Prototype Angle-Domain Repetitive Control-Affine Parameterization Approach

2015 ◽  
Vol 137 (12) ◽  
Author(s):  
Perry Y. Li
Keyword(s):  
Robust Stability ◽  
Repetitive Control ◽  
Periodic Case ◽  
Nonminimum Phase ◽  
Periodic Disturbances ◽  
Compensator Design ◽  
The Stability ◽  
Control Methodology ◽  
Time Periodic ◽  
Model Approach

Angle-domain repetitive disturbances refer to disturbances that are periodic in a generic angle variable which is monotonically increasing with time but not uniformly. This paper extends the classical prototype repetitive control methodology for time periodic disturbances to this situation. Instead of using an internal model approach to derive the control, an affine parameterization approach is adopted which reduces the control design methodology to one of estimating and canceling the disturbance. While the resulting control architectures are similar to the classical time-domain periodic case, the stability conditions are different and depend on the choice of signal norm. This necessitates an alternate compensator design approach for the nonminimum phase terms. Robust stability is also considered in the L2 setting and an affine Q-filter concept is introduced to achieve robust stability.

Prototype Angle Domain Repetitive Control: Design and Robustness

2015 ◽  
Author(s):  
Perry Y. Li
Keyword(s):  
Design Methodology ◽  
Repetitive Control ◽  
Control Design ◽  
Periodic Case ◽  
Periodic Disturbances ◽  
Compensator Design ◽  
The Stability ◽  
Control Methodology ◽  
Time Periodic ◽  
Model Approach

Angle-domain repetitive disturbances refer to disturbances that are periodic in a generic angle variable which is monotonically increasing with time but not uniformly. This paper extends the classical prototype repetitive control methodology for time periodic disturbances to this situation. Instead of using an internal model approach to derive the control, an affine parameterization approach is adopted which reduces the control design methodology to one of estimating and canceling the disturbance. While the resulting control architectures are similar to the classical time-domain periodic case, the stability conditions are different and depend on the choice of signal norms. Compensator design for non-minimum phase plants also need to be modified. Robustness is also considered in the L2 setting and an affine Q-filter concept is introduced to achieve robust stability.

Repetitive Control for Rejection of Periodic Multiplicative Disturbances and Adaptive Identification of the Unknown Period

2004 ◽  
Author(s):  
Sandipan Mishra ◽  
Manabu Yamada ◽  
Masayoshi Tomizuka
Keyword(s):  
Control Algorithm ◽  
Closed Loop ◽  
Design Method ◽  
Repetitive Control ◽  
Adaptive Controller ◽  
Least Mean Square ◽  
Closed Loop System ◽  
Internal Model Principle ◽  
Periodic Disturbances ◽  
The Stability

Repetitive control has been used extensively for rejection of periodic disturbances, in systems that have to follow periodic trajectories. To date, most repetitive controllers have focused on rejection of additive periodic disturbances. This paper suggests the use of a repetitive control algorithm for rejection of periodic multiplicative disturbances. The first result is a simple design method of a new controller to reject the multiplicative disturbance effectively, provided that the period of the disturbance is known. This controller is based on the internal model principle and the design method consists of a simple norm condition. It is shown that this repetitive-type controller can reject the disturbance. The second result is an extension of the first one to the case that the period of the disturbance is unknown. A period estimator is added to the control system to identify the period of the multiplicative disturbance. The algorithm, consisting of an adaptive recursive least mean square method, is simple. It is shown that this adaptive controller can reject the disturbance with an uncertain period and guarantee the stability of the adaptive closed-loop system including the period estimator.

scholarly journals Stability Analysis of Distributed Order Fractional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
H. Saberi Najafi ◽  
A. Refahi Sheikhani ◽  
A. Ansari
Keyword(s):  
Stability Analysis ◽  
Characteristic Function ◽  
Differential Equations ◽  
Density Function ◽  
Robust Stability ◽  
Fractional Differential Equations ◽  
Stability Condition ◽  
Fractional Differential ◽  
The Stability ◽  
Distributed Order

We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function. In this sense, we discover a robust stability condition for these systems based on characteristic function and new inertia concept of a matrix with respect to the density function. Moreover, we check the stability of a distributed order fractional WINDMI system to illustrate the validity of proposed procedure.

scholarly journals Global Exponential Robust Stability of Static Interval Neural Networks with Time Delay in the Leakage Term

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Guiying Chen ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Leakage Term ◽  
Interval Neural Networks ◽  
Global Exponential Robust Stability ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

The stability of a class of static interval neural networks with time delay in the leakage term is investigated. By using the method ofM-matrix and the technique of delay differential inequality, we obtain some sufficient conditions ensuring the global exponential robust stability of the networks. The results in this paper extend the corresponding conclusions without leakage delay. An example is given to illustrate the effectiveness of the obtained results.

Optimization of the Robust Stability Limit for Multi-Cutter Turning Processes

2015 ◽  
Author(s):  
Marta J. Reith ◽  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Robust Stability ◽  
Optimal Parameter ◽  
Stability Limit ◽  
Boundary Function ◽  
Lower Envelope ◽  
Computation Method ◽  
Parameter Region ◽  
Dynamical Parameters ◽  
The Stability ◽  
Machining Parameter

Multi-cutter turning systems bear huge potential in increasing cutting performance. In this study we show that the stable parameter region can be extended by the optimal tuning of system parameters. The optimal parameter regions can be identified by means of stability charts. Since the stability boundaries are highly sensitive to the dynamical parameters of the machine tool, the reliable exploitation of the so-called stability pockets is limited. Still, the lower envelope of the stability lobes is an appropriate upper boundary function for optimization purposes with an objective function taken for maximal material removal rates. This lower envelope is computed by the Robust Stability Computation method presented in the paper. It is shown in this study, that according to theoretical results obtained for optimally tuned cutters, the safe stable machining parameter region can significantly be extended, which has also been validated by machining tests.

A New, Necessary and Sufficient Vertex Solution for Robust Stability Check of Unstructured Convex Combination Matrix Families

2015 ◽  
Author(s):  
Rama K. Yedavalli
Keyword(s):  
Robust Stability ◽  
Convex Combination ◽  
Convexity Property ◽  
Ecological Principles ◽  
Sign Structure ◽  
Previous Solution ◽  
Peer Community ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Complete Dependence

This paper revisits the problem of checking the robust stability of matrix families generated by ‘Unstructured Convex Combinations’ of user supplied or externally supplied Vertex Matrices. A previous solution given by the author for this problem involved complete dependence on the quantitative (eigenvalue information) of a set of special matrices labeled the Kronecker Nonsingularity (KN) matrices. In this solution, the ‘convexity’ property is not explicit and transparent, to the extent that, unfortunately, the accuracy of the solution itself is being questioned and not embraced by the peer community. To erase this unforunate and unwarranted image of this author (in this specific problem) in the minds of the peer community, in this paper, the author treads a new path to find a solution that brings out the convexity property in an explicit and understandable way. In the new solution presented in this paper, we combine the qualitative (sign) as well as quantitative (magnitude) information of these KN matrices and present a vertex solution in which the convexity property of the solution is transparent making it more elegant and accepatble to the peer community, than the previous solution. The new solution clearly underscores the importance of using the sign structure of a matrix in assessing the stability of a matrix. This new solution is made possible by the new insight provided by the qualitative (sign) stability/instability derived from ecological principles. Examples are given which clearly demonstrate effectiveness of the new, convexity based algorithm. It is hoped that this new solution will be embraced by the peer community.

Design of an Observer-Based Repetitive Control System to Reject Periodic Disturbance

2016 ◽  
Vol 25 (06) ◽  
pp. 1650061 ◽  
Author(s):  
Zhen Shao ◽  
Zhengrong Xiang
Keyword(s):  
Control System ◽  
Disturbance Rejection ◽  
Lyapunov Functional ◽  
Repetitive Control ◽  
Sufficient Condition ◽  
Two Dimensional ◽  
Periodic Disturbance ◽  
Repetitive Learning ◽  
The Stability ◽  
2D Model

This paper concerns the design of an observer-based repetitive control system (RCS) to improve the periodic disturbance rejection performance. The periodic disturbance is estimated by a repetitive learning based estimator (RLE) and rejected by incorporation of the estimation into a repetitive control (RC) input. Firstly, the configuration of the observer-based RCS with the RLE is described. Then, a continuous–discrete two-dimensional (2D) model is built to describe the RCS. By choosing an appropriate Lyapunov functional, a sufficient condition is proposed to guarantee the stability of the RCS. Finally, a numerical example is given to verify the effectiveness of the proposed method.

Enhanced Grey Variable Structure Control Methodology of Parallel-Connected DC-AC Inverters for Ultra-Precision Machining

2015 ◽  
Vol 661 ◽  
pp. 29-35
Author(s):  
En Chih Chang ◽  
Hung Liang Cheng ◽  
Chien Hsuan Chang ◽  
Jin Wei Liu ◽  
Chih Hsien Chuang ◽  
...  
Keyword(s):  
Output Voltage ◽  
Variable Structure Control ◽  
Variable Structure ◽  
Precision Machining ◽  
Structure Control ◽  
Highly Nonlinear ◽  
Ultra Precision ◽  
The Stability ◽  
Control Methodology ◽  
Voltage Harmonics

This paper develops an enhanced grey variable structure controlled DC-AC inverter in parallel, and is suitable for the application of ultra-precision machining (UPM). The enhanced grey variable structure control methodology consists of a nonlinear sliding function (NSF) and a grey model, GM(2,1). The NSF has finite system-state convergence time, and thus the AC output voltage regulation and balanced current-sharing among the parallel modules can be achieved. However, once the loading of the UPM is a highly nonlinear condition, the chatter still exists in NSF. The chatter may cause heat losses and high voltage harmonics in parallel-connected DC-AC inverter output, and thus deteriorates the stability and reliability of the UPM. To eliminate the chatter, the control gains of the NSF can be adjusted by the use of the GM(2,1) under system uncertainty bounds are overestimated. With the enhanced methodology, the parallel-connected DC-AC inverter yields a high-quality AC output voltage with low voltage harmonics and fast dynamic response under highly nonlinear loading, thus achieving the stability and reliability of the UPM. Experimental results are performed to demonstrate the enhanced methodology.

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