gain observer is combined with a sliding mode observer to estimate the fault. Based on the estimate of the fault, an FTC scheme is constructed and designed using Linear Matrix Inequalities to ensure an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal{H}_{\infty}$</tex-math> </inline-formula> performance of the faulty system.

Adaptive neural network control of a 2-DOF helicopter system considering input constraints and global prescribed performance

Adaptive neural network control of a 2-DOF helicopter system considering input constraints and global prescribed performance

Exponential-form predefined-time convergent controller and its applications to Van-der-Pol system and 2-DOF helicopter

This paper proposes a predefined-time convergent stabilization controller for a class of nonlinear systems. First, a controller is introduced for linear systems where the convergent time is selected in advance, independent of initial conditions, and can be assigned as a parameter of a control input. The corresponding result is then obtained for a multidimensional system consisting of [Formula: see text] nonlinear differential equations. The block control technique is employed to consequently stabilize each state component by a virtual control until the real control appears. Finally, the presented result is applied to a multivariable nonlinear system to design a predefined-time convergent robust controller. To show effectiveness of the proposed convergent controller, numerical simulations have been carried out for a Van-der-Pol system and a 2-degree-of-freedom (2-DOF) helicopter model.

Full-state constraints and input backlash–based neural network control of a 2-DOF helicopter system

This paper introduces an adaptive neural network compensatory control approach designed for a 2-degree-of-freedom (2-DOF) helicopter system facing challenges such as input backlash and state constraints. The proposed methodology leverages a radial basis function (RBF) neural network to effectively approximate system uncertainties, mitigating the impact of nonlinear dynamics on control performance. To address the presence of nonlinear input backlash, a compensation technique is introduced to enhance the smoothness of input signals. In addition, for enhanced system safety, a barrier Lyapunov function is integrated to impose restrictions on position and velocity states, resulting in constrained control. Through a rigorous analysis using the Lyapunov direct method, this paper demonstrates the effectiveness of the proposed approach in achieving bounded stability of the system. The validation of the approach is further established through the presentation of simulation and experimental results, showcasing its effectiveness and feasibility in real-world applications.

State estimation based actuator fault detection for tandem rotor helicopter with experimental validation

Timely fault detection is essential to flight safety of tandem rotor helicopter. In this paper, a fault detection method is proposed based on state estimation and the deviation between the measured value and the estimated value. Firstly, a polyhedral linear parameter varying (LPV) model is established to solve the nonlinear coupling problem of the helicopter in different moving directions. Then, to obtain actuator fault information, a robust state observer is developed to generate the residual. Meanwhile, a mixed [Formula: see text] algorithm is designed to calculate observer gain by configuring performance parameters, which makes the residuals both sensitive to actuator faults and robust to external disturbances. Furthermore, a dynamic threshold method is introduced to evaluate the residual signal for actuator fault detection. Finally, based on the 3-dof helicopter platform, the effectiveness of the proposed method is verified through comparative simulation and experimental tests.

Adaptive Neural Network-Based Dynamic Surface Control for a 3-DoF Helicopter

Adaptive Neural Network-Based Dynamic Surface Control for a 3-DoF Helicopter

Predefined‐time adaptive backstepping control for a class of nonlinear dynamical systems with parametric uncertainties

SummaryIn this article, we address the problem of achieving predefined‐time control for a class of nonlinear dynamical systems with parameter uncertainties. We introduce an adaptive predefined‐time control algorithm based on integrator backstepping for th order nonlinear systems. Using Lyapunov's stability theory, we establish that the proposed predefined time control approach, combined with an adaptive law, ensures the boundedness of all signals within the closed‐loop system. A notable advantage of our method is its potential to achieve convergence within a predetermined time frame. To validate our approach's efficacy, we present a practical example involving a 2 DOF helicopter, demonstrating the effectiveness of the proposed scheme.

Event-triggered adaptive neural fault-tolerant control for a 2-DOF helicopter system with prescribed performance

In this paper, we focus on an event-triggered adaptive neural fault-tolerant control for a two-degree of freedom (2-DOF) helicopter system with actuator failures. In this design, a radial basis function neural network (NN) is exploited to estimate the uncertainty terms present in the system. A new error transformation technique is employed to make the tracking error of the system satisfy a prescribed performance function. Then, an event triggering mechanism is introduced to reduce the communication burden of the system. Smoothing functions and bounded estimation methods are then used to compensate for actuator failures and measurement errors. The helicopter system is proved to be consistently bounded by the direct method of Lyapunov functions. Finally, simulation and experimental results verify the effectiveness of the control strategy.

Reinforcement Learning Control for a 2-DOF Helicopter With State Constraints: Theory and Experiments

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. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —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.

Robust Fixed-Time Sliding Mode Attitude Control for a 2-DOF Helicopter Subject to Input Saturation and Prescribed Performance

Robust Fixed-Time Sliding Mode Attitude Control for a 2-DOF Helicopter Subject to Input Saturation and Prescribed Performance

Broad Reinforcement Learning for Adaptive Control of a 2-DOF Helicopter System With Unknown Dead Zone

Broad Reinforcement Learning for Adaptive Control of a 2-DOF Helicopter System With Unknown Dead Zone

Neural-Network-Based Adaptive Fixed-Time Control for a 2-DOF Helicopter System With Input Quantization and Output Constraints.

This study proposes a neural-network (NN)-based adaptive fixed-time control method for a two-degree-of-freedom (2-DOF) nonlinear helicopter system with input quantization and output constraints. First, a hysteresis quantizer is employed to mitigate chattering during signal quantization, and adaptive variables are utilized to eliminate errors in the quantization process. Subsequently, the system uncertainties are approximated using a radial basis function NN. Simultaneously, a logarithmic barrier Lyapunov function (BLF) is constructed to prevent the system outputs from violating the constraint boundaries. Based on a rigorous Lyapunov stability analysis and the fixed-time stability criterion, the signals of the closed-loop system are proven to be bounded within a fixed time. Finally, numerical simulations and experiments verified the feasibility of the proposed method.

Interval type-2 evolving fuzzy Kalman filter for processing of unobservable spectral components from uncertain experimental data

In this paper, an interval type-2 evolving fuzzy Kalman filter (IT2EFKF) is designed for processing unobservable spectral components of uncertain experimental data. The primary objective of the methodology proposed in the present research is to provide a novel mathematical tool for interval and spectral processing of uncertain experimental data in order to deal with real-world filtering, tracking, and forecasting problems. 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. Computational results for tracking the Mackey-Glass chaotic time series demonstrate the effectiveness of the proposed approach when compared to related methodologies from the literature, with superior results for RMSE of 0.0026. Experimental results for tracking a 2DoF helicopter illustrate its applicability, with superior results for RMSE and VAF of 0.00156 and 99.9874% for yaw angle, and of 0.00702 and 99.8863% for pitch angle, respectively.

Adaptive Neural Network Control of an Uncertain 2-DOF Helicopter With Unknown Backlash-Like Hysteresis and Output Constraints.

An adaptive neural network (NN) control is proposed for an unknown two-degree of freedom (2-DOF) helicopter system with unknown backlash-like hysteresis and output constraint in this study. A radial basis function NN is adopted to estimate the unknown dynamics model of the helicopter, adaptive variables are employed to eliminate the effect of unknown backlash-like hysteresis present in the system, and a barrier Lyapunov function is designed to deal with the output constraint. Through the Lyapunov stability analysis, the closed-loop system is proven to be semiglobally and uniformly bounded, and the asymptotic attitude adjustment and tracking of the desired set point and trajectory are achieved. Finally, numerical simulation and experiments on a Quanser's experimental platform verify that the control method is appropriate and effective.

Adaptive Broad Learning Neural Network for Fault-Tolerant Control of 2-DOF Helicopter Systems

Adaptive Broad Learning Neural Network for Fault-Tolerant Control of 2-DOF Helicopter Systems

Time-varying uncertainty and disturbance estimator without velocity measurements: Design and application

The uncertainty and disturbance estimator (UDE) technique has been proven to be simple but effective in reconstructing unknown disturbances. However, classic UDE with a constant gain cannot deal with more complicated issues, such as the trade-off between steady-state and transient performance of the estimator, simultaneous attenuation of input disturbances and measurement noises, etc. Motivated by this observation, the design of UDE technique is extended to the time-varying situation and an implementable form of time-varying UDE (TV-UDE) is proposed. In particular, velocity measurements are assumed to be unavailable in the design. A time-varying ordinary differential equation is constructed to build the estimation relationship. A formula for the integration by parts is thereafter introduced to derive an implementable form of the TV-UDE. The classic UDE is shown to be a special case of the TV-UDE. The UDE is combined with a nominal dynamic output-feedback controller to yield a robust control solution to a class of uncertain second-order attitude control systems without velocity measurements. The design of a TV-UDE is discussed with a low initial gain and a higher final gain to avoid transient performance issues. Finally, numerical simulations and physical experiments are carried out on a 2-DOF AERO attitude helicopter platform to demonstrate the control performance of the solution. It is illustrated that the proposed design can effectively reduce the steady-state errors in both the trajectory tracking and target pointing tasks. Meanwhile, the input saturation and peaking phenomena associated with a high-gain estimation are avoided by applying the TV-UDE.