Stability Analysis for Linear Repetitive Process
Industrial processes such as long-wall coal cutting and me- tal rolling, together with certain areas of 2D signal and image processing, exhibit a repetitive, or multipass struc- ture characterized by a series of sweeps of passes through a known set of dynamics. The output, or pass profile, produced on each pass explicitly contributes to that produced on the text. This interpass interaction can lead to the growth of oscillations, and hence a form of instability, in the se- quence of pass profiles which require control strategies that explicitly incorporate the essential repetitive struc- ture of the process in their decision making. This monograph is unique in developing the new techniques necessary for sy- stematic control systems design in the form of a stability theory and computationally feasible stability tests based on finite simulations and polynomial analysis. Its development requires a basic knowledge of linear frequency domain and state-space theory and a knowledge of basic functional ana- lysis would be beneficial. The text is aimed at researchers in the area of control and systems theory and should also be of interest to those working in the related area of signal and image processing.
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GRAPHICAL AND ALGEBRAIC STABILITY TESTS
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Stability analysis for linear repetitive processes
Eric Thomas Alexander Rogers,David H. Owens
Widok krótkiego opisu - 1992
2D linear systems 2D Lyapunov equation 2D transfer-function matrix algorithms applied aQ is stable associated conventional linear asymptotic stability BIBO stability bounded characteristic polynomial cited reference closed-loop stability coefficients companion matrix complex plane condition for stability consider constant pass length conventional linear systems corollary defined delay differential systems denotes derived conventional linear differential and discrete discrete non-unit memory eigenvalues equivalent exists extended linear repetitive feedback control scheme following result follows immediately Further Gj(s holds interpass smoothing lemma limit profile linear repetitive process memory linear repetitive memoryless model of example modulus strictly less natural generalisation necessary and sufficient non-unit memory linear Note particular pass profile polynomial positive definite previous pass problem process of example Proof real scalar Roesser model Rogers and Owens SISO stability margins stability tests stability theory state-space model step response sufficient condition Suppose symmetric matrix theorem unit circle University of Strathclyde yields