Nonlinear Model Uncertainties Research Articles

Finite-time error constraint control for multi-AUV systems with unknown uncertainties based on observer and tan-type barrier Lyapunov function

PurposeAutonomous underwater vehicle (AUV) is widely used in resource prospection and underwater detection due to its excellent performance. This study considers input saturation, nonlinear model uncertainties and external ocean current disturbances. The containment errors can be limited to a small neighborhood of zero in finite time by employing control strategy. The control strategy can keep errors within a certain range between the trajectory followed by AUVs and their intended targets. This can mitigate the issues of collisions and disruptions in communication which may arise from AUVs being in close proximity or excessively distant from each other.Design/methodology/approachThe tracking errors are constrained. Based on the directed communication topology, a cooperative formation control algorithm for multi-AUV systems with constrained errors is designed. By using the saturation function, state observers are designed to estimate the AUV’s velocity in six degrees of freedom. A new virtual control algorithm is designed through combining backstepping technique and the tan-type barrier Lyapunov function. Neural networks are used to estimate and compensate for the nonlinear model uncertainties and external ocean current disturbances. A neural network adaptive law is designed.FindingsThe containment errors can be limited to a small neighborhood of zero in finite time so that follower AUVs can arrive at the convex hull consisting of leader AUVs within finite time. The validity of the results is indicated by simulations.Originality/valueThe state observers are designed to approximate the speed of the AUV and improve the accuracy of the control method. The anti-saturation function and neural network adaptive law are designed to deal with input saturation and general disturbances, respectively. It can ensure the safety and reliability of the multiple AUV systems.

Modeling and Control of a Road Wheel Actuation Module in Steer-by-Wire System

Since the steer-by-wire system removes the mechanical connection and uses electrical signals to drive the system, it has the disadvantage of being less stable in the failure of parts or systems. Therefore, in this paper, we present a methodology for developing a digital model of the road wheel actuator of the steer-by-wire system. First, the detailed dynamics of the road wheel actuator are analyzed and simplified, and the friction model is estimated and compensated to obtain the equilibrium inertia and damping coefficient of the motor and the road wheel actuator. And to verify the accuracy of the digital model developed based on these parameters, the outputs are compared by giving the same inputs under open-loop control. Furthermore, to solve the problem caused by nonlinear disturbance and model uncertainty, a disturbance observer-based position controller is proposed. The validity of the proposed controller and the validity of the digital model development methodology are confirmed by the results of the position control experiment.

Enhanced Hybrid Robust Fuzzy-PID Controller for Precise Trajectory Tracking Electro-Hydraulic Actuator System

The Electro-Hydraulic Actuator (EHA) system integrates electrical and hydraulic elements, enabling it to generate a rapid reaction, a high power-to-weight ratio, and significant stiffness. Nevertheless, EHA systems demonstrate non-linear characteristics and modeling uncertainties, such as friction and parametric uncertainty. Designing a controller for accurate trajectory tracking is greatly challenging due to these limitations. This paper introduces a hybrid robust fuzzy proportional-integral-derivative (HFPID) and (HF+PID) controller. The controller is designed to effectively control a third-order model of an EHA system for trajectory tracking. It is a significant contribution to the development of an intelligent robust controller that can perform well in different environments. Initially, a mathematical model for the EHA system was created using a first-principle approach. Subsequently, the Ziegler-Nichols method was employed to fine-tune the PID controller, while a conventional Fuzzy Logic Controller (FLC) was constructed in MATLAB Simulink utilizing linguistic variables and rule-based control. Without further tuning, the FL and PID controller are combined as a hybrid controller with different structures: Hybrid Fuzzy-PID (HFPID) and Hybrid Fuzzy+PID (HF+PID) controller. The Mean Square Error (MSE) and Root Mean Square Error (RMSE) are utilized as indices to assess the tracking accuracy and robustness of the four controllers. A greater value of MSE and RMSE indicates poorer performance of the controller. The results demonstrate that the HF+PID controller surpasses the other controllers by reaching the lowest MSE and RMSE values. It showcases the efficacy and accuracy in monitoring sinusoidal, multi-sinusoidal, and point-to-point trajectory tracking. Future work should focus on implementing the designed controller on hardware for real-time performance and experimenting with various types of FLC or Hybrid controllers, such as self-tuning fuzzy-PID, to further explore their potential.

A Novel Attitude Control Strategy for a Quadrotor Drone with Actuator Dynamics Based on a High-Order Sliding Mode Disturbance Observer

In the attitude control of quadrotor drones, it is necessary to cope with matched and unmatched disturbances caused by nonlinear couplings, model uncertainties, and external disturbances, as well as to consider the effects caused by actuator dynamics. Aiming to accurately track desired trajectories under the above factors, a novel control strategy is proposed by combining a state feedback control with a high-order sliding mode disturbance observer (HOSMDO). The HOSMDO is motivated by the higher-order sliding mode (HOSM) differentiator and extended state observer (ESO) technique, allowing for the exact robust estimation of disturbances and their arbitrary order derivatives in finite time. Unlike the control schemes based on back-stepping methods, the proposed controller is designed with a holistic mindset. Specifically, a baseline feedback framework is constructed firstly, and the disturbances and relevant derivatives required for the baseline framework are then generated by the HOSMDOs to obtain the overall control scheme. The stability conditions of the controllers designed with and without considering the actuator dynamics are analyzed separately. In the latter case, the actuator dynamics imposed additional constraints on the control parameters. Numerical simulations validate the effectiveness of the proposed control strategy.

VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction, such as Proper Orthogonal Decomposition. The limitation of the linear nature of such operators is typically tackled via a library of local reduction subspaces, which requires the assembly of numerous local ROMs to address parametric dependencies. Our work attempts to define a more generalisable mapping between parametric inputs and reduced bases for the purpose of generative modeling. We propose the use of Variational Autoencoders (VAEs) in place of the typically utilised clustering or interpolation operations, for inferring the fundamental vectors, termed as modes, which approximate the manifold of the model response for any and each parametric input state. The derived ROM still relies on projection bases, built on the basis of full-order model simulations, thus retaining the imprinted physical connotation. However, it additionally exploits a matrix of coefficients that relates each local sample response and dynamics to the global phenomena across the parametric input domain. The VAE scheme is utilised for approximating these coefficients for any input state. This coupling leads to a high-precision low-order representation, which is particularly suited for problems where model dependencies or excitation traits cause the dynamic behavior to span multiple response regimes. Moreover, the probabilistic treatment of the VAE representation allows for uncertainty quantification on the reduction bases, which may then be propagated to the ROM response. The performance of the proposed approach is validated on an open-source simulation benchmark featuring hysteresis and multi-parametric dependencies, and on a large-scale wind turbine tower characterised by nonlinear material behavior and model uncertainty.

Automatic Landing System Design for Unmanned Fixed-Wing Vehicles via Multivariable Active Disturbance Rejection Control

Landing control of unmanned aerial vehicles (UAVs) is challenging because of the strong nonlinear dynamics, multivariable, model uncertainties, wind variations, and sensor noise. Motivated by this fact, this paper investigates an automatic landing system (ALS) that includes trajectory generation and guidance law for the first flight test of a turbine-based combined cycle technology demonstrator. Specifically, the control scheme increases the original model’s order to generate a reasonable monotone-decreasing throttle reference flare trajectory by the pseudospectral method. Subsequently, the guidance law based on innovative multivariable active disturbance rejection control is designed to robustly track the reference altitude and velocity simultaneously with high accuracy. The multivariable extended state observer (ESO) incorporated decoupling algorithm enhances the estimation capability and accuracy of potential problem in cross-coupling dynamics compared to the traditional ESO. It is proven that the closed-loop error dynamic has bounded-input bounded-output stability and an explicit upper bound is given. Numerical simulation verifies that the presented approach has better robustness and higher tracking accuracy for external disturbances and parametric uncertainties than the existing benchmark autolanding controller. Finally, flight tests show that the proposed ALS can land the vehicle effectively and safely under severe wind conditions.

Real-time adaptive sparse-identification-based predictive control of nonlinear processes

This study introduces a sparse identification-based model predictive control (MPC) framework that incorporates on-line updates of the sparse-identified model to account for nonlinear dynamics and model uncertainty in process systems. The methodology involves obtaining a nonlinear first-order ordinary differential equation model using sparse identification for nonlinear dynamics (SINDy), which is integrated into two control schemes: Lyapunov-based MPC (LMPC) for achieving steady-state operation and Lyapunov-based economic MPC (LEMPC) for achieving both closed-loop stability and optimal economic performance. To improve prediction accuracy, an on-line model update scheme is proposed for the SINDy models. Specifically, an error-trigger mechanism that utilizes prediction errors and then uses the most recent process data to update the parameters of the SINDy model in real-time is designed. By incorporating the error-triggered on-line model updates in the SINDy-based LMPC and LEMPC, the dynamic performance of the process is enhanced, ensuring closed-loop stability, optimality, and smooth control actions. Following theoretical results on the boundedness of the closed-loop states and detailed discussions on the selection criteria for parameters of the error-triggered SINDy update scheme, the effectiveness of the proposed methodology is demonstrated through a chemical process example with time-varying disturbances under the LEMPC framework.

Adaptive Super-twisting Sliding Mode Control of Hydraulic Servo Actuator with nonlinear features and modeling uncertainties

This study proposes a novel adaptive super-twisting sliding mode controller (ASTSMC) for hydraulic servo actuator with nonlinear features and modeling uncertainties. In the proposed method, an extended state observer (ESO) is utilized to estimate the value of lumped uncertainties. The core feature of this paper is the combination of ASTSMC with ESO to compensate disturbance in hydraulic servo actuator. Moreover, the proposed ASTSMC does not need to obtain the bound of uncertainties in advance and ensures the sliding variable and its derivative reach to zero in a finite time. In addition, the stability of the closed-loop is proved by Lyapunov theory. Simulation and experiment results demonstrate the proposed ASTSMC can effectively mitigate the lumped uncertainties and obviously improve the tracking performance.

Backstepping Sliding Mode Control Based on Extended State Observer for Hydraulic Servo System

Hydraulic servo system plays an important role in industrial fields due to the advantages of high response, small size-to-power ratio and large driving force. However, inherent nonlinear behaviors and modeling uncertainties are the main obstacles for hydraulic servo system to achieve high tracking performance. To deal with these difficulties, this paper presents a backstepping sliding mode controller to improve the dynamic tracking performance and anti-interference ability. For this purpose, the nonlinear dynamic model is firstly established, where the nonlinear behaviors and modeling uncertainties are lumped as one term. Then, the extended state observer is introduced to estimate the lumped disturbance. The system stability is proved by using the Lyapunov stability theorem. Finally, comparative simulation and experimental are conducted on a hydraulic servo system platform to verify the efficiency of the proposed control scheme.

RISE-based adaptive control of electro-hydraulic servo system with uncertain compensation.

Electro-hydraulic servo system (EHSS) plays an important role in many industrial and military applications. However, its high-performance tracking control is still a challenging mission due to its nonlinear system dynamics and model uncertainties. In this paper, a novel adaptive robust integral method of the sign of the error (ARISE) with extended state observer (ESO) is proposed. Firstly, the nonlinear mathematical model of typical EHSS with modeling uncurtains and uncertain nonlinear is established. Then, ESO is used to estimate the state and lumped disturbance, of which the unknown parameter estimations can be updated by the novel adaptive law. Results shows that the novel controller achieves better tracking performance in maximum tracking error, average tracking error and standard deviation of the tracking error.

A Novel Design of Disturbance Compensator in Active Disturbance Rejection Control

This article aims to describe a novel design method of disturbance compensator in ADRC (Active Disturbance Rejection Control) based on Lyapunov stability theory. Error-based state equation is used to simplify the ADRC structure. The state feedback controller is designed using LQ (Linear Quadratic) method based on a linearized model. The generalized ESO (Extended State Observer) estimates the nonlinear part, model uncertainty, and external disturbance regarded as "total disturbance." Based on the estimate of the disturbance, disturbance compensator is designed using Lyapunov stability theory. In conventional ADRC, after estimating the disturbance compensator rejects the disturbance. But in this paper, it was not simply rejected. Instead the estimate of the disturbance is used in compensator design to make the Lyapunov candidate decrease more quickly. Our method allowed improved the convergence rate of ADRC. A numerical example and IWP (Inertia Wheel Pendulum) stabilization simulation confirmed the new method for effectiveness evaluation.

Adaptive sliding mode control for tunnel boring machine cutterhead telescopic system with uncertainties

PurposeThis paper aims to present an adaptive sliding mode control (ASMC) for tunnel boring machine cutterhead telescopic system with uncertainties to achieve a high-precision trajectory in complex strata. This method could be applied to solve the problems caused by linear and nonlinear model uncertainties.Design/methodology/approachFirst, an integral-type sliding surface is defined to reduce the static tracking error. Second, a projection type adaptation law is designed to approximate the linear and nonlinear redefined parameters of the electrohydraulic system. Third, a nonlinear robust term with a continuous approximation function is presented for handling load force uncertainty and reducing sliding mode chattering. Moreover, Lyapunov theory is applied to guarantee the stability of the closed-loop system. Finally, the effectiveness of the proposed controller is proved by comparative experiments on a scaled test rig.FindingsThe linear and nonlinear model uncertainties lead to large variations in the dynamics of the mechanism and the tracking error. To achieve precise position tracking, an adaptation law was integrated into the sliding mode control which compensated for model uncertainties. Besides, the inherent sliding mode chattering was reduced by a continuous approximation function, while load force uncertainty was solved by a nonlinear robust feedback. Therefore, a novel ASMC for tunnel boring machine cutterhead telescopic system with uncertainties can improve its tracking precision and reduce the sliding mode chattering.Originality/valueTo the best of the authors’ knowledge, the ASMC is proposed for the first time to control the tunnel boring machine cutterhead telescopic system with uncertainties. The presented control is effective not only in control accuracy but also in parameter uncertainty.

Trajectory Planning for Hybrid Unmanned Aerial Underwater Vehicles with Smooth Media Transition

In the last decade, a great effort has been employed in the study of Hybrid Unmanned Aerial Underwater Vehicles, robots that can easily fly and dive into the water with different levels of mechanical adaptation. However, most of this literature is concentrated on physical design, practical issues of construction, and, more recently, low-level control strategies. Little has been done in the context of high-level intelligence, such as motion planning and interactions with the real world. Therefore, we proposed in this paper a trajectory planning approach that allows collision avoidance against unknown obstacles and smooth transitions between aerial and aquatic media. Our method is based on a variant of the classic Rapidly-exploring Random Tree, whose main advantages are the capability to deal with obstacles, complex nonlinear dynamics, model uncertainties, and external disturbances. The approach uses the dynamic model of the HyDrone, a hybrid vehicle proposed with high underwater performance, but we believe it can be easily generalized to other types of aerial/aquatic platforms. In the experimental section, we present simulated results in environments filled with obstacles, where the robot is commanded to perform different media movements, demonstrating the applicability of our strategy.

Improved Third Order PID Sliding Mode Controller for Electrohydraulic Actuator Tracking Control

An electrohydraulic actuator (EHA) system is a combination of hydraulic systems and electrical systems which can produce a rapid response, high power-to-weight ratio, and large stiffness. Nevertheless, the EHA system has nonlinear behaviors and modeling uncertainties such as frictions, internal and external leakages, and parametric uncertainties, which lead to significant challenges in controller design for trajectory tracking. Therefore, this paper presents the design of an intelligent adaptive sliding mode proportional integral and derivative (SMCPID) controller, which is the main contribution toward the development of effective control on a third-order model of a double-acting EHA system for trajectory tracking, which significantly reduces chattering under noise disturbance. The sliding mode controller (SMC) is created by utilizing the exponential rule and the Lyapunov theorem to ensure closed-loop stability. The chattering in the SMC controller has been significantly decreased by substituting the modified sigmoid function for the signum function. Particle swarm optimization (PSO) was used to lower the total of absolute errors to adjust the controller. In order to demonstrate the efficacy of the SMCPID controller, the results for trajectory tracking and noise disturbance rejection were compared to those obtained using the proportional integral and derivative (PID), the proportional and derivative (PD), and the sliding mode proportional and derivative (SMCPD) controllers, respectively. In conclusion, the results of the extensive research given have indicated that the SMCPID controller outperforms the PD, PID, and SMCPD controllers in terms of overall performance.

Robust Adaptive Observer-Based Predictive Control for a Non-Linear Delayed Bilateral Teleoperation System

In this paper, a new robust adaptive nonlinear teleoperation system using an improved extended active observer (IEAOB), adaptive Smith predictor (ASP) and sliding mode control is developed to address the time delay in the communication channels and the nonlinear robot model uncertainties. Firstly, an ASP based on Padé approximation and active observer is designed to compensate for the time delay effect. Specifically, the total network time delay is modelled by Padé approximation, and then an active observer is deployed to estimate the time delay. To ensure the time-varying delay effect is completely suppressed, a sliding mode control algorithm is further developed. Meanwhile, the IEAOB is utilized at both the master and slave sides to deal with the nonlinear model uncertainties, it can provide an accurate robot inertial parameters and friction estimation as well as external force estimation without a structured force model in the presence of disturbances. Finally, the stability of the designed teleoperation system is theoretically studied and the system effectiveness is demonstrated by applying it to a pair of Phantom Omni haptic devices connected via a communication channel with time-varying delays.

Issues of Designing a Model Adaptive Controller Without a State Observer

It can be challenging to develop a controller using conventional techniques for a plant with a linear or nonlinear dynamical system or model uncertainty. Model adaptive control is a new alternative to classical control techniques and a simple way to update controller parameters. Because model reference adaptive control is unable to anticipate the state in real time if the state observer is not designed with, we will reviewsome of the most major disadvantages of the most commonly used design techniques without state observer in this work.

Robust attitude control of the three-dimensional unknown chaotic satellite system

This paper proposes a novel continuous-time robust direct adaptive controller for the attitude control of the three-dimensional unknown chaotic spacecraft system. It considers that the plant’s nonlinear terms, exogenous disturbances, and model uncertainties are unknown and bounded; the controller design is independent of the system’s nonlinear terms. These controller attributes flourish the robust performance of the closed-loop and establish smooth state vector convergence to zero. The proposed controller consists of three parts: (1) a linear controller establishes the stability of the closed-loop at the origin, (2) a nonlinear controller component that autonomously adjusts the feedback gain, and (3) a nonlinear adaptive controller compensates for the model uncertainties and external disturbances using the online estimates of bounds and model uncertainties. The output of this part remains within a given upper and lower bound. The feedback controller gain is large when the state variables are away from the origin and become small in the origin’s vicinity. This feature is novel and contributes to the synthesis of smooth control effort that establishes robust fast and oscillation-free convergence of the state variables to zero. The Lyapunov direct stability analysis assures the global asymptotic robust stability of the closed-loop. Computer simulations and comparative analysis are included to verify the theoretical findings.

A Robust and Adaptive Control Algorithm for Closed-Loop Brain Stimulation.

Developing closed-loop brain stimulation systems can benefit the treatment of neurological and neuropsychiatric disorders and facilitate brain functions. Current designs of closed-loop controllers have used time-invariant linear models of brain activity to devise non-adaptive controllers. However, unmodeled nonlinear dynamics can happen during real-time closed-loop control, leading to nonlinear uncertainty in the brain activity model. Current non-adaptive controllers cannot track the nonlinear model uncertainty and are not robust to noise, both of which can compromise their control performance. Here, within an ℒ1 adaptive control framework, we develop a new discrete-time robust and adaptive closed-loop control algorithm that addresses a general form of nonlinear model uncertainty. We conduct Monte Carlo simulations to validate the robust and adaptive control algorithm and show that it significantly outperforms existing closed-loop control algorithms. Our results can facilitate future designs of precise and safe closed-loop brain stimulation systems to treat neurological and neuropsychiatric disorders and modulate brain functions.

Distributed adaptive neural network constraint containment control for the benthic autonomous underwater vehicles

Multiple Autonomous Underwater Vehicles (AUV) can complete complex ocean exploration missions cooperatively. This paper proposes a containment control algorithm under time-varying constraints by using a neural network for control of multiple benthic AUVs which are called the Ocean Bottom Flying Node (OBFN) systems. The multiple OBFNs in the presence of nonlinear model uncertainties are under the directed topology. First, we define the auxiliary variable and low-order filter. The anti-windup saturation auxiliary system is constructed in presence of the input saturation. Further, the adaptive law and neural network are designed to compensate environmental disturbances and systems model uncertainties, respectively. Moreover, in order to ensure the control performance of OBFN, an exponential boundary constraint is imposed which could constrain the system error convergent rates and bounds. Lyapunov stability theorem and graph theory are used to prove that the multiple OBFN systems are uniformly ultimately bounded. Finally, simulation results for multiple OBFNs illustrate the effectiveness of the proposed algorithm.

Tracking Control of Single-Axis Feed Drives Based on ADRC and Feedback Linearisation

The accuracy of manufacturing highly characterises the performance of industrial motion control. However, detrimental effects such as nonlinear coupling, model uncertainty and unknown external disturbances severely affect trajectory tracking performance. In this paper, we proposed an ADRC and feedback linearisation-based control algorithm for the high-precision trajectory tracking of feed drives. The controller was rigorously designed to ensure the convergence of observer states and tracking error. The applicability of the proposed approach was successfully demonstrated via high-fidelity simulation, and the numerical results based on different tracking methods were compared.