Unknown Time-varying Disturbances Research Articles

Nonlinear adaptive speed control of a permanent magnet synchronous motor: A perturbation estimation approach

This paper presents a nonlinear adaptive control (NAC) scheme for the speed regulation of a permanent magnet synchronous motor (PMSM) based on perturbation estimation and feedback linearizing control. All PMSM system’s unknown nonlinearities, parameter uncertainties, and external disturbances including unknown time-varying load torque disturbance, are defined as lumped perturbation terms, which are estimated by designing perturbation observers. The estimates are used to adaptively compensate the real perturbations and achieve adaptive feedback linearizing control of the original nonlinear system. The proposed control scheme does not require accurate system model and full state feedback. Stability of the close-loop system with proposed NAC is investigated via Lyapunov theory, and the effectiveness of proposed NAC scheme is verified through both simulation and experimental studies. Both simulation and experimental results show that the proposed NAC scheme can provide less regulation error in speed tracking, better dynamic performance and robustness against parameter uncertainties and load torque disturbance, compared with conventional vector control and load torque estimated based control.

Cooperative Control of Multiple Dynamic Positioning Vessels with Input Saturation Based on Finite-time Disturbance Observer

This paper presents a new cooperative control strategy for dynamic positioning of multiple surface vessels subject to unknown time-varying environmental disturbances and input saturation. The vessels are assumed interconnected through a directed topology rather than bidirectional. Two control objectives are considered in this paper. The first one is to make these vessels track desired positions and headings, and the other control objective is to hold the desired formation. For these purposes, we propose a cooperative control which consists of finite-time disturbance observer, auxiliary dynamic system and dynamic surface control technique. A nonlinear finite-time observer is developed to estimate unknown time-varying disturbance. To tackle the input saturation problem, an auxiliary dynamic system is constructed. It is also proved that all signals in the closed-loop control system converge to a small neighborhood of equilibrium state via Lyapunov analysis. Simulation results are given to validate the effectiveness of the proposed control strategy.

A Finite-Time Output Feedback Control Scheme for Dynamic Positioning System of Ships

This paper develops a finite-time output feedback control scheme for dynamic positioning (DP) system of ships in the presence of unmeasured states of ships, unknown dynamic model parameters and unknown time-varying environment disturbances. A novel finite-time extended state observer (FTESO) is first proposed to simultaneously and precisely estimate the unmeasured states of ships, unknown dynamic model parameters, and unknown time-varying environment disturbances in finite time. Second, based on the outputs of FTESO, the terminal sliding mode (TSM) controller is designed to guarantee that the DP system can track the position and heading at desired values in finite time with precise performance. Then, it is proved that all error signals of the closed-loop DP control system can converge to zero in finite time by utilizing the homogeneous method and the Lyapunov stability theory. Finally, the numerical simulations on a supply ship are carried out to illustrate the effectiveness of the proposed finite-time output feedback control scheme.

Error-Driven-Based Nonlinear Feedback Recursive Design for Adaptive NN Trajectory Tracking Control of Surface Ships With Input Saturation

In this paper, we investigate the trajectory tracking control problem of surface ship subject to the dynamic uncertainties, unknown time-varying disturbances and input saturation. To handle the non-smooth input saturation nonlinearity and compensate the ship dynamic uncertainties, Gaussian error function and adaptive neural network technique are employed. In control design, to obtain the transient motion reference signal, finite-time nonlinear tracking differentiator is applied to generate virtual reference signal and to extract the derivative of virtual control law. Referring to the effects of the kinematics subsystem on the kinetics subsystem caused by the error of tracking differentiator, and the effects of the input saturation on the control accuracy and the dynamic quality of the trajectory tracking control system, we propose an error-driven-based nonlinear feedback recursive design technique to design trajectory tracking control law, and employ a new non-quadratic Lyapunov functions to analyze the trajectory tracking control system stability. The proposed control scheme fully embodies the characteristics of the lowgain and high-gain control, and overcomes the effect of tracking differentiator error on closed-loop system by recursive design method. Simulation results verify the effectiveness of our proposed control scheme.

Robust Adaptive Trajectory Linearization Control for Tracking Control of Surface Vessels With Modeling Uncertainties Under Input Saturation

This paper develops a novel adaptive trajectory tracking control strategy to enhance the tracking performance for surface vessels with unmodeled dynamics and unknown time-varying disturbances. A high robustness and precision trajectory tracking controller is presented by using trajectory linearization control (TLC) technology, neural network, extended state observer (ESO), nonlinear tracking differentiator, and auxiliary dynamic system. First, the greatest advantage of this paper is that the TLC technology is first introduced into the field of surface vessels motion control, which provides a new direction for TLC technology research. Then, to further enhance the control performance and robustness of the system, the neural network with minimum learning parameter is used to replace the classical radial basis function neural network to approximate unmodeled dynamics, which can reduce the burden of computing. A novel reduced-order ESO is constructed to estimate unknown time-varying disturbances to achieve real-time compensation. Meanwhile, nonlinear tracking differentiator is employed to realize the derivative of virtual control command, as well as to provide command filtering. In addition, an auxiliary dynamic system is designed to reduce the risk of actuator saturation. The stability of the closed-loop system is guaranteed based on the Lyapunov criteria. Lastly, the comparison results demonstrate the superior performance of the proposed approach.

Adaptive Course Control-Based Trajectory Linearization Control for Uncertain Unmanned Surface Vehicle Under Rudder Saturation

In the presence of the uncertain system dynamics, unknown time-varying disturbances and rudder saturation, this paper develops a novel robust adaptive course control scheme for unmanned surface vehicle (USV). Considering the characteristics of the rudder servo system, a double loop course controller of the practical and concise is proposed by the enhanced trajectory linearization control (TLC) technology. The key features of the developed controller are that, first, the neural networks are employed to online approximate unmodeled dynamics, and adaptive techniques are adopted to deal with completely unknown external disturbances; second, auxiliary systems that are governed by smooth switching functions, are developed in an unprecedented manner to compensate for the saturation constraints on actuators. The main innovation can be summarized as that the TLC technology is applied to the USV motion control field as a new control algorithm, and the enhanced technology based on traditional TLC not only reduces the number of adjustment parameters but also has simple structure and high robustness. Furthermore, a low frequency learning method improves the applicability of the algorithm. The stability analysis is established using the Lyapunov theory. Simulation results and comparison verify the effectiveness of the proposed strategy.

High-Gain Observer-Based Line-of-Sight Guidance for Adaptive Neural Path Following Control of Underactuated Marine Surface Vessels

This paper presents an adaptive neural network dynamic surface control law with time-varying sideslip compensation, which includes a geometric kinematic control design and a dynamic control design, for path following of underactuated marine surface vessels (MSVs) in the presence of unmeasured states, model uncertainties, unknown ocean environmental disturbances, and input saturation. First, a high gain observer based line-of-sight guidance law, capable of estimating and compensating the time-varying sideslip angle induced by the unknown time-varying ocean disturbances, is proposed to generate the desired heading for the dynamic control system of the MSV. Next, considering the input saturation, adaptive neural network dynamic surface velocity control laws, in which the model uncertainties and unknown ocean environmental disturbances of the system are compensated by adaptive radial basis function neural network and the problem of input saturation is solved by introducing auxiliary dynamic systems, are designed to realize the dynamic control target of the path following. The proposed control strategy of path following compensates the ocean environmental disturbances from the perspective of both the geometric kinematics and the dynamics, and all error signals of a closed-loop control system are proven to be uniformly ultimately bounded. The simulations validate the effectiveness of the proposed control strategy for path following of MSVs.

Extremum seeking regulator for a class of SISO time-varying nonlinear systems

This paper proposes an extremum-seeking regulator design based on a Lie bracket averaging technique for time-varying nonlinear systems in the presence of unknown time-varying disturbance dynamics. The approach adopts a post-processing output regulation method for the regulation of nonlinear systems to the unknown minimum of a measured objective function. The stability analysis demonstrates that one can achieve practical output regulation of the unknown optimum equilibrium. A simulation study demonstrates the ability of the proposed technique to solve very general output regulation problems in the absence of exact knowledge of the process dynamics, the disturbance dynamics or a corresponding internal model.

Robust identification of discrete-time linear systems with unknown time-varying disturbance

In this paper, one robust identification method is proposed for the discrete-time linear systems with unknown time-varying disturbance. The disturbance is considered as a time-varying parameter for tracking estimation. A robust recursive least squares method is proposed using a forgetting factor. Moreover a new forgetting scheme to update the covariance matrix is developed to improve the stable convergence property of the time-invariant model parameters and the tracking performance of time-varying disturbance. The convergence performance of parameter estimation is analyzed with a proof. Two examples with different types of time-varying disturbance are shown to illustrate the effectiveness and advantage of the proposed method.

Attitude Controller Design with State Constraints for Kinetic Kill Vehicle Based on Barrier Lyapunov Function

An adaptive attitude controller is designed based on Barrier Lyapunov Function (BLF) to meet the state constraints caused by side window detection. Firstly, the attitude controller is designed based on the BLF, but the stabilization function is complex and its time derivative will cause “differential explosion”. Therefore, Finite-time-convergent Differentiator (FD) is used to estimate the first derivative of the stabilization function. If the tracking error is outside the BLF's convergence domain, BLF controller cannot guarantee the error global convergence. Sliding mode controller (SMC) is used to make the system's error converge to set domain, and then the BLF controller could be used to ensure that the output constraint is not violated. Uncertainties and unknown time-varying disturbances usually make the control precision worse and Nonlinear Disturbance Observer (NDO) is designed for estimation and compensation uncertainties and disturbances. The pseudo rate modulator (PSR) is used to shape the continuous control command to pulse or on-off signals to meet the requirements of the thruster. Numerical simulations show that the proposed method can achieve state constraints, pseudo-linear operation, and high accuracy.

Robust adaptive NN control of dynamically positioned vessels under input constraints

Abstract A robust adaptive neural network (NN) control law is developed for dynamic positioning (DP) of vessels with unknown dynamics and unknown time-varying disturbances under input constraints through incorporating adaptive radial basis function (RBF) NNs, an auxiliary dynamic system and a robust control term into dynamic surface control method. The developed DP control law makes the DP closed-loop system be uniformly ultimately stable and the vessel's position and heading be maintained at the desired values with arbitrarily small errors. The advantages of the proposed control scheme are that: first, the developed DP control law does not require any priori knowledge of vessel dynamics and disturbances under input constraints, and prevents the presence of input constraints from degrading control performance and even destabilizing the DP control system; second, the developed DP control law compensates for not only unknown time-varying disturbances but also NN approximation errors for unknown vessel dynamics. Simulations on two supply vessels are conducted to exhibit the efficiency and control performance of the developed DP control law.

Robust Optimal Adaptive Sliding Mode Control with the Disturbance Observer for a Manipulator Robot System

In this paper, a robust optimal adaptive sliding mode control (OASMC) by using disturbance observer (DOB) is successfully proposed and applied in the manipulator robot system. The control gains are on-line adjusted by the DOB to compensate the unknown time-varying disturbances to optimize and stabilize the control system. The optimal control and sliding mode control are integrated based on the Lyapunov stability theory to obtain the optimal sliding mode control (OSMC). Then, the adaptation control gains are on-line adjusted by the DOB to compensate the unknown time-varying disturbances for the control system. The manipulator robot system is given as the control example to demonstrate the proposed OASMC. From the simulation results, the proposed OASMC successfully demonstrates the optimal, adaptive and robust control performances for the manipulator robot system. The novelty of this paper is that the DOB can correctly estimate the unknown time-varying disturbances to on-line adjust the control gain of OASMC to stabilize the manipulator robot system. The proposed OASMC simultaneously has optimal, adaptive and robust control characteristics.

Adaptive prescribed performance control of QUAVs with unknown time-varying payload and wind gust disturbance

In this paper, a new robust adaptive prescribed performance control (PPC, for short) scheme is proposed for quadrotor UAVs (QUAVs, for short) with unknown time-varying payloads and wind gust disturbances. Under the presented framework, the overall control system is decoupled into translational subsystem and rotational subsystem. These two subsystems are connected to each other through common attitude extraction algorithms. For translational subsystem, a novel robust adaptive PPC strategy is designed based on the sliding mode control technique to provide better trajectory tracking performance and well robustness. For rotational subsystem, a new robust adaptive controller is constructed based on backstepping technique to track the desired attitudes. Finally, the overall system is proved to be stable in the sense of uniform ultimate boundedness, and numerical simulation results are presented to validate the effectiveness of the proposed control scheme.

Robust composite neural dynamic surface control for the path following of unmanned marine surface vessels with unknown disturbances

This article presents a robust composite neural-based dynamic surface control design for the path following of unmanned marine surface vessels in the presence of nonlinearly parameterized uncertainties and unknown time-varying disturbances. Compared with the existing neural network-based dynamic surface control methods where only the tracking errors are commonly used for the neural network weight updating, the proposed scheme employs both the tracking errors and the prediction errors to construct the adaption law. Therefore, faster identification of the system dynamics and improved tracking accuracy are achieved. In particular, an outstanding advantage of the proposed neural network structure is simplicity. No matter how many neural network nodes are utilized, only one adaptive parameter that needs to be tuned online, which effectively reduces the computational burden and facilitates to implement the proposed controller in practice. The uniformly ultimate boundedness stability of the closed-loop system is established via Lyapunov analysis. Comparison studies are presented to demonstrate the effectiveness of the proposed composite neural-based dynamic surface control architecture.

Robust nonlinear control design for dynamic positioning of marine vessels with thruster system dynamics

Considering the dynamics characteristics of thruster systems for dynamically positioned marine vessels with model parameter uncertainties and unknown time-varying ocean disturbances, the dynamic positioning (DP) control problem becomes a mismatched nonlinear control problem. To solve this problem, a DP robust nonlinear control law is developed using the command filtered vectorial backstepping combined with a disturbance observer (DO) and an auxiliary dynamic system (ADS). The DO provides the estimates of mismatched compound disturbances induced by model parameter uncertainties and unknown ocean disturbances. The ADS addresses the effects of thrust saturation constraints. The command filtered vectorial backstepping obviates differentiations of intermediate control function vectors due to introducing command filters and compensates for filtering errors of intermediate control function vectors caused by command filters by means of designed dynamic systems. The developed DP control law is computationally simple and the DP control performance is improved. Under the developed DP control law, the positioning errors of vessels are made as small as desired and all signals in the DP closed-loop control system are uniformly ultimately bounded. The high-fidelity simulation results on a supply vessel validate the developed DP control law.

Dynamic positioning of ships with unknown parameters and disturbances

Robust adaptive control is proposed for the dynamic positioning (DP) of ships with unknown model parameters and unknown time-varying disturbances. Through representing the parameter uncertain ship motion mathematical model and the unknown time-varying disturbances as parametric forms, respectively, constructing an observer for handling disturbances, and using the adaptive vectorial backstepping, the DP robust adaptive control law is designed. The proposed DP control law achieves the global asymptotic regulation of positioning errors, while guaranteeing the global uniform ultimate boundedness of all signals in the DP closed-loop control system. Simulation results involving a supply vessel validate the proposed DP control law.

UDE-based robust boundary control for an unstable parabolic PDE with unknown input disturbance

A novel control strategy, named uncertainty and disturbance estimator (UDE)-based robust control, is applied to the stabilization of an unstable parabolic partial differential equation (PDE) with a Dirichlet type boundary actuator and an unknown time-varying input disturbance. The unstable PDE is stabilized by the backstepping approach, and the unknown input disturbance is compensated by the UDE, which constructs an estimation of the disturbance by filtering the system input and measurable state signals. The proposed UDE-based robust boundary control only requires the spectrum information of the disturbance signal and one boundary output measurement. Stability analysis of the closed-loop systems is carried out, and a numerical example is provided to validate the proposed method.

Sliding mode tracking control of autonomous underwater vehicles with the effect of quantization

This paper develops a trajectory tracking control law for autonomous underwater vehicles (AUVs) with the effect of states and control input quantization. A sliding mode control (SMC) scheme is proposed to conquer the quantization effect by introducing the bound of quantization error into the switching term of the SMC. A finite-time disturbance observer is proposed to observe the unknown time-varying disturbances. The stability analysis demonstrates that the designed tracking controller can force the AUV to track the reference trajectory and guarantee the asymptotic stability of the closed system. Simulation results illustrate the effectiveness of the proposed control method.

Resilient control based on disturbance observer for nonlinear singular stochastic hybrid system with partly unknown Markovian jump parameters

In this paper, the composite anti-disturbance resilient control is considered for nonlinear singular stochastic hybrid system with partly unknown Markovian jump parameters under multiple disturbances. Three kinds of disturbances are included in the studied system. One is generated by an external system and it enters the hybrid system from the channel of the control input. The other one is stochastic white noise. And the third one is the external unknown time-varying disturbance and it is supposed to be H2 norm bounded. By combining the disturbance-observer-based-control scheme, H∞ control technique and resilient control method, a composite anti-disturbance resilient controller is constructed to attenuate and eliminate the affection of these disturbances, and ensures the whole closed-loop system regular, impulse free and stochastically stable with the corresponding control performance. Then, some sufficient conditions and the gains of the controller and observer are obtained by using Lyapunov function method and the linear matrix inequalities (LMIs) technique. Finally, two numerical examples are given to show the effectiveness of presented method.

Reliability-based robust dynamic positioning for a turret-moored floating production storage and offloading vessel with unknown time-varying disturbances and input saturation

In this paper, we derived a mathematical model for a floating production storage and offloading (FPSO) vessel and its buoy mooring system and developed a new robust positioning controller to keep vessels in a desired region in the presence of unknown time-varying disturbances with uncertainties and input saturation. Different materials (chain and polyester) and buoys are considered in the model of mooring system to make the developed model more realistic. We employed a disturbance observer to estimate the disturbances and designed an auxiliary dynamic system integrated with the structural reliability's derivative to quantify the input saturation's influence, and its states are used to the control design. Our proposed controller can keep the structural reliability and heading at desired values with arbitrarily small errors while guaranteeing the uniform ultimate boundedness of all signals in the closed-loop control system. It is easier for the control design because disturbances and input saturation are handled simultaneously and so is the stability analysis because only one Lyapunov function is needed. Simulations are conducted to demonstrate our proposed controller's effectiveness and a comparison with a robust controller based on hyperbolic tangent functions shows our proposed controller can avoid steady errors with desired control goals.