Nonlinear Model Reference Adaptive Control Research Articles

Development of an Adaptive Force Control Strategy for Soft Robotic Gripping

Using soft materials in robotic mechanisms has become a common solution to overcome many challenges associated with the rigid bodies frequently used in robotics. Compliant mechanisms allow the robot to adapt to objects and perform a broader range of tasks, unlike rigid bodies that are generally designed for specific applications. However, soft robotics presents its own set of challenges in both design and implementation, particularly in sensing and control. These challenges are abundant when dealing with the force control problem of a compliant gripping mechanism. The ability to effectively regulate the applied force of a gripper is a critical task in many control operations, as it allows the precise manipulation of objects, which drives the need for enhanced force control strategies for soft or flexible grippers. Standard sensing techniques, such as motor current monitoring and strain-based sensors, add complexities and uncertainties when establishing mathematical models of soft grippers to the required gripping forces. In addition, the soft gripper creates a complex non-linear system, compounded by adding an adhesive-type sensor. This work develops a unique visual force sensor trained on synthetic data generated using finite element analysis (FEA) and implemented by integrating a non-linear model reference adaptive controller (MRAC) to control gripping force on a fixed 6-DOF robot. The robot can be placed on a mobile platform to perform various tasks. The virtual FEA sensor and controller, combined, are termed virtual reference adaptive control (VRAC). The VRAC was compared to other methods and achieved comparable control sensing and control performance while reducing the complexity of the sensor requirements and its integration. The VRAC strategy effectively controlled the gripping force by driving the dynamics to match the desired performance after a limited amount of training cycles. The controller proposed in this work was designed to be generally applicable to most objects that the gripper will interact with and easily adaptable to a wide variety of soft grippers.

Robust Adaptive Control Based on Incremental Nonlinear Dynamic Inversion for a Quadrotor in Presence of Partial Actuator Fault

This paper presents a novel nonlinear robust adaptive trajectory tracking control architecture for stabilizing and controlling a quadrotor in the presence of actuator partial faults. The proposed control strategy utilizes an Incremental Nonlinear Dynamic Inversion (INDI) algorithm as the baseline controller in the inner loop and augments a nonlinear model reference adaptive controller in the outer loop to ensure robustness against unmodeled faults. Additionally, a modified PID controller is introduced in the most outer-loop to track the desired path. The effects of actuator faults are modeled by considering sudden variations in motor thrust and torques. To enhance the control algorithm's robustness, a projection operator is employed in the robust adaptive structure. Comparative performance evaluations with a previous successful algorithm implemented on a quadrotor model demonstrate that the proposed controller achieves full controllability of the faulty quadrotor in pitch, roll, and yaw channels in the presence of actuator partial faults up to 50%.

The nonlinear model reference adaptive impedance control for underwater manipulator operation objects in bilateral teleoperation system

The bilateral teleoperation system is susceptible to model parameter uncertainty and unknown disturbances in both the master and slave manipulators, resulting in instability and inaccuracies in the force and position tracking performance. To address these issues, a novel nonlinear model reference adaptive impedance controller has been designed to achieve coordinated force and position synchronization of dual manipulators. The adaptive control laws, based on sliding mode functions, have been designed to compensate for the uncertainty of the manipulator model. Furthermore, an adaptive estimation law has been employed to appraise the unknown upper bound of external disturbances. This ensures that the closed-loop model parameters of the dual manipulator converge to the reference impedance model respectively. Simultaneously, it enables the position error between the reference model response and the end-effector task space position to asymptotically converge to zero. To verify the effectiveness of the proposed controller, simulations have been conducted on the MATLAB platform and experiments on a single degree of freedom teleoperation system have been performed. The results demonstrate that the controller exhibits strong robustness and has the capability of force-position tracking ability.

A new robust nonlinear control strategy for UIPC in isolated hybrid microgrids

This paper focuses on the control of unified interphase power controller (UIPC) in isolated hybrid microgrids (HmGs), where the UIPC is used as the main component for interconnecting of AC and DC sub-grids. The investigated HmG encompasses two AC sub-grids and one purely storage DC sub-grid (PSDC) and multiple adjustable loads. A robust nonlinear model reference adaptive control (NMRC) strategy is offered for controlling the UIPC, keeping an acceptable two-way power exchange control with uncomplicated topology. Further, a novel configuration for the DC link power converter is suggested using the dual-active-bridge topology. Also, a harmonic-based modeling method is used to model the UIPC's power converter. The proposed configuration provides bidirectional power flow, increased power density, straightforward adaptation of zero-voltage switching, and direct access to cascading and parallelism to increase the ratings and reliability of UIPC. The simulation results illustrate the feasibility of the suggested topology for isolated HmGs.

Nonlinear model reference adaptive control approach for governance of the commons in a feedback-evolving game

The governance of common-pool resources has vital importance for sustainability. However, in the realistic management systems of common-pool resources, the institutions do not necessarily execute the management policies completely, which will induce that the real implementation intensity is uncertain. In this paper, we consider a feedback-evolving game model with the inspection for investigating the management of renewable resource and assume that there exists the implementation uncertainty of inspection. Furthermore, we use the nonlinear model reference adaptive control approach to handle this uncertainty. We accordingly design a protocol, which is an update law of adjusting the institutional inspection intensity. We obtain a sufficient condition under which the update law can drive the actual system to reach the expected outcome. In addition, we provide several numerical examples, which can confirm our theoretical results. Our work presents a novel approach to address the implementation uncertainty in the feedback-evolving games and thus our results can be helpful for effectively managing the common-pool resources in the human social systems.

Adaptive Two-Degrees-of-Freedom Current Control for Solenoids: Theoretical Investigation and Practical Application

In this article, an adaptive two-degrees-of-freedom current control algorithm for solenoids is presented comprising an adaptive pole placement controller in combination with a regularized least-squares parameter estimation law. An additional adaptive feedforward controller takes advantage of the estimated plant parameters to further enhance the tracking performance. The stability of the overall closed-loop system is rigorously proven. The proposed solution differs from existing approaches by the adaptive feedforward controller and the way the parameter estimation is performed. The control concept is applied with the same controller parametrization to three solenoids from different applications, with substantially differing parameters. The experimental results show high tracking performance and fast parameter convergence even with poor initial estimates and despite the nonlinear dependence of the inductance on the current and position. The experimental results are also compared to two benchmark control design paradigms known from the literature, i.e. a second-order sliding mode controller and a nonlinear model reference adaptive control solution, which are both outperformed by the proposed controller.

A Comparative Study of Control Methods for X3D Quadrotor Feedback Trajectory Control

Unmanned aerial vehicles (UAVs), particularly quadrotor, have seen steady growth in use over the last several decades. The quadrotor is an under-actuated nonlinear system with few actuators in comparison to the degree of freedom (DOF); hence, stabilizing its attitude and positions is a significant challenge. Furthermore, the inclusion of nonlinear dynamic factors and uncertainties makes controlling its maneuverability more challenging. The purpose of this research is to design, implement, and evaluate the effectiveness of linear and nonlinear control methods for controlling an X3D quadrotor’s intended translation position and rotation angles while hovering. The dynamics of the X3D quadrotor model were implemented in Simulink. Two linear controllers, linear quadratic regulator (LQR) and proportional integral derivate (PID), and two nonlinear controllers, fuzzy controller (FC) and model reference adaptive PID Controller (MRAPC) employing the MIT rule, were devised and implemented for the response analysis. In the MATLAB Simulink Environment, the transient performance of nonlinear and linear controllers for an X3D quadrotor is examined in terms of settling time, rising time, peak time, delay time, and overshoot. Simulation results suggest that the LQR control approach is better because of its robustness and comparatively superior performance characteristics to other controllers, particularly nonlinear controllers, listed at the same operating point, as overshoot is 0.0% and other factors are minimal for the x3D quadrotor. In addition, the LQR controller is intuitive and simple to implement. In this research, all control approaches were verified to provide adequate feedback for quadrotor stability.

Dual ML-ADHDP method for heterogeneous discrete-time nonlinear multi-agent systems with unknown dynamics and time delay

This paper develops a new dual ML-ADHDP method to solve the optimal consensus problem (OCP) of a class of heterogeneous discrete-time nonlinear multi-agent systems (MASs) with unknown dynamics and time delay. A hierarchical and distributed control strategy is used to transform the original problem into nonlinear model reference adaptive control (MRAC) problems and an OCP of virtual linear MASs. For the nonlinear MRAC problems, a new multi-layer action-dependent heuristic dynamic programming (ML-ADHDP) method is developed to overcome the unknown dynamics and neural network estimation errors, which has higher control accuracy. In order to solve the OCP of virtual linear MASs and improve the convergence speed, a new multi-layer performance index is proposed. Then the ML-ADHDP method is used to solve the coupled Hamiltonian–Jacobi–Bellman equation and obtain the optimal virtual control. Theoretical analysis proves that the original MASs can achieve Nash equilibrium, and simulation results show that the developed dual ML-ADHDP method ensures better convergence speed and higher control accuracy of original MASs.

A Robust Nonlinear Model Reference Adaptive Control for Disturbed Linear Systems: An LMI Approach

In this article, a robust nonlinear model reference adaptive control (MRAC) is proposed for disturbed linear systems, i.e., linear systems with parameter uncertainties, and external time-dependent perturbations or nonlinear unmodeled dynamics matched with the control input. The proposed nonlinear control law is composed of two nonlinear adaptive gains. Such adaptive gains allow the control to counteract the effects of some perturbations and nonlinear unmodeled dynamics ensuring asymptotic convergence of the tracking error to zero, and the boundedness of the adaptive gains. The nonlinear controller synthesis is given by a constructive method based on the solution of linear matrix inequalities. Besides, the simulation results show that, due to the nonlinearities, the rate of convergence of the proposed algorithm is faster than that provided by a classic MRAC.

Anti-Chaos control of a servo system using nonlinear model reference adaptive control

Abstract This work presents a method for anti-chaos control of a servo system affected by parametric uncertainty and constant disturbances. It is based on Nonlinear Model Reference Adaptive Control where the reference model corresponds to a chaotic Duffing oscillator. Only upper and lower bounds on the servo system input gain are assumed known beforehand. It is shown that the solutions of the closed-loop system are Uniformly Ultimately Bounded. Moreover, the chaotic behaviour of the servo system position is verified through the Largest Lyapunov Exponent. The proposed control methodology is tested through experiments.

A New Impedance Controller Based on Nonlinear Model Reference Adaptive Control for Exoskeleton Systems

Robotic exoskeletons are expected to show high compliance and low impedance for human–robot interactions (HRIs). Our study introduces a novel method based on nonlinear model reference adaptive control (MRAC) to reduce the inherent impedance and replace the traditional impedance controller in HRIs. The control law and adaptive law are designed according to a candidate Lyapunov function. A simple system identification and initialization method for the nonlinear MRAC is put forward, which provides a set of better initial values for the controller. From the results of simulation and experiment, our controller can reduce the mechanical impedance and achieve high compliance for HRI. The adaptive control and compliance control can be both achieved by the proposed nonlinear MRAC framework.

The master adaptive impedance control and slave adaptive neural network control in underwater manipulator uncertainty teleoperation

This paper proposes a novel bilateral adaptive control scheme to achieve position and force coordination performance of underwater manipulator teleoperation system under model uncertainty and external disturbance. A new nonlinear model reference adaptive impedance controller with bound-gain-forgetting (BGF) composite adaptive law is designed for the master manipulator force tracking of the slave manipulator. The reference position in task space is obtained from the linear second-order impedance model whose input is the force error of the master and the slave. The adaptive terminal sliding mode control based on adaptive uncertainty compensation is proposed to achieve the master position tracking of the reference position. The radial basis function neural network (RBFNN) local approximation method is proposed for the slave manipulator's position tracking. The RBFNN based on Ge-Lee (GL) matrix is adopted to directly approximate each element of the slave manipulator dynamic, and the robust term with a proper update law is designed to suppress the error between the estimate model and the real model, and the external disturbance. The asymptotic tracking performance and global stability of the teleoperation system are proved with Lyapunov stability theorem. The simulation and experiment verify the performance of the proposed controller in teleoperation manipulator model. The results show that the teleoperation system has a good ability of position and force coordination.

Cooperative modalities in robotic tele-rehabilitation using nonlinear bilateral impedance control

A nonlinear model reference adaptive bilateral impedance controller is proposed that can accommodate various cooperative tele-rehabilitation modes for patient–therapist interaction using a multi-DOF tele-robotic system. In this controller, two reference impedance models are implemented for the master and slave robots using new model reference adaptive control laws for the nonlinear bilateral teleoperation system. “Hand-over-hand” and “adjustable-flexibility” are two modes of patient–therapist cooperation that are realized using the proposed strategy. The Lyapunov-based stability proof guarantees the patient’s and the therapist’s safety during the cooperation and interaction with robots, even in the presence of modeling uncertainties of the multi-DOF teleoperation system. The performance of the proposed bilateral impedance controller is experimentally investigated for upper-limb tele-rehabilitation in the two mentioned cooperation modes.

Hybrid model reference adaptive second order sliding mode controller for automatic train operation

This study presents a non-linear longitudinal dynamic model of high speed trains by considering the rolling stock, train formations, rolling resistance, track environment, etc., and longitudinal controller design for Automatic Train Operation (ATO) as well. For a controller design, a novel hybrid model reference based adaptive super twisting sliding mode control scheme is proposed. The control law comprises a non-linear model reference adaptive control (MRAC) and an adaptive second order sliding mode control (SMC) in order to make the control signal continuous and to alleviate the chattering phenomenon. The adaptive gains of the proposed control law are derived based on Lyapunov approach that ensures global stability with exact tracking in finite time. A linear stable reference model is developed with the ideal train-track parameters to generate the reference trajectory. The effectiveness of the presented concept is demonstrated by introducing load variation, model uncertainties and external disturbances in the non-linear model of the train and its performance is compared with the non-linear MRAC and the second order sliding mode controller.

Nonlinear model reference adaptive impedance control for human–robot interactions

Four nonlinear Model Reference Adaptive Impedance Controllers are introduced, tested, and compared for the control of the robot impedance with uncertainties in model parameters. The intended application area is human–robot interactions (HRI), particularly rehabilitation robots and haptic interfaces. All of the controllers make the closed-loop dynamics of the robot similar to the reference impedance model besides providing asymptotic tracking of the impedance model for the robot end-effector in Cartesian coordinates. The tracking and global stability are proved using Lyapunov stability theorem. Based on the simulations and experiments on a two-DOFs robot, the effectiveness of the proposed controllers is investigated.

Model reference adaptive impedance control in Cartesian coordinates for physical human–robot interaction

In this paper, a nonlinear model reference adaptive impedance controller is proposed and tested. The controller provides asymptotic tracking of a reference impedance model for the robot end-effector in Cartesian coordinates applicable to rehabilitation robotics or any other human–robot interactions such as haptic systems. The controller uses the parameters of a desired stable reference model which is the target impedance for the robot’s end-effector. It also considers uncertainties in the model parameters of the robot. The asymptotic tracking is proven using Lyapunov stability theorem. Moreover, the adaptation law is proposed in joint space for reducing the complexity of its calculations; however, the controller and the stability proof are all presented in Cartesian coordinates. Using simulations and experiments on a two DOFs robot, the effectiveness of the proposed controller is investigated.

Robust control for a direct-driven permanent magnetic synchronous generator without mechanical sensors based on model reference adaptive backstepping control method

This article is concerned with the robust control issues of direct-driven permanent magnetic synchronous generator without mechanical sensors. In this study, a novel nonlinear model reference adaptive backstepping control method is proposed. Extended electromotive force estimation-based rotor position and rotational velocity estimation methods are adopted, in which the stator parameters are identified online. Since the identified parameters are merely used in extended electromotive force estimator, the mathematically controlled plant cannot reflect the actual model, which decreases the robustness of the control. To provide a high-performance robust controller against uncertainties in stator parameters and mechanical torque fluctuation, a torque observer is adopted, and an adaptation law is derived with the identified parameters and estimated mechanical torque, in the sense of the Lyapunov theory. Meanwhile, the feasibility of the substitution of the actual stator parameters and state vector with estimated values is mathematically demonstrated based on the Lyapunov theory. Simulation experiments have been carried out both in surface permanent magnetic synchronous generator and interior permanent magnetic synchronous generator, and the results show that compared to the conventional process-interaction decoupling controller, the proposed controller has better disturbance rejection performance against wind speed perpetuation and parameter uncertainties.

Direct model reference adaptive control (MRAC) design and simulation for the vibration suppression of piezoelectric smart structures

The paper presents control system design based on a non-linear model reference adaptive control law (MRAC) used for the vibration suppression of a smart piezoelectric mechanical structure. Numerical simulation of the proposed control system is performed based on the finite element (FE) model of the structure, modally reduced in order to meet the requirements of the control system design. First the MRAC problem is defined and a direct control algorithm described in the paper is suggested as a solution to the control problem. The basic MRAC algorithm is modified by augmenting the integral term of the control law in order to provide the robustness of the control system with respect to the stability. This approach provides preserving the boundness of the system states and adaptive gains, with small trackings error over large ranges of non-ideal conditions and uncertainties. The efficiency of the suggested control for the vibration suppression is tested and shown through a numerical simulation of the funnel-shaped piezoelectric structure.

Linear and Nonlinear Control Techniques for a Three-Phase Three-Level NPC Boost Rectifier

This paper deals with three control techniques for a three-phase three-level neutral-point-clamped (NPC) boost rectifier to study their relative performance. Linear, nonlinear, and nonlinear model reference adaptive control (MRAC) methods are developed to control power factor (PF) and regulate output and neutral point voltages. These controllers are designed in Simulink and implemented in real time using the DS1104 DSP of dSPACE for validation on a 1.2-kW prototype of an NPC boost rectifier operating at 1.92 kHz. The performance of boost converter with three control methods has been investigated respectively in steady state in terms of line-current harmonic distortion, efficiency, and PF and during transients such as load steps, utility disturbances, reactive power control, and dc-bus voltage tracking behavior. The linear PI controllers are characterized by reduced complexity but poor performance, whereas the nonlinear control technique has improved the converter performance significantly, while nonlinear MRAC exhibits much better performance in a wide operating range

A nonlinear model reference adaptive inverse control algorithm with pre-compensator

In this paper, the reduced-order modeling (ROM) technology and its corresponding linear theory are expanded from the linear dynamic system to the nonlinear one, and H ∞ control theory is employed in the frequency domain to design some nonlinear system s pre-compensator in some special way. The adaptive model inverse control (AMIC) theory coping with nonlinear system is improved as well. Such is the model reference adaptive inverse control with pre-compensator (PCMRAIC). The aim of that algorithm is to construct a strategy of control as a whole. As a practical example of the application, the numerical simulation has been given on matlab software packages. The numerical result is given. The proposed strategy realizes the linearization control of nonlinear dynamic system. And it carries out a good performance to deal with the nonlinear system.