Nonlinear Feedback Control Law Research Articles

Space and time joint optimization for vertical takeoff and landing aircraft in dense obstacles and interference environments

ABSTRACT The Vertical Takeoff and Landing Aircraft (VTOL) is capable of both low-speed hovering and high-speed flight. This paper proposes an autonomous motion planning and anti-wind disturbance control algorithm for the VTOL, implemented spatial and temporal joint motion planning for VTOL, under the limitation of maximum flight speed of the aircraft, VTOL can achieve fully autonomous flight in complex environments, which can realize the autonomous flight of a single aircraft in a complex and dense environment, achieve real-time perception and avoidance of static and dynamic obstacles. The information generated by motion planning includes the position, velocity, and acceleration information of the aircraft, and proposes a wind disturbance estimation and active control strategy in a wind disturbance environment, accurate estimation of wind disturbance is achieved through a state observer, and the wind disturbance was suppressed through nonlinear error feedback control law, implemented wind disturbance estimation and suppression for aircraft in wind disturbance environments, and achieved complete autonomous motion planning and trajectory tracking of VTOL in a complex and wind disturbance environment. Our work can provide a basis for the collaborative control of multiple UAVs.

Fault-tolerant control of automatic carrier landing using direct lift control based on nonsingular terminal sliding mode and active disturbance rejection control

This paper presents a fault-tolerant control scheme, combining nonsingular terminal sliding mode and active disturbance rejection control (NTSM-ADRC) to address actuator failure and external disturbances during the automatic carrier landing process of a carrier-based aircraft using direct lift control (DLC). First, the carrier-based aircraft model, the carrier air-wake model, and the actuator fault model were established. Second, the NTSM-ADRC controller is designed, The unmodeled dynamics of the system, the air-wake disturbance, and the fault term are treated as total disturbances and estimated accurately by extended state observer (ESO). To improve the response characteristics of the controller, the nonlinear error feedback control law is designed by combining the NTSMC. The Lyapunov function is constructed to prove the stability of the closed-loop system. The controller is applied to the aircraft DLC channel, attitude auxiliary channel, and approach power compensation system. The DLC improves the performance of fixed-wing aircraft by directly generating high lift through the flaps to change the aircraft trajectory. Finally, the method is tested by introducing various types of actuator failures. Simulation results demonstrate that the designed longitudinal fault-tolerant carrier landing system exhibits strong robustness and fault tolerance, thereby improving the accuracy of aircraft landing trajectory tracking.

Active Disturbance Rejection Predictive Control for Local Trajectory Planning of Unmanned Ground Vehicles

In this paper, an active disturbance rejection predictive control strategy is proposed for trajectory planning task of unmanned ground vehicles. Rather than error estimation of accurate system modeling, internal error and environment disturbance are processed via single extended state observer. Nonlinear feedback control law is applied to reduce steady-state error significantly. Then motion planning and nonholonomic constraints could be handled via nonlinear model predictive control. Simulation and experiment results show that the proposed algorithm is able to accomplish trajectory planning task with internal error and environment disturbance.

A Virtual Synchronous Generator Secondary Frequency Modulation Control Method Based on Active Disturbance Rejection Controller

In order to solve the frequency modulation (FM) problem caused by load in the virtual synchronous generator (VSG) system under an islanding state, this paper proposes a frequency modulation method based on active disturbance rejection control (ADRC). Firstly, design a nonlinear function using the design rules of nonlinear functions. Then, the extended state observer (ESO) and nonlinear feedback control law (NLSEF) of ADRC are designed based on the nonlinear function. By introducing ADRC into the power–frequency control loop of VSG, error-free frequency modulation of VSG is achieved. Finally, the superiority of the proposed method was verified through experimental comparison.

Robust Hybrid Global Dual Quaternion Pose Control of Spacecraft-Mounted Robotic Systems

We propose a nonlinear hybrid dual quaternion feedback control law for multibody spacecraft-mounted robotic systems (SMRSs) pose control. Indeed, screw theory expressed via a unit dual quaternion representation and its associated algebra can be used to compactly formulate both the forward (position and velocity) kinematics and pose control of -degree-of-freedom robot manipulators. Recent works have also established the necessary theory for expressing the rigid multibody dynamics of an SMRS in dual quaternion algebra. Given the established framework for expressing both kinematics and dynamics of general -body SMRSs via dual quaternions, this paper proposes a dual quaternion control law that achieves simultaneous global asymptotically stable pose tracking for the end effector and the spacecraft base of an SMRS. The proposed hybrid control law is robust to chattering caused by noisy feedback and avoids the unwinding phenomenon innate to continuous-based (dual) quaternion controllers. Additionally, an actuator allocation technique is proposed in the neighborhood of system singularities to ensure bounded control inputs, with minimum deviation from the specified spacecraft base and end-effector trajectories during controller execution.

ADRC‐based control strategy for DC‐link voltage of flywheel energy storage system

AbstractThe direct current (DC)‐link voltage control of the flywheel energy storage system plays an important role in realizing high‐quality grid connection. With the traditional proportional‐integral control, the DC‐link voltage cannot track its reference value quickly and smoothly when the flywheel energy storage system switches from the charging stage to other working stages. Therefore, a DC‐link voltage control strategy for the flywheel energy storage system based on active disturbance rejection control is proposed in this paper to deal with this issue. The DC‐link voltage and its differential value are considered as the state variables in this strategy. The internal and external disturbances, such as load power, switching loss, and parameter uncertainty, are regarded as an expanded state. By inputting the voltage error and the observed disturbance into the nonlinear state feedback control law, the rapidity and anti‐interference of the DC‐link voltage control are ensured under different States of Charge of the flywheel energy storage system. Then, the coefficient freezing method is used to analyze the effects of the disturbance observation bandwidth by nonlinear gain and pole position changes. The DC‐link voltage can track the reference value over a wider frequency range of disturbances. By configuring the appropriate observer structure parameters, the disturbance observation bandwidth under the nonlinear function gain variation is always higher than the expected bandwidth. The effectiveness of the proposed control strategy is verified by simulation results at last.

Three-Dimensional Trajectory Tracking of AUV Based on Nonsingular Terminal Sliding Mode and Active Disturbance Rejection Decoupling Control

This paper presents a nonsingular terminal sliding mode and active disturbance rejection decoupling control (NTSM-ADRDC) scheme for the three-dimensional (3D) trajectory tracking of autonomous underwater vehicles (AUV). Firstly, the AUV model is decoupled into five independent single input–single output (SISO) channels using ADRDC technology. Secondly, the NTSM-ADRDC controller is designed. The linear extended state observer (LESO) is used to observe the AUV state variables, and estimate the total disturbance of the system. In addition, to improve the system error convergence rate, the combination of exponential reaching rate and NTSM constitutes a nonlinear states error feedback control law for the controller. Finally, the stability of the proposed control law is proved using the Lyapunov theory. The simulation results demonstrate the effectiveness and robustness of the designed NTSM-ADRDC trajectory tracking approach.

Orbit acquisition, rendezvous, and docking with a noncooperative capsule in a Mars sample return mission

The Mars sample return mission is intended to perform autonomous rendezvous and docking, aimed at gathering Mars samples, stored in an orbiting capsule. This study focuses on guidance and control techniques for the three phases of a typical Mars sample return mission: (i) orbit acquisition, (ii) phasing and correction maneuvers, and (iii) rendezvous and docking with the orbiting sample (OS) capsule, which is assumed to be a noncooperative spacecraft. The chaser vehicle is assumed to be equipped with both chemical and electrical propulsion. The latter is used in phase (i), in conjunction with nonlinear orbit control. This can be regarded as an autonomous guidance technique also in the presence of nonnominal flight conditions. In phase (ii), a phasing strategy and proper correction maneuvers are designed, to reach suitable parking conditions, identified through the orbital commensurability criterion. Then, a guidance, control, and actuation architecture is proposed for phase (iii), split in arc 1 (proximity maneuvers) and arc 2 (final approach and docking). Feedback linearization is employed for trajectory control, aimed at tracking a reference path, which is iteratively defined from the estimation of the rotational state of the capsule. Two distinct, nonlinear feedback control laws, enjoying quasi-global stability properties, are used for attitude control. Actuation is demanded to a pyramidal array of single-gimbal control momentum gyros, the main thruster, and an arrangement of side thrusters. A large set of perturbations (including navigation and actuation errors) are modeled. Monte Carlo simulations prove that the guidance, control, and actuation architecture at hand is effective to complete safe docking with a noncooperative OS capsule.

Improved Position Sensorless Control for PMLSM via an Active Disturbance Rejection Controller and an Adaptive Full-Order Observer

Position and speed information are very important to realize the efficient control for permanent magnet linear synchronous motor (PMLSM). In order to obtain more accurate position estimation signals, this article investigates an improved position sensorless control method for PMLSM by combining an active disturbance rejection control (ADRC)-based speed controller and an adaptive full-order observer (AFO)-based position estimator. The AFO is constructed based on model reference adaptive system (MRAS), which can obtain more accurate position estimation signal by introducing a current error feedback gain matrix. However, there are lots of thrust fluctuations existing in PMLSM caused by end effect, which will affect the estimation accuracy. Since it is difficult to reduce the influence of thrust fluctuation by only improving the observer itself, an ADRC-based speed controller is designed to improve the anti-interference ability of control system, thereby improving the position estimation accuracy. For the ADRC controller, an second-order linear extended state observer (LESO) is designed to observe the thrust fluctuation and an nonlinear state error feedback (NLSEF) control law is introduced to compensate the observed disturbance. The effectiveness and superiority of the proposed method have been verified by simulation and experimental results.

Control method for permanent magnet synchronous motor based on fractional active disturbance rejection

To improve the response speed and anti-interference ability of a permanent magnet synchronous motor (PMSM), a PMSM control method based on fractional-order active disturbance rejection control (FOADRC) is proposed in this study. First, a fractional-order tracking differentiator (FOTD) and fractional-order extended state observer (FOESO) are designed using the fractional calculus. According to the response speed of the FOTD and the observation effect of the FOESO, a new fastest function and new nonlinear function are designed. Second, a fractional-order active disturbance rejection (FOADR) controller is built based on the new FOTD, new FOESO, and nonlinear feedback control law, and its stability is proven. Finally, the superiority and effectiveness of the proposed strategy are verified through a simulation and experiments.

Unbalanced vibration control of active magnetic bearing using an active disturbance rejection notch decoupling technique

Aiming at the position coupling, gyroscopic effect, and synchronized vibration caused by the unbalance mass in the magnetic bearing rotor, a linear active disturbance rejection notch decoupling control method is proposed. Firstly, a model with coupling and unbalanced vibration of the system was established. The terms of position coupling, gyroscopic effect, and unbalanced vibration in the system are estimated by Extended State Observer and the estimator is treated as the system disturbance to be compensated, then the radially existing coupled and unbalanced vibration systems are decoupled into four independent second-order series-integrated subsystems. The nonlinear state error feedback control law is designed to implement the decoupling control of each subsystem. For the problem of unbalanced vibration of the rotor after decoupling, the suppression method of the dynamic unbalanced force of the same frequency notch filter is designed, and then the closed-loop feedback structure of the new method is deduced, and its frequency characteristics are analyzed. Then the rules and principles of controller parameter selection are summarized using Bode diagram. The simulation results show that the designed linear active disturbance rejection notch decoupling controller not only achieves the decoupling control of the respective degrees of the magnetic bearing rotor but also suppresses the unbalanced vibration of the rotor. At the same time, it solves the influence of the gyroscopic effect on the control under the high-speed running of the magnetic bearing rotor.

A Novel Two-Phase Mode Switching Control Strategy for PMSM Position Servo Systems With Fast-Response and High-Precision

In this article, a novel mode switching control (MSC) strategy is proposed containing a fast-response phase and a high-precision settling phase to meet the requirement of high-quality point-to-point permanent magnet synchronous motor servo systems. In the fast-response stage, an adaptive trajectory planning method is developed to program the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis current profile online based on the reference for the motor to reach the neighborhood of the reference position in minimum time. The chattering in the conventional time-optimal control is overcome and the idea that skipping speed and position loop with preplanned <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis current trajectory is first attempted. After switching, the high-precision settling stage that is responsible for improving the transient performance in terms of reducing the overshoot and settling time is built with the proposed robust composite nonlinear feedback (RCNF) control law. This RCNF method cancels the overall disturbance through an extended state observer. The switching condition for the proposed MSC controller is clarified. Afterward, the whole closed-loop system's stability is strictly proved. Experiments are then conducted based on different scenarios to prove the effectiveness and robustness of the proposed MSC method.

Optimisation of Temperature Control Parameters Based on Plate Heat Exchanger

Plate heat exchanger temperature control has strong coupling and disturbance instability in the control process. To solve these problems, first, a decoupling controller based on state feedback was designed. The parameters are then optimised using a genetic algorithm to suppress external disturbances using an active disturbance rejection controller (ADRC). The trackability and system stability of the built extended state observer (ESO) are analysed. The stabilisation of the system under bounded input conditions is achieved by adjusting the non-linear state error feedback control law coefficients in the ADRC. The simulation results show that the genetic algorithm optimised parameter controller based on state feedback decoupling enables complete decoupling of the temperature control, and the ESO has good tracking performance with better immunity to disturbances.

Rotating mirror servo system control based on modified sliding mode-active disturbance rejection controller

In order to improve the tracking accuracy and robustness of the rotating mirror servo system, a modified sliding mode-active disturbance rejection control (MSM-ADRC) strategy is proposed. Firstly, the structure and working principle of the rotating mirror servo system are analysed, and its mathematical model is established to prepare for the design of the controller. Then, a MSM-ADRC is proposed to reduce the influence of unknown disturbance and improve the tracking accuracy. Among them, the modified sliding mode extended state observation (MSM-ESO) is designed by replacing the traditional nonlinear function with the designed optimal control function, which enhances the observation accuracy of the system state quantity and total disturbance. Meanwhile, an improved approach law is proposed, and an improved sliding mode nonlinear error feedback control law (MSM-NLSEF) is designed based on this approach law, which improves the convergence speed and accuracy of the control law. In addition, the stability of the designed MSM-ESO and MSM-NLSEF is proved. Finally, the proposed control method is validated by simulation and experimental comparison with other state-of-the-art controllers. Results reveal that the proposed control method has satisfying tracking performance and strong disturbance rejection ability.

Rotor position angle control of permanent magnet synchronous motor based on sliding mode extended state observer

ABSTRACT To achieve fast, accurate control of the position angle of the rotor of permanent magnet synchronous motor (PMSM), traditional auto disturbance rejection control often has many adjustable parameters and complex tuning problems. Sliding mode control technology is introduced into the extended state observer (ESO) part of the auto disturbance rejection controller, and a new sliding mode approach law is designed based on several typical sliding mode approaches, which simplifies parameter tuning while retaining the original anti-interference performance of auto disturbance. In addition, the nonlinear state error feedback control law in active disturbance rejection control is enhanced to improve the component order PID control law, which can improve the response speed and robustness of the system, and prove the stability of the controller. Finally, the simulation of the PMSM rotor position control system based on the sliding mode ESO is carried out, and the results verify the validity of the method.

Design of Asynchronous Motor Controller Based on Controlled Lagrangians Method

Asynchronous motor system has the characteristics of high order, strong coupling, and nonlinearity. From the dynamical model, it is the underactuated mechanical system, which means that the dimension of its input space is fewer than the degree of freedom. Following this perspective, the energy based nonlinear control technology-CL (controlled Lagrangians) method is used to solve the control problem in this paper. Based on the expected controlled energy and its derivative with respect to time, controlled Lagrangians and generalized force are constructed, and they produce the controlled equations. In order to ensure the complete matching between the controlled equation and the original equation, the gyroscopic forces containing the first-order term of velocity are innovatively introduced into the generalized force, and the matching conditions are obtained. By solving the matching conditions composed of some partial differential equations, the nonlinear smooth feedback control law can realize the global asymptotic stabilization of not only velocity but also position. Finally, the controlled energy is selected as the Lyapunov function, and the stability is proved according to the LaSalle invariant theorem. The effectiveness of the designed control law is demonstrated in the results of the simulation.

An Improved Extended State Observer-Based Composite Nonlinear Control for Permanent Magnet Synchronous Motor Speed Regulation Systems

This paper addresses the problems of an improved extended state observer (ESO)-based composite nonlinear control for the permanent magnet synchronous motor (PMSM) speed regulation systems, which is primarily constituted by a linear ESO-based feedforward compensation and nonlinear proportional feedback (NPF) control law. Firstly, by taking the parametric perturbations and external disturbances into account, a novel linear ESO is designed and analyzed to estimate the lumped disturbance, such that the system anti-disturbance performance is preserved. Meanwhile, the estimation of system state is also performed. Then, an optimal control synthesis function-based tracking differentiator (TD) is developed to arrange the transition dynamic for the reference velocity value, while its high quality differential signal is facilitated. Furthermore, an adaptive proportional control law is proposed, resulting in the eventual composite nonlinear strategy by incorporating the estimate values into the designed NPF controller. Finally, a PMSM servo system is studied to demonstrate the advantages and effectiveness of the proposed approaches.

Three-agent Time-constrained Cooperative Pursuit-Evasion

This paper considers a pursuit-evasion scenario among three agents– an evader, a pursuer, and a defender. We design cooperative guidance laws for the evader and the defender team to safeguard the evader from an attacking pursuer. Unlike differential games, optimal control formulations, and other heuristic methods, we propose a novel perspective on designing effective nonlinear feedback control laws for the evader-defender team using a time-constrained guidance approach. The evader lures the pursuer on the collision course by offering itself as bait. At the same time, the defender protects the evader from the pursuer by exercising control over the engagement duration. Depending on the nature of the mission, the defender may choose to take an aggressive or defensive stance. Such consideration widens the applicability of the proposed methods in various three-agent motion planning scenarios such as aircraft defense, asset guarding, search and rescue, surveillance, and secure transportation. We use a fixed-time sliding mode control strategy to design the control laws for the evader-defender team and a nonlinear finite-time disturbance observer to estimate the pursuer’s maneuver. Finally, we present simulations to demonstrate favorable performance under various engagement geometries, thus vindicating the efficacy of the proposed designs.

Modeling and control of anterior–posterior and medial–lateral sways in standing posture

To study essential anterior–posterior and medial–lateral sways of the stance caused by rotational movements about the ankle and hip joints, a mathematical model is developed for the 3D postural kinematics and dynamics. The model is in the form of nonlinear differential–algebraic equations corresponding to a biomechanical system with holonomic constraints. A nonlinear feedback control law is further derived for stabilizing the upright stance, whilst eliminating internal torques induced by the constraints on postural movements. Numerical simulations of the model parametrized with experimental data of human body segments illustrate the performance of postural balancing with the proposed control.

Chaotic oscillations of 1D wave equation with or without energy-injections

&lt;abstract&gt;&lt;p&gt;It is interesting and challenging to study chaotic phenomena in partial differential equations. In this paper, we mainly study the problems for oscillations governed by 1D wave equation with general nonlinear feedback control law and energy-conserving or energy-injecting effects at the boundaries. We show that i) energy-injecting effect at the boundary is the necessary condition for the onset of chaos when the nonlinear feedback law is an odd function; ii) chaos never occurs if the nonlinear feedback law is an even function; iii) when one of the two ends is fixed, only the effect of self-regulation at the other end can still cause the onset of chaos; whereas if one of the two ends is free, there will never be chaos for any feedback control law at the other end. In addition, we give a sufficient condition about the general feedback law at one of two ends to ensure the occurrence of chaos. Numerical simulations are provided to demonstrate the effectiveness of the theoretical outcomes.&lt;/p&gt;&lt;/abstract&gt;