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Consider the controller form of a single-input single-output linear system. 1 ... ... i(t) = x(t) + u(t) 1 -a0 -ai -An-1) 1 ... y(t) = (Bo B1 Bn-1) x(t) ... (a) Write down the transfer function H(s) = N(s) D(s) where N(s) is the numerator and D(s) is the denom- inator. (b) Suppose N(s) and D(s) are coprime, i.e., don't have a common factor other than 1, in which case the controller form is a minimal realization. Validate that D(s) = poles of a transfer function and eigenvalues of its associated realization are identical if the realization is minimal. det(sI – A). Discuss whether

Consider the controller form of a single-input single-output linear system. 1 ... ... i(t) = x(t) + u(t) 1 -a0 -ai -An-1) 1 ... y(t) = (Bo B1 Bn-1) x(t) ... (a) Write down the transfer function H(s) = N(s) D(s) where N(s) is the numerator and D(s) is the denom- inator. (b) Suppose N(s) and D(s) are coprime, i.e., don't have a common factor other than 1, in which case the controller form is a minimal realization. Validate that D(s) = poles of a transfer function and eigenvalues of its associated realization are identical if the realization is minimal. det(sI – A). Discuss whether

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the controller form of a single-input single-output linear system. 1 i(t) = x(t) + u(t) 1 -a0 -ai -an-1/ 1 y(t) = (Bo B1 Bn-1) x(t) (a) Write down the transfer function H(s) N(s) D(s) where N(s) is the numerator and D(s) is the denom- inator. (b) Suppose N(s) and D(s) are coprime, i.e., don't have a common factor other than 1, in which case the controller form is a minimal realization. Validate that D(s) = det(sI – A). Discuss whether poles of a transfer function and eigenvalues of its associated realization are identical if the realization is minimal.
Transcribed Image Text:Consider the controller form of a single-input single-output linear system. 1 i(t) = x(t) + u(t) 1 -a0 -ai -an-1/ 1 y(t) = (Bo B1 Bn-1) x(t) (a) Write down the transfer function H(s) N(s) D(s) where N(s) is the numerator and D(s) is the denom- inator. (b) Suppose N(s) and D(s) are coprime, i.e., don't have a common factor other than 1, in which case the controller form is a minimal realization. Validate that D(s) = det(sI – A). Discuss whether poles of a transfer function and eigenvalues of its associated realization are identical if the realization is minimal.
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