scholarly journals Pattern-Moving-Based Partial Form Dynamic Linearization Model Free Adaptive Control for a Class of Nonlinear Systems

Actuators ◽  
2021 ◽  
Vol 10 (9) ◽  
pp. 223
Author(s):  
Xiangquan Li ◽  
Zhengguang Xu
Keyword(s):  
Adaptive Control ◽  
External Disturbance ◽  
Tracking Error ◽  
Estimation Algorithm ◽  
Contraction Mapping Principle ◽  
Pattern Class ◽  
Model Free ◽  
Partial Form ◽  
Zero Sum ◽  
Time Systems

This work addresses a pattern-moving-based partial form dynamic linearization model free adaptive control (P-PFDL-MFAC) scheme and illustrates the bounded convergence of its tracking error for a class of unknown nonaffine nonlinear discrete-time systems. The concept of pattern moving is to take the pattern class of the system output condition as a dynamic operation variable, and the control purpose is to ensure that the system outputs belong to a certain pattern class or some desired pattern classes. The P-PFDL-MFAC scheme mainly includes a modified tracking control law, a deviation estimation algorithm and a pseudo-gradient (PG) vector estimation algorithm. The classification-metric deviation is considered as an external disturbance, which is caused by the process of establishing the pattern-moving-based system dynamics description, and an improved cost function is proposed from the perspective of a two-player zero-sum game (TP-ZSG). The bounded convergence of the tracking error is rigorously proven by the contraction mapping principle, and the validity of the theoretical results is verified by simulation examples.

Model-free adaptive PID control for nonlinear discrete-time systems

2020 ◽  
Vol 42 (10) ◽  
pp. 1797-1807 ◽  
Author(s):  
Shuhua Zhang ◽  
Ronghu Chi
Keyword(s):  
Discrete Time ◽  
Mathematical Analysis ◽  
Pid Control ◽  
Contraction Mapping Principle ◽  
Unknown Parameters ◽  
Model Free ◽  
Discrete Time Systems ◽  
Gradient Parameter ◽  
Adaptive Pid Control ◽  
Time Systems

This work explores a model-free adaptive PID (MFA-PID) control for nonlinear discrete-time systems with rigorous mathematical analysis under a data-driven framework. An improved compact form dynamic linearization (iCFDL) is proposed to transfer the original nonlinear system into an affined linear data model including a nonlinear residual term. Both a time-difference estimator and a gradient parameter estimator are designed to estimate the nonlinear residual uncertainties and the unknown parameters in the iCFDL model. Subsequently, a novel improved CFDL based MFA-PID (iCFDL-MFA-PID) control is proposed by incorporating these two estimators. The results are extended by the use of improved partial format dynamic linearization (iPFDL) and full format dynamic linearization (iFFDL). The theoretical results are shown using contraction mapping principle-based mathematical analysis, as well as simulations.

The model-free adaptive cross-coupled control for two-dimensional linear motor

2019 ◽  
Vol 42 (5) ◽  
pp. 1059-1069
Author(s):  
Baolin Zhang ◽  
Rongmin Cao ◽  
Zhongsheng Hou
Keyword(s):  
Adaptive Control ◽  
Real Time ◽  
Error Estimation ◽  
Tracking Error ◽  
Estimation Method ◽  
Linear Motor ◽  
Experimental Comparison ◽  
Contour Error ◽  
Two Dimensional ◽  
Model Free

In order to improve the contour error accuracy of two-dimensional linear motor, an improved cross-coupled control (CCC) scheme combining real-time contour error estimation and model-free adaptive control (MFAC) is proposed. The real-time contour error estimation method is based on CCC theory and coordinate transformation idea. It can accurately determine the contour error point of regular contour and avoid the influence of tracking error on the contour error. At the same time, for the design of two-axis error controller, only the input and output data generated by two-dimensional linear motor in reciprocating motion are used to design a multiple input multiple output-model-free adaptive control (MIMO-MFAC) algorithm, this algorithm avoids the dependence on accurate mathematical model and reduces the control difficulty. The experimental comparison showed that the proposed method improves the system tracking accuracy and contour accuracy, and verifies the proposed method correctness and effectiveness.

scholarly journals Model-Free Adaptive Control for Unknown Nonlinear Zero-Sum Differential Game

2018 ◽  
Vol 48 (5) ◽  
pp. 1633-1646 ◽  
Author(s):  
Xiangnan Zhong ◽  
Haibo He ◽  
Ding Wang ◽  
Zhen Ni
Keyword(s):  
Adaptive Control ◽  
Differential Game ◽  
Model Free ◽  
Zero Sum

Towards an Adaptive Control Concept for Unknown Nonlinear MIMO Systems

2018 ◽  
Author(s):  
Elmira Madadi ◽  
Dirk Söffker
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Control Method ◽  
Mimo Systems ◽  
Tracking Error ◽  
Underlying Structure ◽  
Unknown Parameters ◽  
Modified Model ◽  
Model Free ◽  
Model Free Control

The design of an accurate model often appears as the most challenging tasks for control engineers especially focusing to the control of nonlinear systems with unknown parameters or effects to be identified in parallel. For this reason, development of model-free control methods is of increasing importance. The class of model-free control approaches is defined by the non-use of any knowledge about the underlying structure and/or related parameters of the dynamical system. Therefore the major criteria to evaluate model-free control performance are aspects regarding robustness against unknown inputs and disturbances to achieve a suitable tracking performance including ensuring stability. Consequently it is assumed that the system plant model to be controlled is unknown, only the inputs and outputs are used as measurements. In this contribution a modified model-free adaptive approach is given as the extended version of existing model-free adaptive control to improve the performance according to the tracking error at each sample time. Using modified model-free adaptive controller, the control goal can be achieved efficiently without an individual control design process for different kinds unknown nonlinear systems. The main contribution of this paper is to extend the modified model-free adaptive control method to unknown nonlinear multi-input multi-output (MIMO) systems. A numerical example is shown to demonstrate the successful application and performance of this method.

scholarly journals Data-Driven Model-Free Adaptive Control of Particle Quality in Drug Development Phase of Spray Fluidized-Bed Granulation Process

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-17 ◽  
Author(s):  
Zhengsong Wang ◽  
Dakuo He ◽  
Xu Zhu ◽  
Jiahuan Luo ◽  
Yu Liang ◽  
...  
Keyword(s):  
Fuzzy Logic ◽  
Adaptive Control ◽  
Drug Development ◽  
Fluidized Bed ◽  
Tracking Error ◽  
Data Driven ◽  
Stability And Convergence ◽  
Development Phase ◽  
Granulation Process ◽  
Model Free

A novel data-driven model-free adaptive control (DDMFAC) approach is first proposed by combining the advantages of model-free adaptive control (MFAC) and data-driven optimal iterative learning control (DDOILC), and then its stability and convergence analysis is given to prove algorithm stability and asymptotical convergence of tracking error. Besides, the parameters of presented approach are adaptively adjusted with fuzzy logic to determine the occupied proportions of MFAC and DDOILC according to their different control performances in different control stages. Lastly, the proposed fuzzy DDMFAC (FDDMFAC) approach is applied to the control of particle quality in drug development phase of spray fluidized-bed granulation process (SFBGP), and its control effect is compared with MFAC and DDOILC and their fuzzy forms, in which the parameters of MFAC and DDOILC are adaptively adjusted with fuzzy logic. The effectiveness of the presented FDDMFAC approach is verified by a series of simulations.

Multi-Motor Synchronization of Multi-Wire Saw Based on Model-Free Adaptive Control

2009 ◽  
Vol 69-70 ◽  
pp. 660-664 ◽  
Author(s):  
Jin Jiang ◽  
Y.X. Dai ◽  
Y.B. Zhang ◽  
R. Tang ◽  
Wan Li Xiong
Keyword(s):  
Adaptive Control ◽  
Control Structure ◽  
Estimation Algorithm ◽  
System Model ◽  
Overall Design ◽  
Model Free ◽  
Wire Saw ◽  
Parameter Estimation Algorithm ◽  
On Line ◽  
Similar Dynamic

Aimed at the problem of multi-motor synchronization in multi-wire saw, Strategy based on model-free adaptive control (MFAC), which has some characteristics such as without accurate system model, without system identification and without complicated manual tuning, is produced. MFAC is based directly on pseudo-partial-derivatives (PPD) derived on-line from the input and output data of the system using a novel parameter estimation algorithm. It is suitable for multi-wire saw in such a complex system which is nonlinearity, strong interference and strong coupling. Overall design of multi-wire saw is analyzed. Control structure of multi-motor is given. Motion model of multi-motor synchronization is established. To speed of main motor for reference, supply spool motor and collect spool motor, which have similar dynamic characteristics with main motor, are adjusted adaptively to follow operation of main motor, and synchronization motion is ensured. The prototype experiments show that the method used is right and feasible.

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