By Cornelius T. Leondes
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Extra info for Advances in Theory and Applications : System Identification and Adaptive Control, Pt 3 of 3
4s + 1. A similar interpretation applies to the denominator of block C, where ζ (t) = w(t) = cx + c 2 t, as in (7). The main function of block Β and the numerators of blocks C and D is to provide the additional controller structure and design parameters required for physical realizability and to achieve sufficiently rapid settling time for z^t) -» z^t) and ^ ( t ) -> z 2 1( t ) . In summary, the transfer-function interpretation, Fig. 4y + y = 0. As a result of this IMAP prefilter action, all nonideal behavior of y(t), including y(t) ~h Ysp» is quickly detected, quantified, and embodied in the composite error signal r|(t).
13. Control synthesis circuit for the idealized expression (88b). C. D. JOHNSON 46 u b = -rb(t)u, (88b) 3 which implies the mildly nonlinear synthesis circuit shown in Fig. 13. The necessary and sufficient condition for satisfaction of (86b) is rank[BN(t)l[F N(t)] + 6F(t)]H(t) = rank[BN(t)L (89a) which implies [F N(t) + 5F(t)]H(t) = BN(t)rF(t) (89b) for some matrix T F (t). At this point, it is convenient to separate F(t) = F N ( t ) + 5F(t) into the sum of another two matrices, as follows: F(t) = F 1 (t) + F 2 (t), (90) where the i-th row of Fj equals the i-th row of F, / / for all t that row has no uncertain perturbations ÔF^ associated with it, and otherwise equals zero.
Note that the estimate Ψ of the nonzero "unknown" Ψ is used in (131). The estimate Ψ may also play a role in expressions like (122) and (123), or appear as a term in the primary control law, depending on the specific nature of the primary control task(s) [see remarks below (123)]. The details of the procedure just outlined are illustrated by the following concrete example. E. SPECIFIC EXAMPLE O F THE [8C] ACCOMMODATION DESIGN METHOD (124)-(131) As a specific example of the [ÔC] accommodation method (124)—(131), we will consider the general second-order case = [A] +bu (132a) H Υ = Ψο Ν AW , (132b) where (A, c N ) = completely observable; c N = (ci, c 2 ); Ψ = unknown, piecewise constant, *0.
Advances in Theory and Applications : System Identification and Adaptive Control, Pt 3 of 3 by Cornelius T. Leondes