Nonlinear Adaptive Control Algorithm Research Articles

Nonlinear adaptive robust control with continuous error reduction mapping

Abstract Achieving high stability and high-precision control by traditional control algorithms is difficult due to the strong nonlinearity, parameter uncertainty, and random disturbance characteristics of electro-hydraulic proportional servo systems. Herein, we developed a nonlinear adaptive control algorithm based on Lyapunov functions. By estimating the parameters and converging their errors, this algorithm solved the parameter adaptation problem. Additionally, based on convergence inference from the nonnegativity of the derivative of Lyapunov functions, the algorithm designed a disturbance mapping through the derived function. The random disturbance was reduced through the mapping, improving the stability of the system under random disturbance. Finally, we carried out continuous derivation and moved the mapping relationship out of the intermediate temporary controller. This reduced the complexity of the calculation during controller design, prevented performance degradation of the error convergence algorithm after complex calculation, and enhanced the robustness of the algorithm. The algorithm was verified through the simulation model established by Simulink and experience. Results showed that the nonlinear adaptive control algorithm demonstrates fast response, high accuracy, and strong anti-interference ability compared with the high-gain robust control algorithm. It realizes the adaptation of unknown parameters and reduces the control error introduced by random disturbance.

Rejection of Synchronous Vibrations of AMB System Using Nonlinear Adaptive Control Algorithm with a Novel Frequency Estimator

This paper focuses on the synchronous vibration suppression of an active magnetic bearing (AMB) system without a rotating speed sensor. One of the most intractable problems with AMB systems is the synchronous vibration caused by the mass imbalance of the rotor. Moreover, practically all existing unbalance control algorithms require the rotating speed sensor to determine rotation speed. However, in some unique applications, it is impossible to install and use the rotating speed sensor as intended. This study provided a nonlinear adaptive control (NAC) algorithm and a modified frequency estimator to address the above issues. The proposed approach can suppress current and displacement vibrations by regulating the control structure. The frequency estimator calculates the rotating speed based on the position of the rotor at different moments, which has a quick response time, high precision, and effective tracking. The NAC algorithm can achieve unbalanced control based on the period iteration strategy. Additionally, the Lyapunov method is used to demonstrate the stability of the NAC algorithm. Finally, the experimental and simulation results also confirm the effectiveness and reliability of the overall control scheme. The results from simulations and experiments indicate that the novel frequency estimator can track the speed accurately and that its error can be regulated to within ±0.05 Hz. The overall control schema can reduce the displacement vibration’s amplitude by 72.2% and the current vibration’s amplitude by 65.6%.

Parameter Identification and Control Algorithm of Electrohydraulic Servo System for Robotic Excavator Based on Improved Hammerstein Model

In view of the nonlinearity and time-varying characteristics of the electrohydraulic servo system of the robotic excavator, a nonlinear adaptive identification and control algorithm based on improved Hammerstein model is proposed. The Hammerstein algorithm model can approximate the nonlinear system with enough precision, but for the time-varying systems is not satisfactory. In order to compensate for the influence of time-varying factors, the fuzzy control module is designed to adaptively update the forgetting factor. The experimental results show that the improved Hammerstein model error is about 40.11% less than the classical Hammerstein model error. This proves that the improved Hammerstein model is feasible and effective to describe the electrohydraulic servo system of the robotic excavator.

A new multimodel approach by Laguerre filters on sliding window for nonlinear system identification and control

This paper proposes an online identification procedure on sliding window with the synthesis of a nonlinear adaptive predictive control for a new nonlinear model resulting in multimodel approach. Such a model is entitled ARX-Laguerre multimodel obtained by expanding the conventional ARX multimodel on independent Laguerre orthonormal bases. It allows a significant parameter number reduction as well as a simple recursive representation compared with the ARX-multimodel. This parametric reduction is provided from an optimal iteratif identification approach of the Laguerre poles presented in Adaily et al. (2013). We propose to combine and carry out this identification approach on a sliding window to achieve an online identification procedure of the ARX-Laguerre multimodel for real time procedure depending on Fourier coefficients that are identified by a regularized square error. This property allows to synthese a new nonlinear adaptive predictive control on sliding window. We develop the general form of a new predictor and so, we propose an optimization algorithm formulated as a quadratic programming (QP) under linear constraints for an adaptive control law. The performances of the proposed online identification procedure and the developed nonlinear adaptive control algorithm are illustrated on a benchmark system as the continuous stirred tank reactor system (CSTR) with respect to the process parameter uncertainties.

Adaptive Nonlinear Control Algorithm for a Self-Balancing Robot

We previously developed a novel composite wheel-leg-track explosive ordnance disposal (EOD) robot with high mobility, able to switch between a track or a self-balancing motion mode according to environmental conditions, named Scorpio. In this paper, we propose an adaptive nonlinear control algorithm for improving the stability of the robot in the self-balancing mode. First, a model of the dynamics of the robot was established, with which we designed the nonlinear cascade controller for combined balance and motion control. With our system, the attitude of the robot is estimated using a Kalman filtering algorithm. Based on this, an adaptive adjustment algorithm amends the parameters of the controller in real time according to the state of the robot, for improved stability. In addition, we formulated an adaptive zero-offset angle identification algorithm to compensate for deviations caused by changes to the robot's center of gravity (due to changes to its mechanical structure), ensuring that this stability could be maintained. Results of experiments conducted to verify their operation show that self-balancing control of Scorpio can be achieved with the proposed algorithms.

Design and experiment of adaptive modified super-twisting control with a nonlinear sliding surface for a quadrotor helicopter

Quadrotor unmanned aerial vehicle is a nonlinear system of 6-degree-of-freedom motion. In order to handle the nonlinearity that causes undesirable behavior, robustness of flight control has been studied. In this work, we consider the combination of higher order sliding mode control and nonlinear time-varying sliding surface for robustness and accuracy in tracking. An adaptive super-twisting control, a second-order sliding mode control, is utilized to compensate for the uncertainty and perturbation of a quadrotor system. A time-varying sliding surface is designed with a nonlinear function to provide varying properties of closed-loop dynamics and to improve control performance with energy consumption reduction. The proposed control system performance including energy consumption was compared among nonlinear adaptive super-twisting control algorithm, linear adaptive super-twisting control algorithm, and linear super twisting controllers, without and under wind disturbance. The robustness and effectiveness of the proposed control system are demonstrated by several times simulation and experiment using a quadrotor helicopter test bed.

Observer-Based Adaptive Output Feedback Control for Miniature Aerial Vehicle

In this paper, we propose an observer-based adaptive output feedback flight tracking system for the miniature aerial vehicle (MAV) in the presence of bounded uncertainty. The proposed design has two parts. First, a state feedback based nonlinear adaptive control algorithm is designed by assuming that all the states are available for feedback. The convergence analysis with the state feedback based design is derived by using the Lyapunov method. Second, we replace the unknown velocity states by a linear observer to develop adaptive output feedback flight tracking system for the MAV. The convergence analysis with the observer-based output feedback design is shown by using a singularly perturbed method. The analysis shows that the performance achieved under state feedback can be recovered by using an output feedback based design. Evaluation results are given to demonstrate the effectiveness of the proposed design for real-time applications.

Linear Matrix Inequality-Based Nonlinear Adaptive Robust Control of Quadrotor

In this paper, we propose a novel linear matrix inequality-based nonlinear adaptive robust control algorithm to design the attitude and position controllers for an X-configuration quadrotor helicopter. The inner loop of the autopilot controls the attitude and altitude of the quadrotor, and the outer loop controls its position in the Earth-fixed coordinate frame. By assuming knowledge of the bounds of the quadrotor’s uncertain parameters (e.g., mass and moments of inertia) and predetermined bounds on the external and unstructured disturbances (e.g., wind gusts and unmodeled dynamics), we attain a guaranteed transient and steady-state tracking performance. We demonstrate the performance of the controllers via two illustrative examples. In the first example mission, the quadrotor follows an altitude reference trajectory in the presence of wind gusts and delivers a package of uncertain mass midflight. The second example presents an autonomous waypoint flight in the presence of wind disturbances. The results of our simulations indicate that our controller design is useful for a variety of quadrotor applications, including precise trajectory tracking, autonomous waypoint navigation in the presence of disturbances, and package delivery without loss of performance.

Nonlinear Adaptive Predictive Functional Control Based on the Takagi–Sugeno Model for Average Cracking Outlet Temperature of the Ethylene Cracking Furnace

The conventional PID control has been proven insufficient and incapable for this particular petro-chemical process. This paper proposes a nonlinear adaptive predictive functional control (NAPFC) algorithm based on the Takagi–Sugeno (T-S) model for average cracking outlet temperature (ACOT) of the ethylene cracking furnace. In this algorithm, in order to overcome the effect on system performance under model mismatch, the structure parameters of the T-S fuzzy model are confirmed, and the model consequent parameters are identified online using the forgetting factor least-square method. Prediction output is calculated according to the identified parameters instead of computing the Diophantine equation, thereby obtaining directly the predictive control law and avoiding the complex computation of the inverse of the matrix. Application results on ACOT of the ethylene cracking furnace show the proposed control strategy has strong tracking ability and robustness.

A novel adaptive robust control architecture for bilateral teleoperation systems under time‐varying delays

SummaryBilateral teleoperation technology has caused wide attentions due to its applications in various remote operation systems. The communication delay becomes one of the main challenging issues in the teleoperation control design. Meanwhile, various nonlinearities, parameter variations, and modeling uncertainties existing in manipulator and environment dynamics need to be considered carefully in order to achieve good control performance. In this paper, a globally stable nonlinear adaptive robust control algorithm is developed for bilateral teleoperation systems to deal with these control issues. Namely, the unknown dynamical parameters of the environmental force are estimated online by the improved least square adaptation law. A novel communication structure is proposed where only the master position signal is transmitted to the slave side for the tracking design, and the online estimators of the environmental parameters are transmitted from the slave to the master to replace the traditional environmental force measurement. Because the estimated environmental parameters are not power signals, the passivity problem of the communication channel and the trade‐off limitation between the transparency performance and robust stability in traditional teleoperation control are essentially avoided. The nonlinear adaptive robust control is subsequently developed to deal with nonlinearities, unknown parameters, and modeling uncertainties of the master, slave, and environmental dynamics, so that the guaranteed transient and steady‐state transparency performance can be achieved. The experiments on two voice‐coil motor‐driven manipulators are carried out, and the comparative results verify that the proposed control algorithm achieves the excellent control performance and the guaranteed robust stability simultaneously under time delays. Copyright © 2014 John Wiley & Sons, Ltd.

Fault tolerant small satellite attitude control using adaptive non-singular terminal sliding mode

The Attitude Control System (ACS) plays a pivotal role in the whole performance of the spacecraft on the orbit; therefore, it is vitally important to design the control system with the performance of rapid response, high control precision and insensitive to external perturbations. In the first place, this paper proposes two adaptive nonlinear control algorithms based on the sliding mode control (SMC), which are designed for small satellite attitude control system. The nonlinear dynamics describing the attitude of small satellite is considered in a circle reference orbit, and the stability of the closed-loop system in the presence of external perturbations is investigated. Then, in order to account for accidental or degradation fault in satellite actuators, the fault-tolerant control schemes are presented. Hence, two adaptive fault-tolerant control laws (continuous sliding mode control and non-singular terminal sliding mode control) are developed by adopting the nonlinear analytical model to describe the system, which can guarantee global asymptotic convergence of the attitude control error with the existence of unknown external perturbations. The nonlinear hyperplane based Terminal sliding mode is introduced into the control law design; therefore, the system convergence performance improves and the control error is convergent in “finite time”. As a result, the study on the non-singular terminal sliding mode control is the emphasis and the continuous sliding mode control is used to compare with the non-singular terminal sliding mode control. Meanwhile, an adaptive fuzzy algorithm has been proposed to suppress the chattering phenomenon. Moreover, several numerical examples are presented to demonstrate the efficacy of the proposed controllers by correcting for the external perturbations. Simulation results confirm that the suggested methodologies yield high control precision in control. In addition, actuator degradation, actuator stuck and actuator failure for a period of time are simulated to demonstrate the fault recovery capability of the fault tolerant controllers. The numerical results clearly demonstrate the good performance of the adaptive non-singular terminal control in the event of actuator fault compare with the continuous sliding mode control.

Active control of frequency varying disturbances in a diesel engine

In this paper a method for active vibration isolation of frequency varying tonal disturbances in an engine mounted on a raft is presented. An adaptive nonlinear control algorithm with frequency tracking is introduced to tackle this problem. The studied process is a true MIMO-system with strong cross-couplings and high background noise level. The controller performance is first validated by extensive simulations and then by test bed implementation. It is shown that the proposed method is robust to measurement noise and additional output disturbances, while yielding a high level of vibration suppression with fast convergence rate.

Frequency-adaptive Backup-Roll Eccentricity Compensation with Force Feedback

In this paper we present a novel nonlinear adaptive control algorithm aiming at improving the thickness performances of metal strip rolling mills by actively compensating the periodic disturbances due to the eccentricity of the rolls. The main feature of the proposed Roll Eccentricity Compensation method consists in the capability of estimating the frequency of the disturbance without the need to install proximity sensors for synchronization. The proposed compensation scheme relies on a generalized nonlinear phase-locked loop, whose parameters are adapted online to achieve asymptotic cancellation of the unknown perturbation. The local asymptotic stability of the closed-loop system in presence of model uncertainty is proven by a two-time scale averaging analysis.

Spacecraft Attitude and Orbit Coupled Nonlinear Adaptive Synchronization Control

Precise dynamic model of spacecraft is essential for the space missions, to be completed successfully. Nevertheless, the independent orbit or attitude dynamic models can not meet high precision tasks. This paper developed a 6-DOF relative coupling dynamic model based upon the nonlinear relative motion dynamics equations and attitude kinematics equations described by MRP. Nonlinear synchronization control law was designed for the coupled nonlinear dynamic model, whose close-loop system was proved to be global asymptotic stable by Lyapunov direct method. Finallly, the simulation results illustrate that the nonlinear adaptive synchronization control algorithm can robustly drive the orbit and attitude errors to converge to zero.

Observer-Based Speed Tracking Control for Sensorless Permanent Magnet Synchronous Motors With Unknown Load Torque

The tracking control problem is addressed for sensorless (nonsalient-pole surface) permanent magnet synchronous motors with unknown constant load torque. Assuming that only stator currents and voltages are available for feedback, a novel sixth order nonlinear adaptive control algorithm is designed, which does not rely on nonrobust open loop integration of motor dynamics and guarantees, under persistency of excitation, local exponential rotor speed tracking.

Tracking Control for Sensorless Induction Motors with Uncertain Load Torque and Resistances

The rotor speed and flux modulus tracking problem for sensorless induction motors with uncertain constant load torque and uncertain both rotor and stator resistances is addressed. A new ninth order dynamic nonlinear adaptive control algorithm is designed: it relies on a novel closed loop observer for the unmeasured state variables (rotor speed and luxes) which is adaptive with respect to the uncertain parameters (load torque and motor resistances). Local exponential stability of the origin of the closed loop tracking and estimation error dynamics is guaranteed under suitable conditions including persistency of excitation which depends on reference signals only.

Fault Tolerant Reconfigurable Satellite Formations Using Adaptive Variable Structure Techniques

This paper proposes two adaptive nonlinear control algorithms based on a variable-structure control design for multiple spacecraft formation flying. The nonlinear dynamics describing the motion of the follower spacecraft relative to the leader spacecraft are considered for the case in which the leader spacecraft is in an elliptical reference orbit, and the stability of such a formation in the presence of external perturbations is investigated. This paper presents fault-tolerant control schemes to account for accidental or degradation faults in spacecraft sensors and thrusters. The nonlinear analytical model describing the system is used to develop two adaptive fault-tolerant control laws (continuous sliding mode control and nonsingular terminal sliding mode control) that guarantee global asymptotic convergence of the position tracking error in the presence of unknown follower spacecraft mass and external disturbances. Several numerical examples are presented to demonstrate the efficacy of the proposed controllers to maintain the relative motion by correcting for initial offsets and external perturbation effects that tend to disperse the formation. Simulation results confirm that the suggested methodologies yield submillimeter formation, keeping precision and effectiveness in ensuring formation maneuvering. In addition, an abrupt blockage of the relative position sensors, thruster failure for a period of time, and thruster degradation (amidst formation keeping and reconfiguration maneuvers) are simulated to demonstrate the fault recovery capability of the controllers. The numerical results clearly establish the robustness of the proposed reconfigurable adaptive control scheme for precise formation keeping in the event of sensor and thruster faults.

Characterization of Semi-active Control System Dynamics with Magneto-rheological Suspensions

This paper characterizes two semi-active control algorithms through strategy analysis and parametric simulation study. A brief literature review discloses two kinds of semi-active controls: non-model based skyhook-like control policy (or skyhook variations), and model-based clipped semi-active control strategies. Both can be formulated as a bi-state control algorithm. In this paper, the no-jerk skyhook control policy is chosen to represent bi-state strategies, while a nonlinear adaptive semi-active control algorithm without need of clipping control signals is selected for comparison study. Then the studied MR suspension and its model setup are presented. In the paper we explain dynamic analysis approach and controller tuning for this simulation study. While analytic analysis of strategies is based on linear base-excited vibration systems by using transmissibility plots, simulation study adopts sine-sweep excitations so that comparison of transient dynamics could be stressed out and simultaneously the vibration isolation capability compared in the frequency domain by directly observing the time domain data. In addition, one pure-tone excitation case is simulated to explain higher harmonics inherent with bi-state skyhook controls. From the simulation study, the effectiveness of both semi-active controls can be observed for vibration isolation. In addition, the adaptability of both selected controls is compared regarding plant variations and different excitation profiles, both of which are typical in vehicle suspension systems. Finally the characteristics of these two semi-active controls are summarized from the simulation findings.

MODEL-BASED IDENTIFICATION AND ADAPTIVE CONTROL OF THE CORE MODULE IN A TYPICAL CELL CYCLE PATHWAY VIA NETWORK AND SYSTEM CONTROL THEORIES

The loss of cell cycle control is often associated with cancers and other different diseases. With the accumulation of omics data, the network for molecule interactions in the cell cycle process will become much clearer. The identification of the crucial modules in a giant network and investigation of inherent control relations are very important to the understanding of the molecular mechanisms of diseases for new drug design. The paper proposes novel techniques in analyzing such core regulatory modules based on network and system control theories. We initially define the degree of participation (DOP) and the rate of activity (ROA) for indentifying core module components, and then the diverse contribution elasticity functions for quantifying pairwise regulatory or control activities between those components, thus facilitating the decomposition of expanded core modules and the formation of feedback loops within the control schema. Motivated by the inherent regulatory mechanisms, we expound a kind of multiphase nonlinear adaptive control algorithm in repelling abnormal genetic mutations, which directly and indirectly impact cancer development in biological cells and organs. Experimental predictions are also elucidated within the work, helping those in vivo design, verification and performance evaluation.

An adaptive tracking control from current measurements for induction motors with uncertain load torque and rotor resistance

The problem of controlling sensorless induction motors with uncertain constant load torque and rotor resistance on the basis of stator current measurements only is addressed. A new eighth-order dynamic nonlinear adaptive control algorithm is designed, which relies on a closed loop adaptive observer for the unmeasured state variables (rotor speed and fluxes) and for the uncertain parameters and is not based on non-robust open loop integration of flux dynamics. Local exponential stability of the closed loop tracking and estimation error dynamics is achieved under persistency of excitation conditions which restrict the reference signals and may be interpreted in terms of motor observability and rotor resistance identifiability.