By Torkel Glad, Lennart Ljung
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Additional info for Control Theory: Multivariable and Nonlinear Methods
By the pole polynomial we mean the characteristic polynomial for the A-matrix: det('xI - A). The order of the system is thus equal to the number of poles (counted with multiplicity). '" of Poles From the Transfer Function Matrix realize a multi variable system, G (s ), in minimal state space form may be laborious. Therefore, it would be convenient if the poles could be calculated directly from G(s). In the 8180 case this is simple: The poles are the zeros of the denominator polynomial all cancellations between numerator and denominator).
15) is computed. A state space representation that is both controllable and observable is said to be a minimal realization of the system. There is then no other state representation with lower dimension of the state vector that realizes the same input-output relationship. 4). We see that a mode Xi with corresponding row vector Bi = 0 is not influenced at all by the input. If any row in B is zero for a system given in diagonal form, the system is thus not controllable. We then speak of the uncontrollable modes as the state variables Xi, with associated eigenvalue Ai, corresponding to the rows with Bi = O.
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. 10) The first term in the right hand side then represents the cooling due to th( inflow of cold water (normally, To; ::; To, so this will give the decrease 0 temperature).
Control Theory: Multivariable and Nonlinear Methods by Torkel Glad, Lennart Ljung