By Nikolai Michailovich Filatov, Heinz Unbehauen
This monograph demonstrates how the functionality of assorted recognized adaptive controllers may be superior considerably utilizing the twin impression. The alterations to include twin regulate are learned individually and independently of the most adaptive controller with no complicating the algorithms. a brand new bicriterial strategy for twin keep an eye on is built and utilized to varied varieties of renowned linear and nonlinear adaptive controllers. functional purposes of the designed controllers to a number of real-time difficulties are provided. This monograph is the 1st e-book delivering a whole exposition at the twin keep an eye on 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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Additional resources for Adaptive dual control: theory and applications
The dual version of an adaptive GMV controller will be designed below using the bicriterial approach. 5. Comparison of bicriterial and explicit dual control approaches 4. 38) where Y(z), U(z) and Ξ(z) are the z-transforms of the output y(t), the control u(t) and the disturbance ξ(t), respectively, d being the time delay, the polynomials A( z −1 ) , B( z −1 ) are as in eqs. 37), and C ( z −1 ) = 1 + c1 z −1 + ... + cnC z −n C . 39) So far as the time delay d is not zero, B( z −1 ) assumes the polynomial B( z −1 ) = b0 + b1 z −1 + ...
1982). This property leads to unsatisfactory performance and is investigated in detail in Chapter 4. The bicriterial approach, which is introduced in Chapter 4 (an example has already been given in Sec. 3), is free from this shortcoming, and the magnitude of excitations is determined directly by the parameter θ(k), as indicated in eq. 20). Some dual controllers based on minimization of one cost function with constraints for other cost function were presented by Alster and Belanger (1974) and Bodyansky and Solovjova (1987), but the advantages of these approaches over the ones with the cost functions as in eq.
19), taking the expectation (compare Appendix D) and using the terms of eqs. 28) u ( k − 1) = q1u( k − 1) + ... 29) where and c1 is independent of u(k ) . Differentiation of the eq. 28) gives the condition for the minimum as ∂J kc = 2[bˆ12 (k ) + pb1 (k )]u (k ) − 2bˆ1 (k ) w(k + 1) ∂ u (k ) + 2( pˆ 0T (k )bˆ1 (k ) + pbT p (k ))m 0 (k ) 1 0 +2ru (k ) + 2ru (k − 1) = 0 . Thus the minimization of eq. 28) gives the cautious control action as uc (k ) = bˆ1 (k ) w(k + 1) − [bˆ1 (k ) pˆ 0T (k ) + pbT p (k )] m0 (k ) + ru (k − 1) 1 0 bˆ12 (k ) + pb1 (k ) + r .
Adaptive dual control: theory and applications by Nikolai Michailovich Filatov, Heinz Unbehauen