By Nikolai Michailovich Filatov, Heinz Unbehauen
This monograph demonstrates how the functionality of assorted recognized adaptive controllers might be superior considerably utilizing the twin impact. The transformations to include twin keep an eye on are learned individually and independently of the most adaptive controller with no complicating the algorithms. a brand new bicriterial technique for twin regulate is constructed and utilized to varied sorts of renowned linear and nonlinear adaptive controllers. functional functions of the designed controllers to a number of real-time difficulties are offered. This monograph is the 1st booklet delivering a whole exposition at the twin regulate challenge from the inception within the early Sixties to the current cutting-edge aiming at scholars and researchers in adaptive keep an eye on in addition to layout engineers in undefined.
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Extra info for Adaptive dual control: theory and applications
3. Design of the Dual Version of the GMV controller 43 where the orders of the polynomials L (with parameters li ) and G (with parameters g i ) are nL = d − 1 and nG = n − 1 , respectively. Substituting eq. 47) into eq. 51) Ξ (z ) is the z-transform of the filtered disturbance ξ (k ) with variance σ 2 . The orders ξ of the polynomials F ( z −1 ) and H ( z −1 ) are nF = nB + d − 1 and nH = nC + nR with h0 = −1 . First, the case of C ( z −1 ) = 1 is considered for controller synthesis; and, afterwards, the convergence of the desired dual controller is shown for the case of C ( z −1 ) ≠ 1 .
Method is based on approximations of the main cost function and the introduction of an uncertainty index as a second criterion. 3. 1. Classification of Adaptive Controllers 19 Especially in case of the CE controller the unknown system state x (k ) is replaced by its estimate xˆ (k ) u(k ) = ϕ k [ xˆ (k )] . 2) The CE controller is the optimal solution of the LQG control problem (Bar-Shalom and Tse, 1976). The notion of separation is more general than the CE assumption and is given below. 3) where the function ψ k differs from the optimal deterministic feedback ϕ k .
Simulation results for the adaptive dual GMV controller (d=4). 3. GMV Controller for the Plant with Time Delay d=7 Now the same plant as described above by eq. 38) is considered but with a larger time delay (d=7). Again, the adaptive dual GMV controller, according to eqs. 62), will be applied and compared to the adaptive standard GMV controller based on the CE assumption. 1052 z − 2 . The plant parameters are assumed to be unknown and constant. 1z −2 . For the control signal, upper and lower limits of ±500 have again been chosen.
Adaptive dual control: theory and applications by Nikolai Michailovich Filatov, Heinz Unbehauen