3-DOF Helicopter System Research Articles

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.

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

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.

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.

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.

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.

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 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.

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.

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.

Order Reduction Approach to Velocity Sensorless Performance Recovery PD-Type Attitude Stabilizer for 2-DOF Helicopter Applications

In this article, we exhibit an order reduction output-feedback attitude stabilization scheme for 2-degree-of-freedom (2-DOF) helicopters by considering system nonlinearity and parameter variations in the controller and observer design tasks. As the first merit, the proposed observer for the angular velocity contains the disturbance estimation mechanism as a subsystem assisting the main estimator, which is independent of the system parameter information. As the second advantage, the resultant observer renders it possible to design an improved proportional-derivative-type controller that includes the active damping term and nonlinearly structured design parameters, reducing the closed-loop system order to 1. The Quanser 2-DOF helicopter system experimentally validates the practical merit of the proposed technique.

Adaptive Neural Network Control of a 2-DOF Helicopter System with Input Saturation

Adaptive Neural Network Control of a 2-DOF Helicopter System with Input Saturation

Adaptive neural network control of an uncertain 2-DOF helicopter system with input backlash and output constraints

Adaptive neural network control of an uncertain 2-DOF helicopter system with input backlash and output constraints

LQR-based MIMO PID control of a 2-DOF helicopter system with uncertain cross-coupled gain

This work deals with designing multi-input multi-output (MIMO) proportional-integral-derivative (PID) controllers to achieve linear quadratic (LQ) performance of a laboratory-based two degree-of-freedom (2-DOF) helicopter system with norm-bounded uncertainties in the cross-coupled gain. It is shown that, for such an uncertain system, the MIMO PID design problem can be recast as a full-state feedback control for an augmented uncertain system. Consequently, a simple linear matrix inequality problem is solved to determine the PID parameters in order to achieve robust LQ performance. The efficacy of the proposed controller is shown through extensive simulations and experiments.

LQR control of a 3-DOF helicopter system

LQR control of a 3-DOF helicopter system

An Improved Robust Predictive Control Approach Based on Generalized 3rd Order S-PARAFAC Volterra Model Applied to a 2-DoF Helicopter System

This paper proposes a generalized robust predictive control approach based on 3rd order S-PARAFAC Volterra Model. The main idea is to use the predictive control law based on the latter model with taking into account the parameter and operation uncertainties resulting from the measurement noise and the robust identification technique named Unknown But Bounded Error (UBBE). One of the advantages is the convexity of the objective function with respect to the parameter uncertainty set. The min-max optimization problem becomes thus simpler, by minimizing the objective function in the worst-case only over the set of uncertain models. This work proposes a new generalized nonlinear robust control algorithm dedicated for uncertain processes. In this algorithm we optimize a quadratic criterion and take into account the physical and geometrical constraints due to parameter uncertainties. The performances of this work are illustrated and validated on a benchmark as a continuous stirred-tank reactor system (CSTR) and on an experimental 2-DoF helicopter system.

Super twisting observer based full order sliding mode control

In this paper, a super twisting observer-based full order sliding mode control is proposed for a non-linear uncertain system. The super twisting observer estimates an $$n{-}$$ th system state and the derivative of the $$n{-}$$ th system state. It ensures finite convergence of estimation error to zero. The proposed method retains attractive features of full order sliding mode control like finite-time convergence of system states, continuous control, and the system’s full order dynamics when the system is in the sliding mode. The scheme is validated on a 2-DOF helicopter system laboratory setup, and the performance is compared with two well-known observers, i.e., a non-linear extended state observer and a sliding mode observer-based control using two-link manipulator example.