Single-link Flexible Joint Robot Research Articles

Robust model reference control of linear parameter‐varying systems with disturbances

This paper deals with the design and analysis of robust model reference control systems for a class of linear parameter-varying (LPV) systems with disturbances. Two types of robust model reference control systems are proposed to achieve a prescribed tracking performance. The first type is the LPV H ∞ state-feedback model reference control system and the second type is the LPV H ∞ output-feedback model reference control system. Based on the notion of quadratic stability, necessary and sufficient conditions for the existence of LPV reference models are given. Also, a parameterisation of LPV reference models is derived in this study. A practical example of a single-link flexible-joint robot is given to illustrate the design steps and to show the effectiveness of the proposed LPV H ∞ model reference controllers.

Fault detection observer design in finite‐frequency domain for Lipschitz non‐linear systems

This study is about H − / H ∞ fault detection observer design in finite-frequency domain for Lipschitz non-linear systems with actuator fault. To make the generated residual sensitive to fault while robust against disturbance, the authors derive design conditions for the fault detection observer to achieve H − fault sensitivity performance in finite-frequency domain and H ∞ disturbance attenuation performance. The authors further transform the design conditions as a set of linear matrix inequalities to facilitate the observer design. Besides, some extra design degrees of freedom parameters are provided in the proposed method to further reduce some conservatism. Numerical simulations of a single-link flexible joint robot are conducted to verify the effectiveness of the proposed approach.

Coexistence of single- and multi-scroll chaotic orbits in a single-link flexible joint robot manipulator with stable spiral and index-4 spiral repellor types of equilibria

This paper reports various chaotic phenomena that occur in a single-link flexible joint (SLFJ) robot manipulator. Four different cases along with subcases are considered here to show different types of chaotic behaviour in a flexible manipulator dynamics. In the first three cases, a partial state feedback as joint velocity and motor rotor velocity feedback is considered, and the resultant autonomous dynamics is considered for analyses. In the fourth case, the manipulator dynamics is considered as a non-autonomous system. The system has (1) one stable spiral and one saddle-node foci, (2) two saddle-node foci and (3) one marginally stable nature of equilibrium points. We found single- and multi-scroll chaotic orbits in these cases. However, with the motor rotor velocity feedback, the system has two unstable equilibria. One of them has an index-4 spiral repellor. In the non-autonomous case, the SLFJ robot manipulator system has an inverse crisis route to chaos and exhibits (1) transient chaos with a stable limit cycle and (2) chaotic behaviour. In all the four cases, the SLFJ manipulator dynamics exhibits coexistence of chaotic orbits, i.e. multi-stability. The various dynamical behaviours of the system are analysed using available methods like phase portrait, Lyapunov spectrum, instantaneous phase plot, Poincare map, parameter space, bifurcation diagram, 0–1 test and frequency spectrum plot. The MATLAB simulation results support various claims made about the system. These claims are further confirmed and validated by circuit implementation using NI Multisim.

Continuous–discrete-time adaptive observers for nonlinear systems with sampled output measurements

ABSTRACTThis paper considers the continuous–discrete-time adaptive observer (CDAO) design for a class of nonlinear systems with unknown constant parameters and sampled output measurements. The proposed observer is actually an impulsive system, since the observer state flows according to a set of differential equations and with instantaneous state jumps corresponding to measured samples and their estimates, and an inter-sample output predictor is used to predict the output during sampling intervals. By assuming appropriate persistent excitation conditions and following a technical lemma, an upper bound of the sampling intervals is derived, with which the convergence of the observer state and unknown parameters can be ensured. Finally, the proposed observer is used in examples of chaotic oscillators and single-link flexible-joint robot manipulator to show the effectiveness.

Robust Generation of Limit Cycles in Nonlinear Systems: Application on Two Mechanical Systems

This paper studies inducing robust stable oscillations in nonlinear systems of any order. This goal is achieved through creating stable limit cycles in the closed-loop system. For this purpose, the Lyapunov stability theorem which is suitable for stability analysis of the limit cycles is used. In this approach, the Lyapunov function candidate should have zero value for all the points of the limit cycle and be positive in the other points in the vicinity of it. The proposed robust controller consists of a nominal control law with an additional term that guarantees the robust performance. It is proved that the designed controller results in creating the desirable stable limit cycle in the phase trajectories of the uncertain closed-loop system and leads to induce stable oscillations in the system's output. Additionally, in order to show the applicability of the proposed method, it is applied on two practical systems: a time-periodic microelectromechanical system (MEMS) with parametric errors and a single-link flexible joint robot in the presence of external disturbances. Computer simulations show the effective robust performance of the proposed controllers in generating the robust output oscillations.

Adaptive observer-based fault estimation for a class of Lipschitz nonlinear systems

Abstract Fault input channels represent a major challenge for observer design for fault estimation. Most works in this field assume that faults enter in such a way that the transfer functions between these faults and a number of measured outputs are strictly positive real (SPR), that is, the observer matching condition is satisfied. This paper presents a systematic approach to adaptive observer design for joint estimation of the state and faults when the SPR requirement is not verified. The proposed method deals with a class of Lipschitz nonlinear systems subjected to piecewise constant multiplicative faults. The novelty of the proposed approach is that it uses a rank condition similar to the observer matching condition to construct the adaptation law used to obtain fault estimates. The problem of finding the adaptive observer matrices is formulated as a Linear Matrix Inequality (LMI) optimization problem. The proposed scheme is tested on the nonlinear model of a single link flexible joint robot system.

Adaptive backstepping control using combined direct and indirect adaptation for a single-link flexible-joint robot

In this paper, a new tuning functions–based adaptive backstepping controller using combined direct and indirect adaptation for a single–link flexible–joint robot is presented. In this approach, the parameter estimation is driven by a weighted combination of tracking and identification errors. At first, the x–swapping filter identifier with a gradient–type update law is presented for a class of parametric strict–feedback nonlinear systems. Then, the main steps of the controller design for a single–link flexible–joint robot manipulator model are described. The closed–loop error dynamics is shown to be globally stable by using the Lyapunov stability approach. Finally, simulation results are given to illustrate the tracking performance of a single–link flexible–joint robot manipulator with the proposed adaptive control scheme.

Unknown Input Observer Based Robust Fault Estimation for Systems Corrupted by Partially-Decoupled Disturbances

Robust fault estimation plays an important role in real-time monitoring, diagnosis, and fault-tolerance control. Accordingly, this paper aims to develop an effective fault estimation technique to simultaneously estimate the system states and the concerned faults, while minimizing the influences from process/sensor disturbances. Specifically, an augmented system is constructed by forming an augmented state vector composed of the system states and the concerned faults. Next, an unknown input observer (UIO) is designed for the augmented system by decoupling the partial disturbances and attenuating the disturbances that cannot be decoupled, leading to a simultaneous estimate of the system states and the concerned faults. In order to be close to the practical engineering situations, the process disturbances in this study are assumed not to be completely decoupled. In the first part of this paper, the existence condition of such an UIO is proposed to facilitate the fault estimation for linear systems subjected to process disturbances. In the second part, robust fault estimation techniques are addressed for Lipschitz nonlinear systems subjected to both process and sensor disturbances. The proposed technique is finally illustrated by the simulation studies of a three-shaft gas turbine engine and a single-link flexible joint robot.

Design of impulsive adaptive observers for improvement of persistency of excitation

SummaryThe development of adaptive observer techniques for nonlinear systems in the output canonical form is proposed applying additional impulsive feedback in the observer equations. The stability of new impulsive adaptive observer is investigated. It is shown that under some conditions, the proposed impulsive feedback can improve the rate of the observer convergence or relax the requirement on persistency of excitation, which is usually introduced to ensure convergence of the parameter estimates. The proposed feasibility conditions include positivity of dwell time (boundedness of impulse frequency) and solvability of some Lyapunov‐like matrix inequalities. The results are illustrated by simulation for three examples (including a single link flexible joint robot example). Copyright © 2014 John Wiley & Sons, Ltd.

SATURATED PROPORTIONAL DERIVATIVE CONTROL OF A SINGLE-LINK FLEXIBLE-JOINT MANIPULATOR

This paper considers the control of a single-link flexible-joint robot manipulator subject to actuator saturation. Alternative controllers are proposed and compared to one found in literature. In particular, a controller with proportional and derivative components is guaranteed to provide a total torque less than a chosen value, thereby disallowing actuator saturation. It is shown that an equilibrium point of the closed-loop system is asymptotically stable. Additionally, it is shown that the controllers are robust to modelling errors. Finally, this paper presents simulation results demonstrating the performance of the proposed control architecture.

H ∞ filtering for singular bilinear systems with application to a single-link flexible-joint robot

In this paper, we consider the H ∞ filters design for singular bilinear systems. The approach is based on the parameterized solution of a set of constrained Sylvester equations. The exponential convergence and l 2 gain attenuation problems are solved by using the bounded real lemma, which leads to linear matrix inequalities (LMI) formulation. Finally, a detailed design procedure is given for the estimation of the states of a flexible joint robot, which demonstrates the effectiveness of the proposed method.

Robust fault detection and isolation for a class of uncertain single output non‐linear systems

The problem of robust fault detection and isolation (FDI) is studied for a class of uncertain single output non-linear systems with q faults. By designing a switching law, a robust state observer is developed such that its state responses can asymptotically converge to the true system states for both fault-free and faulty cases. Based on this robust state observer and other q + 1 FDI observers, an efficient scheme is presented such that the FDI can be achieved for the considered single output non-linear systems. The theoretical results are illustrated through an example of a single-link flexible joint robot.

Fuzzy Passivity Control of Flexible Joint Robot

This paper researches a fuzzy control method for passive flexible joint robot. Stability control method applying T-S fuzzy model is employed for single-link flexible joint robot. T-S fuzzy model is used to approximate the flexible joint robot firstly, and then fuzzy controller is developed based on the principle of parallel distributed compensation. The fuzzy controller is also applied to the passive properties of model error. The stability conditions are proposed by Lyapunov function and linear matrix inequalities are also applied to solve the controller parameters. Simulation results show that the proposed method of application value.

Modelling and control of flexible joint robot based on Takagi–Sugeno fuzzy approach and its stability analysis via sum of squares

This article proposes a Takagi–Sugeno (T-S) fuzzy model of single-link rotary flexible joint robot. The proposed control method is based on parallel distributed control. The parameters of T-S controller are improved by distributed population genetic algorithm (GA) with chaos GA. Using Hermite–Biehler theorem in distributed population, GA is made to have a fast convergence. Dividing search space into several sub-spaces causes a better response, and chaos disturbance helps the whole algorithm to reach a best answer. The stability of the controller is analysed via the sum of squares programming, and finally, it is implemented on the plant.

Quantized feedback stabilization for a class of linear systems with nonlinear disturbances

The quantized feedback stabilization problem for a class of linear system with nonlinear disturbances is addressed, in which the system and controller are connected via a communication channel. In this case, the effect of quantization errors is studied. A practical quantized scheme is designed such that the transmission error decays to zero exponentially. Meanwhile, a sufficient condition in terms of linear matrix inequality for input-to-state stability (ISS) of the system is presented with regard to the transmission error. Therefore, a quantized stabilization of the system is guaranteed based on the ISS property. A simulation example for the single-link flexible joint robot is presented to demonstrate the effectiveness of the result.

Fuzzy adaptive dynamic surface control for a single-link flexible-joint robot

In this paper, a fuzzy adaptive controller is proposed for a single-link flexible-joint robot. Fuzzy logic systems are used to approximate unknown nonlinearities, and then a fuzzy state observer is designed to estimate the immeasurable states. By combining the adaptive backstepping design with dynamic surface control (DSC) technique, a fuzzy adaptive output-feedback backstepping control approach is developed. It is proved that all the signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded (SGUUB), and both the observer and tracking errors converge to a small neighborhood of the origin by appropriate choosing the design parameters. The simulation results are provided to demonstrate the effectiveness of the proposed controller. Two key advantages of our scheme are that (i) the proposed control method does not require that the link velocity and actuator velocity of single-link flexible-joint robot be measured directly, and (ii) the problem of “explosion of complexity” is avoided.

Cascade fuzzy logic control of a single-link flexible-joint manipulator

This paper presents the design and control of a single-link flexible-joint robot manipulator. A cascade fuzzy logic controller (FLC) was used to remove link vibrations and to obtain fast trajectory tracking performance. The cascade FLC structure includes 3 different FLCs. The input variables of the first and the second FLCs are the motor rotation angle error, its derivative, and the end-point deflection error its derivative, respectively. The outputs of these controllers are the inputs of the third FLC, which yields the control signal to the flexible robot arm. All of the FLCs were embedded in a DS1103 real-time control board. Several experiments were conducted to verify the controller performance. In the step-response experiments, the error of motor rotation angle was obtained as less than 0.12° and there was no steady-state error in the end-point deflection. In trajectory tracking experiments with the same FLC structure, small errors and phase shifts in the system variables occurred. Model parameters of the flexible arm such as link length and spring stiffness were changed to test the robustness of the FLC. It was seen that the FLCs were very robust to internal and external disturbances. Considering the results of the experiments, the proposed FLC structure shows efficient control performance in flexible robot arms.

Fault, State, and Unknown Input Reconstruction in Nonlinear Systems Using Sliding Mode Observers

In this paper, a new approach to estimation of unknown inputs and faults in a class of nonlinear systems is presented. The approach is based on the design of a cascade connection of two sliding mode observers. The first observer is used for the estimation of state and unknown inputs and the second is used for the fault detection and isolation. An important feature of the proposed approach is that the state trajectories do not leave the sliding manifold even in the presence of unknown inputs and faults. This allows for faults and unknown inputs to be completely reconstructed based on the information retrieved from the equivalent output injection signals. The proposed approach is tested on a nonlinear model of single link flexible joint robot system.

IMPULSIVE ADAPTIVE OBSERVERS: IMPROVING PERSISTENCY OF EXCITATION

AbstractThe development of adaptive observer techniques for nonlinear systems in the output canonical form is proposed applying additional impulsive feedbacks in the observer equations. The stability of new impulsive adaptive observers is investigated. It is shown that under some conditions the proposed impulsive feedbacks can improve the rate of the observer convergence or relax the requirement on persistency of excitation, which is frequently needed to ensure convergence of the parameter estimates. The proposed feasibility conditions include positivity of dwell time (boundedness of impulse frequency) and solvability of some Lyapunov-like hybrid matrix inequalities. The results are illustrated by simulation for three examples (including a single link flexible joint robot example).

Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation

This paper presents a fault detection and isolation (FDI) scheme for a class of Lipschitz nonlinear systems with nonlinear and unstructured modeling uncertainty. This significantly extends previous results by considering a more general class of system nonlinearities which are modeled as functions of the system input and partially measurable state variables. A new FDI method is developed using adaptive estimation techniques. The FDI architecture consists of a fault detection estimator and a bank of fault isolation estimators. The fault detectability and isolability conditions, characterizing the class of faults that are detectable and isolable by the proposed scheme, are rigorously established. The fault isolability condition is derived via the so-called fault mismatch functions, which are defined to characterize the mutual difference between pairs of possible faults. A simulation example of a single-link flexible joint robot is used to illustrate the effectiveness of the proposed scheme.