A globally stable state feedback controller for flexible joint robots

The paper addresses the problem of controlling the joints of a flexible joint robot with a state feedback controller and proposes a gradual way of extending such a controller towards the complete decoupling of the robot dynamics. The global asymptotic stability for the state feedback controller with gravity compensation is proven, followed by some theoretical remarks on its passivity properties. By proper parameterization, the proposed controller structure can implement a position, a stiffness or a torque controller. Experimental results on the DLR lightweight robots validate the method.     

Stability analysis and robust control for fixed-scale teleoperation

In this article we present a new theorem that reduces the stability problem of teleoperators from a structured singular value problem to a maximum singular value problem. A control scheme realizing an ideal response for fixed-scale teleoperation is proposed and its stability is proven analytically. Next, the ideal control scheme is extended to control schemes with a higher stability robustness. Also, for these more complicated schemes, stability analyses are performed making use of the new theorem and stability conditions are derived. Experiments on a 1-d.o.f. setup are conducted to confirm the validity of the proposed control schemes.     

Initial experiments on a leg mechanism with a flexible geared joint and footpad

In the present work, a leg mechanism together with a flexible joint system is designed and constructed. The leg mechanism is expected to walk on uneven terrain and be subject to certain impact or contact forces. The effect of the designed flexible gear system and footpad on shock absorption is a main concern. The joint torque of the motor gear and the contact force of the foot are analyzed with different control schemes. The control performance of the leg movement by these methods is also presented. The proposed control methodology could next be applied to a newly designed two-link leg mechanism. It is hoped that the present study can be extended to an exoskeleton leg mechanism that is being developed.     

Performance analysis of an electrohydraulic impedance controller for robotic interaction control

Performance of an electrohydraulic impedance controller, developed in the physical domain, for controlling the contact forces during robotic interaction tasks is analyzed in this paper. The impedance controller is capable of varying the mechanical impedance of the manipulator during an interaction task and thus controls the interaction force. An electrohydraulic servo actuator, appended to a 1-d.o.f. manipulator arm, acts as the controller in the physical domain. The controller performance depends on the physical parameters such as size of the actuator, bulk modulus of the oil, etc., of the hydraulic system. The influence of these physical parameters on the controller performance is analyzed through frequency analysis and acceptable ranges of values for these parameters are determined. Controller sensitivity, stability of the constrained manipulator system and its frequency response are analyzed theoretically and results are presented. The limitation of application of the controller for practical applications is also analyzed and the results are presented.     

Stability and weighted sensitivity analysis of robust controller for heat exchanger

This study presents a parametric system identification approach to estimate the dynamics of a chemical plant from experimental data and develops a robust PID controller for the plant. Parametric system identification of the heat exchanger system has been carried out using experimental data and prediction error method. The estimated model of the heat exchanger system is a time-delay model and a robust PID controller for the time-delayed model has been designed considering weighted sensitivity criteria. The mathematical background of parametric system identification, stability analysis, and ${{\rm H}_\infty }$ weighted sensitivity analysis have been provided in this paper. A graphical plot has been provided to determine the stability region in the $( {{K_{\rm p}},{K_{\rm i}}} )$, $( {{K_{\rm p}},{K_{\rm d}}} )$ and $( {{K_{\rm i}},{K_{\rm d}}} )$ plane. The stability region is a locus dependent on parameters of the controller and frequency, in the parameter plane.     

An improved approach to robust stability analysis and controller synthesis for LPV systems

This paper revisits the problem of robust stability analysis and synthesis for linear parameter varying (LPV) systems. By introducing two new slack variables, new conditions for the polyquadratic stability and for the affine quadratic stability of LPV systems are presented in terms of linear matrix inequalities. These results are then applied for robust controller synthesis. Owing to the extra freedom degree introduced by the real slack variable, this proposed approach could lead to less conservative results than that of from the literature, especially for robust controller synthesis. The effectiveness and superiority are demonstrated by the comparison between this proposed approach and the existing results on a well‐known numerical example. Copyright © 2010 John Wiley & Sons, Ltd.     

Stability analysis and controller synthesis for discrete linear time-delay systems with state saturation nonlinearities

The problem of global asymptotic stability analysis and controller synthesis for a class of discrete linear time-delay systems with state saturation nonlinearities is investigated. With the introduction of a free matrix whose infinity norm is less than or equal to 1, the state of discrete linear time-delay systems with state saturation is bounded by a convex hull, which makes it feasible to apply a suitable Lyapunov functional to obtain a sufficient condition for global asymptotic stability. It is also shown that this condition can be extended to controller synthesis and discrete time-delay systems with partial state saturation. The obtained results are expressed in terms of matrix inequalities that can be solved by the presented iterative linear matrix inequality approach. The effectiveness of these results is demonstrated by some numerical examples.     

Stability analysis and controller synthesis for discrete uncertain singular fuzzy systems with distinct difference matrices in the rules

This paper mainly studies an extended discrete singular fuzzy model incorporating the multiple difference matrices in the rules and discusses its stability and design issues. By embracing additional algebraic constraint, traditional discrete Takagi-Sugeno (T-S) fuzzy model can be extended to a generalised discrete singular Takagi-Sugeno (GDST-S) model with individual difference matrices E_i in the locally singular models, where it can describe a larger class of physical or non-linear systems. Based on the linear matrix inequality (LMI) approach, we focus on deriving some explicit stability and design criteria expressed by the LMIs for the regarded system. Thus, the stability verification and controller synthesis can be performed by the current LMI tools. Finally, some illustrative examples are given to illustrate the effectiveness and validity of the proposed approach.     

Modeling and simulation for fatigue life analysis of robots with flexible joints under percussive impact forces

This paper presents a method for modeling and analyzing the fatigue life of robots with flexible joints, with a particular focus on applications under percussive impact forces. This development is motivated by growing interests in robotic automation for operations with percussive impact tools. The most important characteristic of percussive operations is the repetitive impacts generated by the tool, such as a percussive rivet gun. After modeling of a flexible joint robot, a forced vibration solution is provided by including the impact forces generated by the percussive gun, projecting them onto the robot joint space and treating them in terms of the Fourier transform. As a result, the joint angular displacements can be solved using a standard vibration method. Then the joint stresses can be determined through Hooke's law. To consider the stress variations caused by the robot operating at different poses using different rivets, a multiple-loading fatigue model is applied from which an equation is derived to determine the total number of the rivets that can be riveted before robot's fatigue failure. Based on simulation using our model, the following observations are received. First, the joint torsional stresses vary with robot's position and orientation. Second, no joint will always experience the maximum stress and the joint stress dominancy also varies with robot's position and orientation. Third, at a given riveting point, the rivet gun direction considerately affects the joint stresses. Fourth, the fatigue life of each joint is different; therefore robot's fatigue life should be evaluated based on the shortest joint fatigue life.     

Stability analysis and controller design for consensus in discrete-time networks with heterogeneous agent dynamics

In this paper, we study the heterogeneous consensus problem in directed networks consisting of first- and second-order agents that can only receive the position states of their neighbors. Necessary and sufficient conditions on the controller parameters are obtained in order to achieve consensus in the network. The mathematical expressions of the consensus equilibria are given for two different scenarios. Furthermore, we propose a systematic method for choosing controller parameters to ensure stability in a network of agents with heterogeneous dynamics. Several numerical examples are also provided to illustrate the theoretical results.     

Design, analysis and experimental validation of a robust nonlinear path following controller for marine surface vessels

The problem of path following for marine surface vessels using the rudder angle is addressed in this paper. A four-degree-of-freedom nonlinear surface vessel model, together with the Serret-Frenet equations, is introduced to describe the ship dynamics and path following error dynamics. While similar models have been used and reported in the literature for path following control algorithm development, the novelty of the approach presented in this work lies in the following aspects. (a) The back-stepping nonlinear controller design is based on feedback dominance, instead of feedback linearization and nonlinearity cancelation; (b) additional design parameters are employed in the Lyapunov function that lead to simplification of the controller in the design procedure and normalization of different variables in the Lyapunov function to improve the controller performance; (c) relying on feedback dominance and the introduction of the additional parameters in the Lyapunov function, the resulting controller is almost linear, with very benign nonlinearities allowing for analysis and evaluation; and (d) the performance of the nonlinear controller, in terms of path following, is analyzed for robustness in the presence of model uncertainties. The simulation results are presented to verify and illustrate the analytic development and the effectiveness of the resulting control against rudder saturation and rate limits, and delays in the control execution, as well as measurement noises. Furthermore, the control design is validated by experimental results conducted in a tank using a model ship.     

Design and performance analysis of tracking controller for uncertain nonlinear composite system using neural networks

Based on high order dyna mi c neural network, paper presents the tracking problem for uncertain nonlinear composite system,which contain s external disturbance,whose nonlinear ities are assumed to be unknown.A smooth contr oller is designed to guarantee a uniform ultimate boundedness property for the tracking error and a ll other signals in the closed loop.Certain meas ures are utilized to test its performance.No a priori knowledge of an upper bound on the “ optimal" weight and modeling error is required;the weights of neural networks are updated on-line.N umerical simulations performed on a simple example i llustrate and clarify the approach.     

Stability analysis and controller design for a class of delay systems via observer based on network

This paper focuses on the problem of stability analysis and controller design for a class of delay systems based on networked control systems. By introducing some free matrix variables, some criteria for stability analysis and observer-based control law design can be obtained by the solving of linear matrix inequalities. A numerical example is also offered to prove the effectiveness of the proposed method.