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By Torkel Glad, Lennart Ljung

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Extra resources for Control Theory: Multivariable and Nonlinear Methods

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20) £=0 The interpretation is completely analogous to the continuous time case. 3). Everything concerning continuous systems also applies to discrete time systems if the Laplace table is exchanged for the Z-transform table. -;'00 = z-+l lim(z - l)Y(z) if the left hand side exists. 6 Discrete Time Systems 39 Transfer Operators The transfer operator is considerably more straightforward in discrete time than in continuous time. u(t) = G(q)u(t) £=0 f=O The transfer operator has, formally, been obtained by exchanging z for q in the definition of the transfer function matrix.

Its behavior can be described in the following simplified way. The lower part is the "cold part" into which water flows with temperature Te,. The flow is fe (m 3 froin). The upper part is the "hot part" with input water temperature TH; and flow f H. When the flows "meet" (in separate pipes), the hot water heats the cold water to temperature Te. At the same time it is itself cooled to the temperature TH. , Til and Te- By setting up the heat balance in the cold part we find that the temperature changes according to dTe Ve- ::::; fe(To.

Everything concerning continuous systems also applies to discrete time systems if the Laplace table is exchanged for the Z-transform table. -;'00 = z-+l lim(z - l)Y(z) if the left hand side exists. 6 Discrete Time Systems 39 Transfer Operators The transfer operator is considerably more straightforward in discrete time than in continuous time. u(t) = G(q)u(t) £=0 f=O The transfer operator has, formally, been obtained by exchanging z for q in the definition of the transfer function matrix. Other than that, the same comments apply as for the continuous time case.

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