Optimal Feedback Design of Delayed Linear Systems With Experimental Validation

2003 ◽  
Author(s):  
Jie Sheng ◽  
J. Q. Sun
Keyword(s):  
Linear Systems ◽  
Experimental Validation ◽  
System Response ◽  
Discretization Method ◽  
Feedback Controls ◽  
Stability Boundaries ◽  
Absolute Value ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
And Performance

This paper presents an application of semi-discretization method to stability analysis of feedback controls of linear systems with time delay. The method develops a mapping of the system response in a finite dimensional state space. Minimization of the largest absolute value of the eigenvalues of the mapping leads to optimal control gains. Experimental validation is presented to demonstrate the method. We have found that the semi-discretization method provides accurate stability boundaries and performance contours in the parametric space of control gains, and offers an alternative to the classic design approaches of feedback controls.

Feedback Controls and Optimal Gain Design of Delayed Periodic Linear Systems

2005 ◽  
Vol 11 (2) ◽  
pp. 277-294 ◽  
Author(s):  
Jie Sheng ◽  
J. Q. Sun
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
System Response ◽  
Discretization Method ◽  
Feedback Controls ◽  
Periodic Linear ◽  
Dimensional State Space ◽  
And Performance ◽  
The Stability ◽  
Time Invariant

In this paper we present an application of a semi-discretization method to the stability analysis of PID feedback controls of linear systems with time delay. The method develops a mapping of the system response in a finite-dimensional state space. Minimization of the largest absolute value of the eigenvalues of the mapping leads to optimal control gains. Numerical examples of both time-invariant and periodic linear systems are presented to demonstrate the method. The tracking control problem of linear systems with time delay is also discussed. We have found that the semi-discretization method provides accurate stability boundaries and performance contours in the parametric space of control gains, and offers an alternative to the classic design approaches of feedback controls.

Optimal Feedback Controls of Linear Systems With Time Delay

2003 ◽  
Author(s):  
Jie Sheng ◽  
Ozer Elbeyli ◽  
J. Q. Sun
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
System Response ◽  
Feedback Controls ◽  
Optimal Feedback ◽  
Periodic Linear ◽  
Dimensional State Space ◽  
And Performance ◽  
The Stability ◽  
Time Invariant

This paper presents an application of semi-discretization method to stability analysis and optimal design of PID feedback controls of time invariant and periodic linear systems with time delay. The method develops a mapping of the system response in a finite dimensional state space, and produces the stability boundaries and performance contours in the parametric space of control gains. Optimal feedback gains that minimize the largest absolute value of the eigenvalues of the mapping have been studied for different cases where the performance contours are either closed or open.

Optimal Cutting Parameters for Precision Machining Process

2010 ◽  
Vol 431-432 ◽  
pp. 381-384
Author(s):  
Qing Hua Song ◽  
Wei Xiao Tang ◽  
Xing Ai ◽  
Yi Wan
Keyword(s):  
Cutting Parameters ◽  
Machining Process ◽  
Precision Machining ◽  
Depth Of Cut ◽  
Stable Limit ◽  
Finite Dimensional ◽  
Stability Chart ◽  
Dimensional State Space ◽  
And Performance ◽  
Optimal Cutting Parameters

Semi-discretization method is applied to construct stability chart and performance contour in the parametric space for milling processes. The method creates a mapping of the system responses in a finite dimensional state space. Based on the discipline of that, the smaller the largest absolute value (μmax) of the characteristic multipliers of the mapping is, the faster the system converges to zero, minimization of μmax leads to optimal stable limit. The optimal limits are obtained by using stability chart and performance contours. Additional, a novel analytical method for selection of optimal depth of cut (axial depth of cut) is presented. An example of 2-DOF down-milling model is employed to demonstrate the method. It is shown that the spindle speeds corresponding to the optimal depths of cut locate the left side of the resonant spindle speeds, and the optimal cutting parameters pair (spindle speed and depth of cut) can be used to offer high finishing accuracy in precision machining.

Robustness Analysis of Optimally Designed Feedback Control of Linear Periodic Systems With Time-Delay

2007 ◽  
Author(s):  
Jie Zhang ◽  
Jian-Qiao Sun
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Robustness Analysis ◽  
System Response ◽  
Discretization Method ◽  
Robust Analysis ◽  
Periodic Linear ◽  
Dimensional State Space ◽  
The Stability ◽  
Linear Periodic Systems

In this paper, we present an application of a semi-discretization method to the stability and robust analysis of optimally designed PID feedback control of a periodic linear system with time delay. The semi-discretization method uses a mapping of the system response in a finite-dimensional state space. Minimization of the largest absolute value of the eigenvalues of the mapping leads to optimal control gains. The robust analysis examines the stability region of system parameters with modeling errors when the control gains are set to be the optimal ones. Extensive numerical examples of stability regions are presented in the paper.

Relation of Statistically Significant, Abnormal, and Typical WAIS-R VIQ-PIQ Discrepancies to Full Scale IQs

2000 ◽  
Vol 16 (2) ◽  
pp. 107-114 ◽  
Author(s):  
Louis M. Hsu ◽  
Judy Hayman ◽  
Judith Koch ◽  
Debbie Mandell
Keyword(s):  
Graphical Method ◽  
The United States ◽  
Full Scale ◽  
True Score ◽  
Absolute Value ◽  
Normative Population ◽  
The Us ◽  
The Mean ◽  
And Performance ◽  
Quadratic Models

Summary: In the United States' normative population for the WAIS-R, differences (Ds) between persons' verbal and performance IQs (VIQs and PIQs) tend to increase with an increase in full scale IQs (FSIQs). This suggests that norm-referenced interpretations of Ds should take FSIQs into account. Two new graphs are presented to facilitate this type of interpretation. One of these graphs estimates the mean of absolute values of D (called typical D) at each FSIQ level of the US normative population. The other graph estimates the absolute value of D that is exceeded only 5% of the time (called abnormal D) at each FSIQ level of this population. A graph for the identification of conventional “statistically significant Ds” (also called “reliable Ds”) is also presented. A reliable D is defined in the context of classical true score theory as an absolute D that is unlikely (p < .05) to be exceeded by a person whose true VIQ and PIQ are equal. As conventionally defined reliable Ds do not depend on the FSIQ. The graphs of typical and abnormal Ds are based on quadratic models of the relation of sizes of Ds to FSIQs. These models are generalizations of models described in Hsu (1996) . The new graphical method of identifying Abnormal Ds is compared to the conventional Payne-Jones method of identifying these Ds. Implications of the three juxtaposed graphs for the interpretation of VIQ-PIQ differences are discussed.

scholarly journals Characteristic phenomena in combustion

1997 ◽  
Vol 1 (2) ◽  
pp. 147-159
Author(s):  
Dirk Meinköhn
Keyword(s):  
State Space ◽  
Reaction Diffusion ◽  
Stationary Solutions ◽  
The State ◽  
State Variable ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Singularity Order ◽  
The Relationship ◽  
Stable Stationary Solutions

For the case of a reaction–diffusion system, the stationary states may be represented by means of a state surface in a finite-dimensional state space. In the simplest example of a single semi-linear model equation given. in terms of a Fredholm operator, and under the assumption of a centre of symmetry, the state space is spanned by a single state variable and a number of independent control parameters, whereby the singularities in the set of stationary solutions are necessarily of the cuspoid type. Certain singularities among them represent critical states in that they form the boundaries of sheets of regular stable stationary solutions. Critical solutions provide ignition and extinction criteria, and thus are of particular physical interest. It is shown how a surface may be derived which is below the state surface at any location in state space. Its contours comprise singularities which correspond to similar singularities in the contours of the state surface, i.e., which are of the same singularity order. The relationship between corresponding singularities is in terms of lower bounds with respect to a certain distinguished control parameter associated with the name of Frank-Kamenetzkii.

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