Class Of Uncertain Mechanical Systems Research Articles

Reinforcement learning based adaptive control for uncertain mechanical systems with asymptotic tracking

This paper mainly focuses on the development of a learning-based controller for a class of uncertain mechanical systems modeled by the Euler-Lagrange formulation. The considered system can depict the behavior of a large class of engineering systems, such as vehicular systems, robot manipulators and satellites. All these systems are often characterized by highly nonlinear characteristics, heavy modeling uncertainties and unknown perturbations, therefore, accurate-model-based nonlinear control approaches become unavailable. Motivated by the challenge, a reinforcement learning (RL) adaptive control methodology based on the actor-critic framework is investigated to compensate the uncertain mechanical dynamics. The approximation inaccuracies caused by RL and the exogenous unknown disturbances are circumvented via a continuous robust integral of the sign of the error (RISE) control approach. Different from a classical RISE control law, a tanh(·) function is utilized instead of a sign(·) function to acquire a more smooth control signal. The developed controller requires very little prior knowledge of the dynamic model, is robust to unknown dynamics and exogenous disturbances, and can achieve asymptotic output tracking. Eventually, co-simulations through ADAMS and MATLAB/Simulink on a three degrees-of-freedom (3-DOF) manipulator and experiments on a real-time electromechanical servo system are performed to verify the performance of the proposed approach.

Leader–follower Stackelberg game oriented adaptive robust constraint-following control design for fuzzy exoskeleton robot systems

To comprehensively enhance the robust tracking performance, a leader–follower Stackelberg game oriented adaptive robust constraint-following control scheme has been proposed for a class of uncertain mechanical systems. In the proposed scheme, a fuzzy set-theoretic description represents the uncertainties (possibly fast time-varying), and an adaptive robust constraint-following control ensures the robust stability. With the fuzzy uncertainty description and control performance analysis, a leader–follower game theory is employed to obtain multiple optimal gains for the proposed control scheme. Further, the existence of these optimal parameters can be verified. The proposed approach is successfully applied to a lower limb exoskeleton (LLE) robot system for rehabilitation training.

Robust tracking control design with a novel leakage-type adaptive mechanism for an uncertain lower limb exoskeleton robot

In this paper, a novel adaptive robust control approach has been proposed for a class of uncertain mechanical systems. First, aiming for the unknown uncertainties which may be fast time-varying, a novel adaptive mechanism in leakage-type will be developed. Unlike the prevalent adaptive methods, this adaptive mechanism put forward mainly accounts for estimating all the lumped uncertainty terms, and does not require any information of uncertainties other than they are bounded; Second, through transforming the gait following assignment to the constraint control, an adaptive robust constraint-following controller constructed will render the constraints uniformly bounded and uniformly ultimately bounded. To testify the efficacy of proposed approach, a lower limb exoskeleton robot is considered as an illustrative example, the simulations indicate that the proposed control can indeed improve the level of passive rehabilitation training.

Adaptive friction compensation for a class of mechanical systems based on LuGre model

AbstractThis paper deals with the problem of friction compensation for a class of uncertain mechanical systems based on LuGre model. The objective is to develop control laws such that the position variable of the system tracks a periodic desired signal or a constant desired signal. Since the friction behavior of the system with periodic desired signals is largely different from that of the system with constant desired signals, two different adaptive control methods are presented for the two cases, respectively. For the case of periodic desired signals, an adaptive repetitive learning control method is presented, and for the case of constant desired signals, an adaptive dynamic state feedback control method is presented. Both the control laws can guarantee that all the signals in the closed loop system are bounded and the tracking errors converge to zero. Several numerical simulations are carried out to show effectiveness of the proposed control algorithms.

Robust tracking control for a class of uncertain mechanical systems

ABSTRACTIn this paper, it is proposed a control structure to solve the tracking problem in a class of uncertain mechanical systems. It is considered that the system is affected by unknown disturbances, discontinuous friction and uncertainties. The proposed control algorithm is based on the twisting control algorithm plus a nested signum term, moreover a disturbance estimator is used as feedback to the controller in order to compensate the non modelled parameters and uncertainties of the plant, also a velocity observer is proposed. Through the usage of Lyapunov tools, it is shown that the closed-loop nonlinear system is globally asymptotically stable and achieves zero steady-state position error, also, it is shown that while being asymptotically stable and homogeneous of degree q<0, these systems approach the equilibrium point in finite time. Numerical simulations and real-time experiments carried out in a mass-spring-damper system show the performance and effectiveness of the control structure.

Reconfigurable Tolerant Control of Uncertain Mechanical Systems With Actuator Faults: A Sliding Mode Observer-Based Approach

This paper studies a key issue of developing reconfigurable fault-tolerant control to retain a nominal feedback controller and simultaneously handles actuator faults and system uncertainty, while the closed-loop system is stabilized with all control objectives achieved. A theoretical architecture of a reconfigurable control design is presented for a class of uncertain mechanical systems by using an observer technique. As a stepping stone, a nonlinear observer-based estimation mechanism is designed to reconstruct uncertain dynamics and actuator faults with the estimation error converging to zero within finite time. A reconfigurable control effort is then synthesized from the reconstructed knowledge. This control power operates as a compensation control part, and it is added to the nominal control part to accommodate system uncertainties and actuator faults. It is proved that the overall system resulted from the developed control framework has the same control performance of the nominal closed-loop system, including certain system dynamics and the nominal control effort. The effectiveness of the scheme is validated on a serial robotic manipulator.

Immersion and invariance adaptive velocity observer for a class of Euler–Lagrange mechanical systems

This paper addresses the problem of velocity estimation for a class of uncertain mechanical systems. Using advantages of immersion and invariance technique with input–output filtered transformation, a proper immersion and dynamical auxiliary filter have been constructed in the designed estimator. Uniform global asymptotic convergence of the velocity estimator has been proved for the system with parametric uncertainties. In the presence of perturbations on the input and output, the performance analysis of the estimator has been theoretically investigated and illustrated by simulation results.

Reliable Robust Control Design for Uncertain Mechanical Systems

In this article, we consider the problem of reliable H∞ control for a class of uncertain mechanical systems with input time-varying delay and possible occurrence of actuator faults. In particular, we assume that linear fractional transformation (LFT) uncertainty formulations appear in the mass, damping, and stiffness matrices. The main objective is to design a state feedback reliable H∞ controller such that, for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop system is robustly asymptotically stable while satisfying a prescribed H∞ performance constraint. By constructing an appropriate Lyapunov–Krasovskii functional (LKF) and using linear matrix inequality (LMI) approach, a new set of sufficient conditions are derived in terms of LMIs for the existence of robust reliable H∞ controller. Further, Schur complement and Jenson's integral inequality are used to substantially simplify the derivation in the main results. The obtained results are formulated in terms of LMIs which can be easily verified by the standard numerical softwares. Finally, numerical examples with simulation result are provided to illustrate the applicability and effectiveness of the proposed reliable H∞ control scheme. The numerical results reveal that the proposed theory significantly improves the upper bound of time delays and minimum feasible H∞ performance index over some existing works.

Robust sampled‐data H∞ control for mechanical systems

This article addresses the issue of robust sampled‐data control for a class of uncertain mechanical systems with input delays and linear fractional uncertainties which appear in all the mass, damping, and stiffness matrices. Then, a novel Lyapunov–Krasovskii functional is constructed to obtain sufficient conditions under which the uncertain mechanical system is robustly, asymptotically stable with disturbance attenuation level about its equilibrium point for all admissible uncertainties. More precisely, Schur complement and Jenson's integral inequality are utilized to substantially simplify the derivation of the main results. In particular, a set of sampled‐data controller is designed in terms of the solution of certain linear matrix inequalities that can be solved effectively using available MATLAB software. Finally, a numerical example with simulation result is provided to show the effectiveness and less conservativeness of the proposed sampled‐data control scheme. © 2014 Wiley Periodicals, Inc. Complexity 20: 19–29, 2015

Comments on “A Simple Nonlinear Observer for a Class of Uncertain Mechanical Systems”

For original paper see Y. Su. ibid., vol.52, no.7, p.1340-5, (2007). This article presents a comment on the paper ldquoa simple nonlinear observer for a class of uncertain mechanical systemsrdquo.

A Simple Nonlinear Observer for a Class of Uncertain Mechanical Systems

A simple nonlinear observer is proposed for a class of uncertain nonlinear multiple-input-multiple-output (MIMO) mechanical systems whose dynamics are first-order differentiable. The global asymptotic observation of the proposed observer is proved. Thus, the observer can be designed independently of the controller. Furthermore, the proposed observer is formulated without any detailed model knowledge of the system. These advantages make it easy to implement. Numerical simulations are included to illustrate the effectiveness of the proposed observer.

Adaptive realization of desired constraint stabilization dynamics in the control of multibody systems

This paper presents a novel way of stabilizing the constraint drift dynamics in the numerical simulation of multibody systems. This formulation is applicable for a large class of uncertain mechanical systems described by nonlinear differential algebraic equations that are subject to holonomic constraints. In the absence of uncertainty in the system inertia parameters, it is possible to develop stabilization relationships that suppress the accumulation of error in the constraint equations during the time integration process. In order to account for ignorance in the parameters, we propose a model reference adaptive control scheme that ensures the asymptotic realization of the desired (reference) constraint violation dynamics. Special attention is given to the case of redundantly actuated systems, as is typical for robotics. For this class of problems, we direct special attention to optimization criteria that achieve any desired manoeuvre using minimum control effort and coordination between the redundant set of actuators. An example application demonstrates the effectiveness and practicality of the proposed adaptive control formulation.

Second order sliding mode control for robot arms with time base generators for finite-time tracking

A novel chattering-free dynamic sliding mode controller for a class of uncertain mechanical systems is proposed in order to account globally for a time-varying sliding regime for all time and for any initial condition. The new sliding surface, parametrized by a time base generator, plays the role of moving, and rotating continuously the nominal sliding surface, while shifting is done through a known, state-independent, vanishing vector to eliminate the reaching phase for any initial condition, a weaker assumption in comparison to some moving sliding surface designs. In this way, the closed-loop system yields finite-time convergence of tracking errors, whose convergence time can be fixed independently of initial conditions, in contrast to terminal sliding mode wherein convergence time depends on initial conditions. To implement the controller, the upper bound of the derivative of the sliding surface is required, a weaker assumption in contrast to some dynamic sliding mode controllers. The performance of the closed-loop system is visualized through simulation.

Controllers which guarantee robustness with respect to unmodelled flexibilities for a class of uncertain mechanical systems

AbstractWe consider a class of uncertain mechanical systems containing flexible elements and subject to memoryless output‐feedback controllers. The damping and stiffness properties of some of the flexible elements are parametrized linearly in μ−1 and μ−2 respectively, where μ &gt; 0 and these components become more rigid as μ approaches zero. We propose a class of ‘stabilizing’ controllers for a system model in which the above components are rigid. Subject to a ‘linear growth condition’, the controllers also stabilize the model in which the components are flexible provided μ &gt; 0 is sufficiently small.