A Unified Design Approach to Repetitive Learning Control for Systems Subject to Fractional Uncertainties

2017 ◽  
Vol 140 (6) ◽  
Author(s):  
Mingxuan Sun ◽  
He Li ◽  
Yanwei Li
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Tracking Error ◽  
Estimation Method ◽  
Learning Control ◽  
Closed Loop System ◽  
Repetitive Learning ◽  
Context Of Learning ◽  
Asymptotical Convergence ◽  
Synthesis Approach

Fractional uncertainties are involved in many practical systems. Currently, there is a lack of research results about such general class of nonlinear systems in the context of learning control. This paper presents a Lyapunov-synthesis approach to repetitive learning control (RLC) being unified due to the use of the direct parametrization and adaptive bounding techniques. To effectively handle fractional uncertainties, the estimation method for such uncertainties is elaborated to facilitate the controller design and convergence analysis. Its novelty lies in the less requirement for the knowledge about the system undertaken. Unsaturated- and saturated-learning algorithms are, respectively, characterized by which both the boundedness of the variables in the closed-loop system undertaken and the asymptotical convergence of the tracking error are established. Experimental results are provided to verify the effectiveness of the presented learning control.

scholarly journals Robust H∞ Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions

2021 ◽  
Vol 26 (1) ◽  
pp. 21
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano ◽  
Nashwa Ahmad Kamal
Keyword(s):  
Design Methodology ◽  
Closed Loop ◽  
Complex Analysis ◽  
Controller Design ◽  
Filter Design ◽  
Design Procedure ◽  
Elliptic Functions ◽  
Loop System ◽  
Closed Loop System ◽  
Loop Shaping

In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO controller considering that elliptic functions have a double periodicity. The gain and phase margins of the closed-loop system can be selected appropriately with this new loop shaping design procedure. The loop shaping design methodology consists of implementing suitable filters to obtain a desired frequency response of the closed-loop system by selecting appropriate poles and zeros by the Abel theorem that are fundamental in the theory of the elliptic functions. The elliptic function properties are implemented to facilitate the loop shaping controller design along with their fundamental background and contributions from the complex analysis that are very useful in the automatic control field. Finally, apart from the filter design, a PID controller loop shaping synthesis is proposed implementing a similar design procedure as the first part of this study.

Backstepping Based Adaptive Control of Magnetic Levitation System

2013 ◽  
Vol 341-342 ◽  
pp. 945-948 ◽  
Author(s):  
Wei Zhou ◽  
Bao Bin Liu
Keyword(s):  
Parameter Uncertainty ◽  
Closed Loop ◽  
Controller Design ◽  
Magnetic Levitation ◽  
Adaptive Controller ◽  
Closed Loop System ◽  
Actual System ◽  
Levitation System ◽  
Magnetic Levitation System ◽  
Control Accuracy

In view of parameter uncertainty in the magnetic levitation system, the adaptive controller design problem is investigated for the system. Nonlinear adaptive controller based on backstepping is proposed for the design of the actual system with parameter uncertainty. The controller can estimate the uncertainty parameter online so as to improve control accuracy. Theoretical analysis shows that the closed-loop system is stable regardless of parameter uncertainty. Simulation results demonstrate the effectiveness of the presented method.

scholarly journals A stable proportional–proportional integral tracking controller with self-organizing fuzzy-tuned gains for parallel robots

2019 ◽  
Vol 16 (1) ◽  
pp. 172988141881995
Author(s):  
Francisco G Salas ◽  
Jorge Orrante-Sakanassi ◽  
Raymundo Juarez-del-Toro ◽  
Ricardo P Parada
Keyword(s):  
Stability Analysis ◽  
Performance Index ◽  
Closed Loop ◽  
Tracking Error ◽  
Parallel Robots ◽  
Control Loop ◽  
Closed Loop System ◽  
Proportional Integral ◽  
The Stability ◽  
Self Organizing

Parallel robots are nowadays used in many high-precision tasks. The dynamics of parallel robots is naturally more complex than the dynamics of serial robots, due to their kinematic structure composed by closed chains. In addition, their current high-precision applications demand the innovation of more effective and robust motion controllers. This has motivated researchers to propose novel and more robust controllers that can perform the motion control tasks of these manipulators. In this article, a two-loop proportional–proportional integral controller for trajectory tracking control of parallel robots is proposed. In the proposed scheme, the gains of the proportional integral control loop are constant, while the gains of the proportional control loop are online tuned by a novel self-organizing fuzzy algorithm. This algorithm generates a performance index of the overall controller based on the past and the current tracking error. Such a performance index is then used to modify some parameters of fuzzy membership functions, which are part of a fuzzy inference engine. This fuzzy engine receives, in turn, the tracking error as input and produces an increment (positive or negative) to the current gain. The stability analysis of the closed-loop system of the proposed controller applied to the model of a parallel manipulator is carried on, which results in the uniform ultimate boundedness of the solutions of the closed-loop system. Moreover, the stability analysis developed for proportional–proportional integral variable gains schemes is valid not only when using a self-organizing fuzzy algorithm for gain-tuning but also with other gain-tuning algorithms, only providing that the produced gains meet the criterion for boundedness of the solutions. Furthermore, the superior performance of the proposed controller is validated by numerical simulations of its application to the model of a planar three-degree-of-freedom parallel robot. The results of numerical simulations of a proportional integral derivative controller and a fuzzy-tuned proportional derivative controller applied to the model of the robot are also obtained for comparison purposes.

Finite-time dissipative control for networked control systems with hybrid-triggered scheme

2020 ◽  
pp. 014233122094650
Author(s):  
Qian Zhang ◽  
Huaicheng Yan ◽  
Shiming Chen ◽  
Xisheng Zhan ◽  
Xiaowei Jiang
Keyword(s):  
Control Systems ◽  
Finite Time ◽  
Closed Loop ◽  
Controller Design ◽  
Networked Control Systems ◽  
Sufficient Conditions ◽  
Networked Control ◽  
Closed Loop System ◽  
Network Resources ◽  
Dissipative Control

This paper is concerned with the problem of finite-time dissipative control for networked control systems by hybrid triggered scheme. In order to save network resources, a hybrid triggered scheme is proposed, which consists of time-triggered scheme and event-triggered scheme simultaneously. Firstly, sufficient conditions are derived to guarantee that the closed-loop system is finite-time bounded (FTBD) and [Formula: see text] dissipative. Secondly, the corresponding controller design approach is presented based on the derived conditions. Finally, a numerical example is presented to show the effectiveness of the proposed approach.

Speed Model Predictive Control Based on the Track Error Rate

2013 ◽  
Vol 336-338 ◽  
pp. 839-842
Author(s):  
Jin Huang ◽  
Cheng Zhi Yang ◽  
Ji Feng Wang
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Closed Loop ◽  
Tracking Error ◽  
Matlab Simulation ◽  
Closed Loop System ◽  
Index Function ◽  
Dynamical Characteristics ◽  
Simulation Results ◽  
Controlled Object

In order to make the controlled object have better dynamical characteristics, through introducing the differential item of error into optimal performance index function of tracking error, an improved algorithm of model predictive control is discussed in this paper. The theoretical analysis and Matlab simulation results show that it has better controlled quality and stronger robustness for closed-loop system.

scholarly journals Robust Synchronization Controller Design for a Class of Uncertain Fractional Order Chaotic Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Lin Wang ◽  
Chunzhi Yang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Closed Loop ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Closed Loop System ◽  
Synchronization Problem ◽  
Robust Synchronization ◽  
Lyapunov Stability Criterion ◽  
Theoretical Results

Synchronization problem for a class of uncertain fractional order chaotic systems is studied. Some fundamental lemmas are given to show the boundedness of a complicated infinite series which is produced by differentiating a quadratic Lyapunov function with fractional order. By using the fractional order extension of the Lyapunov stability criterion and the proposed lemma, stability of the closed-loop system is analyzed, and two sufficient conditions, which can enable the synchronization error to converge to zero asymptotically, are driven. Finally, an illustrative example is presented to confirm the proposed theoretical results.

scholarly journals Composite Immersion and Invariance Based Adaptive Attitude Control of Asteroid-Orbiting Spacecraft in Elliptic Orbit

2021 ◽  
Author(s):  
Keum W Lee ◽  
Sahjendra N Singh
Keyword(s):  
Attitude Control ◽  
Closed Loop ◽  
Tracking Error ◽  
Loop System ◽  
Closed Loop System ◽  
Immersion And Invariance ◽  
State Dependent ◽  
Dependent Vector ◽  
Yaw Angle ◽  
Angle Tracking

Abstract This paper proposes a new composite noncertainty-equivalence adaptive (CNCEA) control system for the attitude (roll, pitch, and yaw angle) control of a spacecraft in an orbit around a uniformly rotating asteroid based on the immersion and invariance (I&I) theory. For the design, it is assumed that the asteroid's gravitational parameters and the spacecraft's inertia matrix are not known. In contrast to certainty-equivalence adaptive (CEA) or noncertainty-equivalence adaptive (NCEA) systems, the CNCEA attitude control system's composite identifier uses the attitude angle tracking error, a nonlinear state-dependent vector function, and model prediction error for parameter estimation. The Lyapunov analysis shows that in the closed-loop system, the Euler angles asymptotically track the reference attitude trajectories. Interestingly, there exist two parameter error-dependent attractive manifolds, to which the closed-loop system's trajectories converge. Moreover, the composite identifier using two types of error signals provides stronger stability properties in the closed-loop system. Simulation results are presented for the attitude control of a spacecraft orbiting in the vicinity of the asteroid 433 Eros. These results show precise nadir pointing attitude regulation, despite uncertainties in the system.

Energetically-Optimal Discrete and Continuous Stabilization of the Rimless Wheel With Torso

2019 ◽  
Author(s):  
Wankun Sirichotiyakul ◽  
Aykut C. Satici ◽  
Eric S. Sanchez ◽  
Pranav A. Bhounsule
Keyword(s):  
Closed Loop ◽  
Estimation Method ◽  
Linear Quadratic Regulator ◽  
Region Of Attraction ◽  
Closed Loop System ◽  
Linear Quadratic ◽  
Walking Gait ◽  
Rimless Wheel ◽  
The Impact ◽  
Discrete Controller

Abstract In this work, we discuss the modeling, control, and implementation of a rimless wheel with torso. We derive and compare two control methodologies: a discrete-time controller (DT) that updates the controls once-per-step and a continuous-time controller (CT) that updates gains continuously. For the discrete controller, we use least-squares estimation method to approximate the Poincaré map on a certain section and use discrete-linear-quadratic-regulator (DQLR) to stabilize a (closed-form) linearization of this map. For the continuous controller, we introduce moving Poincaré sections and stabilize the transverse dynamics along these moving sections. For both controllers, we estimate the region of attraction of the closed-loop system using sum-of-squares methods. Analysis of the impact map yields a refinement of the controller that stabilizes a steady-state walking gait with minimal energy loss. We present both simulation and experimental results that support the validity of the proposed approaches. We find that the CT controller has a larger region of attraction and smoother stabilization as compared with the DT controller.

scholarly journals Computational Efficiency-Based Adaptive Tracking Control for Robotic Manipulators with Unknown Input Bouc–Wen Hysteresis

Sensors ◽  
2019 ◽  
Vol 19 (12) ◽  
pp. 2776 ◽  
Author(s):  
Kan Xie ◽  
Yue Lai ◽  
Weijun Li
Keyword(s):  
Computational Efficiency ◽  
Closed Loop ◽  
Tracking Error ◽  
Control Unit ◽  
Robotic Manipulators ◽  
Lyapunov Theory ◽  
Loop System ◽  
Unknown Input ◽  
Closed Loop System ◽  
Adaptive Tracking Control

In order to maintain robotic manipulators at a high level of performance, their controllers should be able to address nonlinearities in the closed-loop system, such as input nonlinearities. Meanwhile, computational efficiency is also required for real-time implementation. In this paper, an unknown input Bouc–Wen hysteresis control problem is investigated for robotic manipulators using adaptive control and a dynamical gain-based approach. The dynamics of hysteresis are modeled as an additional control unit in the closed-loop system and are integrated with the robotic manipulators. Two adaptive parameters are developed for improving the computational efficiency of the proposed control scheme, based on which the outputs of robotic manipulators are driven to track desired trajectories. Lyapunov theory is adopted to prove the effectiveness of the proposed method. Moreover, the tracking error is improved from ultimately bounded to asymptotic tracking compared to most of the existing results. This is of important significance to improve the control quality of robotic manipulators with unknown input Bouc–Wen hysteresis. Numerical examples including fixed-point and trajectory controls are provided to show the validity of our method.

Error-based output tracking for a one-dimensional wave equation with harmonic type disturbance

2020 ◽  
Vol 37 (4) ◽  
pp. 1447-1467
Author(s):  
Ziqing Tian ◽  
Xiao-Hui Wu
Keyword(s):  
Wave Equation ◽  
Closed Loop ◽  
Tracking Error ◽  
Difficult Case ◽  
Closed Loop System ◽  
One Dimensional ◽  
Output Tracking ◽  
Planning Approach ◽  
Uniformly Bounded ◽  
Dimensional Wave

Abstract In this paper, we consider output tracking for a one-dimensional wave equation, where the boundary disturbances are either collocated or non-collocated with control. The regulated output and the control are supposed to be non-collocated with control, which represents a difficult case for output tracking of PDEs. We apply the trajectory planning approach to design an observer, in terms of tracking error only, to estimate both states of the system and the exosystem from which the disturbances are produced. An error-based feedback control is proposed by solving a standard regulator equation. It is shown that (a) the closed-loop system is uniformly bounded whenever the exosystem is bounded; (b) when the disturbance is zero, the closed-loop is asymptotically stable; and (c) the tracking error converges to zero asymptotically as time goes to infinity. Numerical simulations are performed to validate the effectiveness of the proposed control.

Sign in / Sign up

Export Citation Format

Share Document