scholarly journals A Unified Approach to Design Robust Controllers for Nonlinear Uncertain Engineering Systems

2018 ◽  
Vol 8 (11) ◽  
pp. 2236 ◽  
Author(s):  
Laura Celentano
Keyword(s):  
Nonlinear System ◽  
Tracking Control ◽  
Mimo Systems ◽  
Broad Class ◽  
Tracking Error ◽  
Reference Signal ◽  
Joint Space ◽  
Control Laws ◽  
Vectorial Function

This paper presents new theorems, which allow to design in a unified way robust proportional-derivative (PD)-type control laws without chattering for a broad class of uncertain nonlinear multi-input multi-output (MIMO) systems, subject to bounded disturbances and noises, of great theoretical and engineering relevance. These controllers are used to track a reference signal with bounded second derivative with the tracking error norm smaller than a prescribed value. The proposed control laws are simple to design and implement, above all for robotic systems, both in the case of a trajectory assigned in the joint space and in the workspace. The obtained theoretical results can have numerous applications. In this paper four significant applications are provided. The first one concerns the solution of a nonlinear equations system or the determination of an equilibrium point of a nonlinear system. The second case study deals with the inversion of a nonlinear vectorial function or the kinematic inversion of a robot. The third application concerns: (A) the tracking control of a robot with parametric uncertainties, with and without measurement noise on velocity, both in the joint space and the workspace; (B) the impedance control of a robot interacting with a human operator. The fourth case study addresses the tracking control of an uncertain nonlinear system that does not belong to the class of mechanical systems. Finally, an appendix is included, providing six easy examples, which show how the results proposed in the paper can eliminate and/or reduce serious disadvantages existing in the robust control literature for significant classes of linear and nonlinear uncertain systems.

Practical Tracking Control of a Class of Uncertain Surface Vessels Under Weak Assumptions on Uncertainties and Reference Trajectories

2021 ◽  
Author(s):  
Jian Li ◽  
Wenqing Xu ◽  
Zhaojing Wu ◽  
Yungang Liu
Keyword(s):  
Tracking Control ◽  
Broad Class ◽  
Tracking Error ◽  
Reference Trajectory ◽  
Unknown Parameters ◽  
Related Literature ◽  
Surface Vessels ◽  
Control Scheme ◽  
Reference Trajectories ◽  
Theoretical Results

Abstract This paper is devoted to the tracking control of a class of uncertain surface vessels. The main contributions focus on the considerable relaxation of the severe restrictions on system uncertainties and reference trajectory in the related literature. Specifically, all the system parameters are unknown and the disturbance is not necessarily to be differentiable in the paper, but either unknown parameters or disturbance is considered but the other one is excluded in the related literature, or both of them are considered but the disturbance must be continuously differentiable. Moreover, the reference trajectories in the related literature must be at least twice continuously differentiable and themselves as well as their time derivatives must be known for feedback, which are generalized to a more broad class ones that are unknown and only one time continuously differentiable in the paper. To solve the control problem, a novel practical tracking control scheme is presented by using backstepping scheme and adaptive technique, and in turn to derive an adaptive state-feedback controller which guarantees that all the states of the resulting closed-loop system are bounded while the tracking error arrives at and then stay within an arbitrary neighborhood of the origin. Finally, simulation is provided to validate the effectiveness of the proposed theoretical results.

scholarly journals Model-Free Optimized Tracking Control Heuristic

Robotics ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 49 ◽  
Author(s):  
Ning Wang ◽  
Mohammed Abouheaf ◽  
Wail Gueaieb ◽  
Nabil Nahas
Keyword(s):  
Tracking Control ◽  
Tracking Error ◽  
Reference Signal ◽  
Control Algorithms ◽  
Learning Tools ◽  
Control Effort ◽  
Control Loops ◽  
Model Free ◽  
Architectural Framework ◽  
Model Free Control

Many tracking control solutions proposed in the literature rely on various forms of tracking error signals at the expense of possibly overlooking other dynamic criteria, such as optimizing the control effort, overshoot, and settling time, for example. In this article, a model-free control architectural framework is presented to track reference signals while optimizing other criteria as per the designer’s preference. The control architecture is model-free in the sense that the plant’s dynamics do not have to be known in advance. To this end, we propose and compare four tracking control algorithms which synergistically integrate a few machine learning tools to compromise between tracking a reference signal and optimizing a user-defined dynamic cost function. This is accomplished via two orchestrated control loops, one for tracking and one for optimization. Two control algorithms are designed and compared for the tracking loop. The first is based on reinforcement learning while the second is based on nonlinear threshold accepting technique. The optimization control loop is implemented using an artificial neural network. Each controller is trained offline before being integrated in the aggregate control system. Simulation results of three scenarios with various complexities demonstrated the effectiveness of the proposed control schemes in forcing the tracking error to converge while minimizing a pre-defined system-wide objective function.

scholarly journals Adaptive Fuzzy H∞ Robust Tracking Control for Nonlinear MIMO Systems

2015 ◽  
Vol 15 (1) ◽  
pp. 34-45
Author(s):  
Sanxiu Wang ◽  
Kexin Xing ◽  
Zhengchu Wang
Keyword(s):  
Tracking Control ◽  
Mimo Systems ◽  
Tracking Error ◽  
Approximation Error ◽  
Nonlinear Function ◽  
Robust Tracking ◽  
Robust Tracking Control ◽  
Fuzzy Logic Systems ◽  
Adaptive Fuzzy ◽  
Control Scheme

Abstract In this paper an adaptive fuzzy H∞ robust tracking control scheme is developed for a class of uncertain nonlinear Multi-Input and Multi-Output (MIMO) systems. Firstly, fuzzy logic systems are introduced to approximate the unknown nonlinear function of the system by an adaptive algorithm. Next, a H∞ robust compensator controller is employed to eliminate the effect of the approximation error and external disturbances. Consequently, a fuzzy adaptive robust controller is proposed, such that the tracking error of the resulting closed-loop system converges to zero and the tracking robustness performance can be guaranteed. The simulation results performed on a two-link robotic manipulator demonstrate the validity of the proposed control scheme.

scholarly journals Robust Tracking Control for Vehicle Lateral Dynamics with Uncertain Parameters and External Nonlinearities

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Huihui Pan ◽  
Yifu Zhang ◽  
Weichao Sun
Keyword(s):  
Tracking Control ◽  
Controller Design ◽  
Reference Signal ◽  
Dynamic Surface Control ◽  
Parameter Uncertainties ◽  
Robust Tracking Control ◽  
Sideslip Angle ◽  
Dynamic Surface ◽  
Control Laws ◽  
Yaw Rate

This paper focuses on the problem of tracking control for vehicle lateral dynamic systems and designs an adaptive robust controller (ARC) based on backstepping technology to improve vehicle handling and stability, in the presence of parameter uncertainties and external nonlinearities. The main target of controller design has two aspects: the first target is to control the sideslip angle as small as possible, and the second one is to keep the real yaw rate tracking the desired yaw rate. In order to compromise the two indexes, the desired sideslip angle is planned as a new reference signal, instead of the ideal “zero.” As a result, the designed controller not only accomplishes the control purposes mentioned above, but also effectively attenuates both the changes of vehicle mass and the variations of cornering stiffness. In addition, to overcome the problem of “explosion of complexity” caused by backstepping method in the traditional ARC design, the dynamic surface control (DSC) technique is used to estimate the derivative of the virtual control. Finally, a nonlinear vehicle model is employed as the design example to illustrate the effectiveness of the proposed control laws.

scholarly journals Adaptive fractional PID control of biped robots with time-delayed feedback

2019 ◽  
Vol 277 ◽  
pp. 01007 ◽  
Author(s):  
◽  
P Joel Perez ◽  
Jose P. Perez ◽  
Mayra Flores Guerrero ◽  
Ruben Perez P. ◽  
...  
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Fractional Order ◽  
Degrees Of Freedom ◽  
Tracking Error ◽  
Reference Signal ◽  
Biped Robot ◽  
Control Laws ◽  
Adaptive Neural Networks ◽  
Fractional Order Pid

This paper presents the application of Fractional Order Time- Delay adaptive neural networks to the trajectory tracking for chaos synchronization between Fractional Order delayed plant, reference and Fractional Order Time-Delay adaptive neural networks. The proposed new control scheme is applied via simulations to control of a 4-DOF Biped Robot [1]. The main methodologies, on which the approach is based, are Fractional Order PID the Fractional Order Lyapunov-Krasovskii functions methodology. The structure of the biped robot is designed with two degrees of freedom per leg, corresponding to the knee and hip joints. Since torso and ankle are not considered, it is obtained a 4-DOF system, and each leg, we try to force this biped robot to track a reference signal given by undamped Duffing equation. The tracking error is globally asymptotically stabilized by two control laws derived based on a Lyapunov-Krasovski functional.

Constrained Tracking Control by Gain-Scheduled Feedback With Optimal State Resets: A General Servo Problem and an Online Optimization Method

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Nobutaka Wada ◽  
Hidekazu Miyahara ◽  
Masami Saeki
Keyword(s):  
Tracking Control ◽  
Control Algorithm ◽  
Optimization Problem ◽  
Control Method ◽  
Actuator Saturation ◽  
Tracking Error ◽  
Reference Signal ◽  
Optimal Solution ◽  
Optimization Method ◽  
Experimental Result

In this paper, a tracking control problem for discrete-time linear systems with actuator saturation is addressed. The reference signal is assumed to be generated by an external dynamics. First, a design condition of a controller parameterized by a single scheduling parameter is introduced. The controller includes a servo compensator to achieve zero steady-state error. Then, a control algorithm that guarantees closed-loop stability and makes the tracking error converge to zero is given. In the control algorithm, the controller state as well as the scheduling parameter is updated online so that the tracking control performance is improved. Then, it is shown that the decision problem of the scheduling parameter and the controller state can be transformed into a convex optimization problem with respect to a scalar parameter. Based on this fact, we propose a numerically efficient algorithm for solving the optimization problem. Further, we propose a method of modifying the control algorithm so that the asymptotic tracking property is ensured even when the numerical error exists in the optimal solution. A numerical example and an experimental result are provided to illustrate effectiveness of the proposed control method.

scholarly journals Adaptive Fuzzy Tracking Control for a Permanent Magnet Synchronous Motor via Backstepping Approach

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Jinpeng Yu ◽  
Junwei Gao ◽  
Yumei Ma ◽  
Haisheng Yu
Keyword(s):  
Permanent Magnet ◽  
Tracking Control ◽  
Reference Model ◽  
Permanent Magnet Synchronous Motor ◽  
Tracking Error ◽  
Reference Signal ◽  
Small Neighborhood ◽  
Parameter Uncertainties ◽  
Fuzzy Logic Systems ◽  
Load Torque

The speed tracking control problem of permanent magnet synchronous motors with parameter uncertainties and load torque disturbance is addressed. Fuzzy logic systems are used to approximate nonlinearities, and an adaptive backstepping technique is employed to construct controllers. The proposed controller guarantees the tracking error convergence to a small neighborhood of the origin and achieves the good tracking performance. Simulation results clearly show that the proposed control scheme can track the position reference signal generated by a reference model successfully under parameter uncertainties and load torque disturbance without singularity and overparameterization.

Robust Tracking Control for a Class of Nonlinear Systems

2012 ◽  
Vol 479-481 ◽  
pp. 2161-2164
Author(s):  
Yang Yu ◽  
Wei Wang
Keyword(s):  
Nonlinear Systems ◽  
Tracking Control ◽  
Tracking Error ◽  
Reference Signal ◽  
Linear Matrix ◽  
Robust Tracking ◽  
Robust Tracking Control ◽  
Controlled System ◽  
Stabilization Control ◽  
S Model

This paper deals with the problem of fizzy robust tracking control for a class of nonlinear systems. The nonlinear system is approximated by T-S model, considering the modeling error. The tracking error of the controlled system following the reference signal is studied, and the tracking error’s exponential stability. The coherence of tracking control and stabilization control of the fuzzy systems is proved by using Lyapunov function theory combining with linear matrix inequalities (LMIs).Simulation results demonstrate the effectiveness of the proposed approach and conditions.

scholarly journals Fixed-Time Trajectory Tracking Control for Nonholonomic Mobile Robot Based on Visual Servoing

2021 ◽  
Author(s):  
OU Meiying ◽  
Haibin Sun ◽  
Zhenxing Zhang ◽  
Shengwei Gu
Keyword(s):  
Mobile Robot ◽  
Tracking Control ◽  
Visual Servoing ◽  
Tracking Error ◽  
Fixed Time ◽  
Camera Model ◽  
Trajectory Tracking Control ◽  
Control Laws ◽  
Time Control ◽  
Time Simulation

Abstract This paper aims to discuss fixed-time tracking control problem for a nonholonomic wheeled mobile robot based on visual servoing. At first, by making use of the pinhole camera model, the robot system model with uncalibrated camera parameters is given. Then, the tracking error system between the mobile robot and desired trajectory is proposed. Thirdly, on the basis of fixed-time control theory and Lyapunov stability analysis, fixed-time tracking control laws are proposed for the robot, which can make the robot achieve the desired value in a fixed time. Simulation results are given at the end.

scholarly journals A learning-based optimal tracking controller for continuous linear systems with unknown dynamics: Theory and case study

2020 ◽  
Vol 53 (5-6) ◽  
pp. 778-787
Author(s):  
Jingren Zhang ◽  
Qingfeng Wang ◽  
Tao Wang
Keyword(s):  
Reinforcement Learning ◽  
Control Problem ◽  
Tracking Control ◽  
Tracking Error ◽  
Infinite Horizon ◽  
Learning Method ◽  
Optimal Tracking ◽  
Optimal Tracking Control ◽  
Tracking Controller

In this article, a novel continuous-time optimal tracking controller is proposed for the single-input-single-output linear system with completely unknown dynamics. Unlike those existing solutions to the optimal tracking control problem, the proposed controller introduces an integral compensation to reduce the steady-state error and regulates the feedforward part simultaneously with the feedback part. An augmented system composed of the integral compensation, error dynamics, and desired trajectory is established to formulate the optimal tracking control problem. The input energy and tracking error of the optimal controller are minimized according to the objective function in the infinite horizon. With the application of reinforcement learning techniques, the proposed controller does not require any prior knowledge of the system drift or input dynamics. The integral reinforcement learning method is employed to approximate the Q-function and update the critic network on-line. And the actor network is updated with the deterministic learning method. The Lyapunov stability is proved under the persistence of excitation condition. A case study on a hydraulic loading system has shown the effectiveness of the proposed controller by simulation and experiment.

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