By Efim N. Rosenwasser Dr. rer. nat. Dr. Eng., Bernhard P. Lampe Dr. rer. nat. Dr. Eng. (auth.)
ISBN-10: 1846284317
ISBN-13: 9781846284311
ISBN-10: 1846284325
ISBN-13: 9781846284328
The move functionality method is widespread in classical regulate idea for its effortless dealing with and actual that means. even supposing using move capabilities is well-established for linear time-invariant platforms, it isn't compatible for non-stationary platforms between that are sampled-data structures and approaches with periodically various coefficients. Computer-controlled continuous-time procedures are a vital subset of periodic sampled-data platforms which aren't treatable utilizing usual move functions.
Having demonstrated the facility of the parametric move functionality to unravel this challenge for single-input, single-output structures in past paintings, the authors expand those tools, which comprise time-dependence, to the belief of the parametric move matrix in a whole exposition of research and layout tools for multiple-input, multiple-output (MIMO) sampled-data systems.
Multivariable Computer-controlled Systems is split into 3 parts:
• initial algebraic fabric describing the demonstrated basics of polynomial and rational matrices worthwhile for the certainty of later chapters.
• keep watch over difficulties, very important of their personal correct yet which actually have a monstrous relating what follows (eigenvalue project and using z- and zeta-transforms in discrete systems).
• Frequency equipment for the research of MIMO sampled-data structures (parametric discrete-time versions; balance; stochastic equipment; H2 optimization and L2 design).
Appendices overlaying simple mathematical formulae and the outline of 2 MATLAB® toolboxes around out this self-contained consultant to multivariable keep watch over systems.
Of exact curiosity to researchers in computerized keep an eye on and to improvement engineers operating with complicated keep watch over know-how, Multivariable Computer-controlled Systems also will curiosity mathematical regulate theorists and graduate scholars learning complex tools of computer-based control.
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Additional info for Multivariable Computer-controlled Systems: A Transfer Function Approach
Example text
51) , Dρ (λ) = a1 (λ)a2 (λ) · · · aρ (λ) . 50) are used, then these relations can be written in the form D1 (λ) = a1 (λ), D2 (λ) = a1 (λ)a2 (λ), ... D1 (λ) = h1 (λ), D2 (λ) = h21 (λ)h2 (λ), Dρ (λ) = ... hρ1 (λ)hρ−1 (λ) · · · hρ (λ) . 2 5. 53) where all numbers λi are different. 51) that every invariant polynomial ai (λ) permits a factorisation of the form ai (λ) = (λ − λ1 )µ1i · · · (λ − λq )µqi , (i = 1, . . 54) with 0 ≤ µpi ≤ µp,i+1 ≤ νpρ , (p = 1, . . , q) . 54) are called elementary divisors of the polynomial matrix A(λ) in the field C.
An−1 B . 89) The matrix Qc (A, B) is named controllability matrix of the pair (A, B). Some statements regarding the controllability of pairs are listed now: a) If the pair (A, B) is controllable, and the n × n matrix R is non-singular, then also the pair (A1 , B1 ) with A1 = RAR−1 , B1 = RB is controllable. 89) we obtain Qc (A1 , B1 ) = RB RAB . . RAn−1 B == RQc (A, B) , from which follows rank Qc (A1 , B1 ) = rank Qc (A, B) = n, because R is non-singular. 53. e. AL = LA. Then the following statements are true: 1.
8. The above stated irreducibility criteria will be formulated alternatively. 41. A necessary and sufficient condition for the pair (a(λ), b(λ)) to be irreducible, is the existence of a pair (αl (λ), βl (λ)), such that the matrix Ql (λ) = a(λ) b(λ) βl (λ) αl (λ) becomes unimodular. For the pair [a(λ), c(λ)] to be irreducible, it is necessary and sufficient that there exists a pair [αr (λ), βr (λ)], such that the matrix Qr (λ) = αr (λ) c(λ) βr (λ) a(λ) becomes unimodular. 9. 42. Necessary and sufficient for the irreducibility of the pair (a(λ), b(λ)), with the n × n and n × m polynomial matrices a(λ) and b(λ), is the condition rank Rh (λi ) = rank a(λi ) b(λi ) = n , (i = 1, .
Multivariable Computer-controlled Systems: A Transfer Function Approach by Efim N. Rosenwasser Dr. rer. nat. Dr. Eng., Bernhard P. Lampe Dr. rer. nat. Dr. Eng. (auth.)
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