Single-link Flexible Manipulator System Research Articles

Q-learning based model-free input-output feedback linearization control method⋆

Input-output feedback linearization is a nonlinear control method that relies on a precise dynamical model. Combining Q-learning techniques, an input-output feedback linearization correction framework is presented to accomplish model-free feedback linearization of affine nonlinear systems in order to tackle the problem caused by the unknown dynamics model. This framework formulates a model reference tracking control problem that guides the input-output relationship of the nonlinear system into a linear relationship. Due to the two Lie derivative terms present in the feedback linearized controller, the controller is designed as a dual network structure. To overcome the issue of coupling in the dual-network controller, a model-free Q-learning method is presented to solve the unknown controller network weights. The proposed method is experimentally validated on a single-link flexible joint manipulator system, and the resultant linearized system exhibits dynamics similar to the desired linear system in a new tracking task, proving the effectiveness of the proposed method.

Time-Delayed Acceleration Feedback Control of a Single-Link Flexible Manipulator Using Kalman Filter

The design problem of a discrete controller with time delay and acceleration feedback for a single-link flexible manipulator system is addressed in this paper. The dynamical model of a single-link flexible manipulator system is presented by the adoption of the finite element method and Lagrange’s equation. Based on the random-walk process and the discrete reduction method, an augmented discretized delay-free state derivate space equation containing the random noise is established. An acceleration-based Kalman filtering method is developed in order to estimate the system state and external excitation necessary for the controller design. In light of the estimated augmented states, a hybrid controller that combines a feedback control algorithm and a feedforward control algorithm is designed according to optimal control theory and Moore–Penrose theory. Numerical simulation results show that the proposed controller can damp out the vibration response of the flexible manipulator system effectively upon external excitations. Moreover, it is further revealed that the control performance of the presented method can be improved by adding the time delay appropriately.

Incipient fault prediction based on generalised correntropy filtering for non-Gaussian stochastic systems

In this paper, the problem of incipient fault prediction is studied for the nonlinear stochastic system with non-Gaussian noises and actuator fault. The incipient fault is expressed as a nonlinear function with two unknown parameters (the occurring time of fault and the incipient fault evolution rate). Based on the generalised correntropy criterion, the fault detection filter is proposed, and then the occurring time of fault can be obtained. Once the fault is detected, the unknown fault evolution rate is estimated by designing a new generalised correntropy filter-based. According to the estimated fault occurrence time and the estimated fault evolution rate, the trend of incipient fault can be predicted. Finally, the simulation results of a single-link robotic flexible manipulator system are given to show that the proposed method is validated.

Boundary Disturbance Observer-Based Control of a Vibrating Single-Link Flexible Manipulator

This paper examines the boundary disturbance observer-based control for a vibrating single-link flexible manipulator system possessing external disturbances. Two new boundary anti-disturbance control strategies are presented to eliminate vibration, track disturbance, and determine angle position for the flexible manipulator system. Achieving rigorous analysis with no model reduction, the derived control can ensure the angle positioning and bounded stability in the controlled system. By appropriately designing parameters, the resulting simulation results can demonstrate the control performance.

Event-triggered boundary quantization control for flexible manipulator based on partial differential equations dynamic model

In this paper, we consider boundary control for a single-link flexible manipulator system described by partial differential equations (PDEs). Existing researches on controller design rarely consider the problem of communication capacity constrains during signal transmission. To deal with this problem, an adaptive control is designed to achieve the input quantization by using the random quantizer. Besides, a triggering event is addressed on the basis of relative threshold strategy for relieving communication load between controller and actuator. The proposed scheme is able to ensure that all closed-loop signals are globally uniformly bounded, and the angular tracking error and vibration converge to a residual set. Simulation results are presented to illustrate the effectiveness of the proposed scheme.

A High-Efficient Finite Difference Method for Flexible Manipulator with Boundary Feedback Control

The paper presents a high-efficient finite difference method for solving the PDE model of the single-link flexible manipulator system with boundary feedback control. Firstly, an abstract state-space model of the manipulator is derived from the original PDE model and the associated boundary conditions of the manipulator by using the velocity and bending curvature of the flexible link as the state variables. Then, the second-order implicit Crank-Nicolson scheme is adopted to discretize the state-space equation, and the second-order one-sided approximation is used to discretize the boundary conditions with excitations and feedback control. At last, the state-space equation combined with the boundary conditions of the flexible manipulator is transformed to a system of linear algebraic equations, from which the response of the flexible manipulator can be easily solved. Numerical simulations are carried out to simulate the manipulator under various excitations and boundary feedback control. The results are compared with ANSYS to demonstrate the accuracy and high efficiency of the presented method.

An Adaptive Fuzzy Control Method of Single-Link Flexible Manipulators with Input Dead-Zones

Flexible manipulators are widely used in aerospace industry and precision instrument manufacturing industry. However, due to the mechanism flexibility, the system dynamics have high nonlinearity and complexity, which make controller design pretty challenging. Moreover, in real production, electromechanical systems, including flexible manipulators, usually suffer from nonlinear input dead-zones and unknown system parameters/structures. Considering the above problems, an adaptive fuzzy control method is proposed, which can make the flexible link reach a desired rotation angle within finite time and simultaneously suppress the vibration of the manipulator. In the meantime, the system uncertainties are compensated, and the effect of input dead-zones is eliminated. In addition, the stability of the equilibrium point for the single-link flexible manipulator system is proven by rigorous theoretical analysis. Finally, the effectiveness and robustness of the proposed control method are verified by numerical simulations.

Sliding Mode Fault Tolerant Tracking Control for a Single-Link Flexible Joint Manipulator System

In this paper, the fault-tolerant tracking control problem for a class of single-link flexible joint manipulator (SFJM) system with uncertainty, fault, nonlinear function, and unmatched disturbance is investigated. An observer-based sliding mode control approach is designed. Concretely, first of all, the SFJM dynamic system with uncertainty, fault, and unmatched disturbance is established. Then, by transforming the system into two subsystems, a novel composite observer is proposed to estimate the fault and disturbance, respectively. Furthermore, a robust sliding mode controller, which contains a third-order sliding mode surface, a continuous control strategy, and a visual estimated fault signal, is constructed. In the control scheme, an adaptive law is also concluded to compensate for the estimation error. Finally, the proposed method is applied to the SFJM system and the simulation results illustrate the effectiveness of the proposed method.

Development of an experimental single-link flexible manipulator system

Demand for the applications of flexible manipulator due to their benefits has received attention from the industries. However, the flexibility of flexible manipulator has resulted in structural vibration and needs to be studied accordingly. This paper presents the development of a laboratory facility constituting of single-link flexible manipulator system. A new experimental rig flexible manipulator system constrained to move horizontally was designed, developed and fabricated. The experimental equipment setup and method of capturing data are presented. Experimental works have been done to highlight the effect of forces on hub-angle and end-point vibration of the flexible manipulator. Impact test was carried out to identify the dominant mode of vibration of the flexible manipulator. Result from the impact test was compared with the experimental data recorded for model validation and verification. The experimental result demonstrated that the reasonable accuracy with only 1.31% of error was obtained for the dominant mode of vibration. The experimental rig developed incorporating the sensors and actuators deployed may direct future researchers towards significant applications of flexible manipulator in the industrial sector and to promote better productivity.

Amplitude and Frequency Estimation of Exponentially Decaying Sinusoids

An online method for amplitude and frequency estimation of exponentially decaying sinusoids is proposed with a moving-window discrete Fourier transform (MWDFT) filter and frequency-locked loop. The tuned filter characteristics of MWDFT is modified into more flat characteristic around the center frequency with negative feedback, which increases the bandwidth of the filter. An adaptive sampling pulse adjustment mechanism is incorporated in the proposed structure for online estimation of frequency. Hence, the frequency error was exploited to achieve synchronization between in-phase component of MWDFT and input signal of estimation. The amplitude is estimated in online from the in-phase and quadrature-phase components of MWDFT. The performance of the proposed method is compared with the existing techniques and experimentally validated on single-link flexible manipulator system for the online estimation of frequency and amplitude of tip deflection signal. The experimental investigation prove that the proposed online technique performs well over the existing techniques.

FAULT TOLERANT CONTROL FOR SENSOR FAULT OF A SINGLE-LINK FLEXIBLE MANIPULATOR SYSTEM

This paper presents a new approach for sensor fault tolerant control (FTC) of a single-link flexible manipulator system (FMS) by using Finite Element Method (FEM). In this FTC scheme, a new control law is proposed where it is added to the nominal control. This research focuses on one element without any payload assumption in the modelling. The FTC method is designed in such way that aims to reduce fault while maintaining nominal FMS controller without any changes in both faulty and fault free cases. This proposed FTC approach is achieved by augmenting Luenberger observer that is capable of estimating faults in fault detection and isolation (FDI) analysis. From the information provided by the FDI, fault magnitude is assessed by using Singular Value Decomposition (SVD) where this information is used in the fault compensation strategy. For the nominal FMS controller, Proportional- integral- derivative (PID) controller is used to control the FMS where it follows the desired hub angle. This work proved that the FTC approach is capable of reducing fault with both incipient and abrupt signals and in two types of faulty conditions where the sensor is having loss of effectiveness and totally malfunction. All the performances are compared with FTC with Unknown Input Observer (FTC-UIO) method via the integral of the absolute magnitude of error (IAE) method.

Modelling of a Flexible Single-Link Manipulator Using Metaheuristic Algorithms

This study presents development of approaches with cuckoo search algorithm (CS) and differential evolutionary algorithm (DE) for modelling of flexible single-link manipulator system (FSLMS). Details of simulation study, model selection, optimization and result analyses are given in this study. A mathematical model of a (FSLMS) has been developed and modelled as a pinned-free, an Euler-Bernoulli flexible beam using finite element method (FEM) based on Lagrangian approach analysis. A bang-bang input torque was applied and the dynamic response of the system was investigated. Next, a suitable model structure is selected and optimized using intelligent optimization techniques (CS) and (DE). Mean squared error (MSE), One Step Ahead (OSA) prediction, correlation tests have been performed for validation and verification of the obtained model in characterizing the manipulator system. A comparative assessment of the two models in characterizing the manipulator system is presented in time and frequency domains. It has been demonstrated that the CS and DE modelling techniques have performed well in approximating the system response and the result obtained through CS and DE are nearly same in modelling a single-link flexible manipulator system.

Vibration and tip deflection control of a Single-link flexible manipulator

In this paper, a hybrid control scheme for vibration and tip deflection control of a single link flexible manipulator system is presented. The purpose of this control is for input tracking, vibration control of hub angle and tip deflection control. The control scheme consists of a resonant controller and a fuzzy logic controller (FLC).The resonant controller is used as the inner loop feedback controller for vibration control using the resonant frequencies at different resonant modes of the system which were determined from experiment. The fuzzy logic controller is designed as the outer loop feedback controller for the tracking control and to achieve zero steady state error. The performance of the proposed control scheme is investigated via simulations and the results show the effectiveness of the control scheme, in addition the controller is tested to show it robustness using different values of payload.

A Review on Fault-Tolerant Control for Single-Link Flexible Manipulator System

In this paper, a review of the historical development of fault- tolerant control, some proposals for the terminology in the field of supervision, fault detection and tolerance control are presented. The directions in which the subject is going are summarised and some pointers are given as to the likely issues and where new research effort is required. The paper provides a basic literature review covering most areas of fault-tolerant control of single-link flexible manipulator system.

Dynamic Modelling of a Single-Link Flexible Manipulator System: A Particle Swarm Optimisation Approach

This paper presents investigations into modelling of a single-link flexible manipulator system using the particle swarm optimisation (PSO) algorithm. PSO is a population-based search algorithm and is initialised with a population of random solutions, called particles. Basic PSO with best model can hardly provide suitable solutions in the case of real-world multimodal problems. In order to improve diversity in the population set and hence to improve the global searching capability a local version of PSO with time varying inertia and acceleration coefficients is proposed and used in this work. The effectiveness of the algorithm in modelling is validated and verified in terms of tracking, stability and the ability of the derived model in capturing a system's dynamics. The effect of swarm size on the convergence of the proposed PSO algorithm is also analysed. Time domain and frequency domain results of derived models clearly show the potential of the modelling technique and the proposed algorithm in solving such control problems.

반력모멘트 추정기를 이용한 단일 링크 유연 조작기의 진동제어

In this paper, a novel vibration control scheme for a single-link flexible manipulator system without using a vibration feedback sensor is proposed. In order to achieve the vibration information of the flexible link, a reaction moment estimator based on the dynamic characteristics of the flexible manipulator is proposed. While the manipulator is maneuvering the reaction moment is reciprocally acting on the flexible link and the hub inertia due to the vibration of the link. A sliding mode controller based on the equivalent rigid body dynamics corresponding to the proposed flexible manipulator is then augmented with the reaction moment estimator to realize a decentralized control system. The reaction moment estimator is implemented via the first order low pass filter. The performance of the proposed control scheme is verified by computer simulation and experiment.

Control of Flexible Manipulator Systems

This paper presents an investigation into the development of open-loop and closed-loop control strategies for flexible manipulator systems. Shaped torque inputs, including Gaussian-shaped and low-pass (Butter-worth and elliptic) filtered input torque functions, are developed and used in an open-loop configuration and their performance studied in comparison to a bang-bang input torque through experimentation on a single-link flexible manipulator system. Closed-loop control strategies that use both collocated (hub angle and hub velocity) and non-collocated (end-point acceleration) feedback are then proposed. A collocated proportional and derivative (PD) control is first developed and its performance studied through experimentation. The collocated control is then extended to incorporate, additionally, non-collocated feedback through a proportional integral derivative (PID) configuration. The performance of the hybrid collocated and non-collocated control strategy thus developed is studied through experimentation. Experimental results verifying the performance of the developed control strategies are presented and discussed.

Modelling of a single-link flexible manipulator system: theoretical and practical investigations

SummaryThis paper presents theoretical and experimental investigations into modelling a single-link flexible manipulator system. An analytical model of the manipulator, characterised by an infinite number of modes, is developed using the Lagrange's equation and modal expansion method. This is used to develop equivalent time-domain and frequency-domain working models of the system in state-space and transfer function forms respectively. The model parameters are then estimated experimentally using system's measured input/output data. The model thus obtained is validated through experimentation and results including the effect of payload on system characteristics presented and discussed.