By Nikolai Michailovich Filatov, Heinz Unbehauen

This monograph demonstrates how the functionality of assorted famous adaptive controllers should be enhanced considerably utilizing the twin impression. The variations 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 process for twin keep an eye on is built and utilized to varied different types of well known linear and nonlinear adaptive controllers. functional purposes of the designed controllers to numerous real-time difficulties are provided. This monograph is the 1st e-book supplying a whole exposition at the twin keep watch over challenge from the inception within the early Sixties to the current state-of-the-art aiming at scholars and researchers in adaptive regulate in addition to layout engineers in undefined.

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**Example text**

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 + ... + bn B z − n B , b0 ≠ 0 . 41) where Ya ( z ) and W(z) are the z-transforms of the auxiliary signal ya (k ) and the setpoint w(k), respectively, P( z −1 ) = p0 + p1 z −1 + ...

The following values have been chosen for the GMV algorithm: 4. 6. 4 z −2 . 4. 7. Simulation results for the adaptive controller based on the CE assumption Upper and lower limits of ±500 are used for the control signal. The controller based on the CE assumption can be obtained from eq. 61), with P(k) set to 0. 8. 9. The simulation results for the GDC according to eq. 5 are shown in Fig. 10. 10, the adaptive dual controller provides better control 4. BICRITERIAL SYNTHESIS METHOD FOR DUAL CONTROLLERS 48 performanc and a smaller overshoot.

21) was used, where P(k) is the covariance matrix of the estimation error. 23) while Wittenmark and Elevitch (1985) as well as Allison et al. (1995a) used the covariance of the estimate of the first parameter b1 of the ARX model of the system. Instead of the well-known innovational cost measure of Milito et al. (1982), see also eq. 24) can be used in the bicriterial design method. 25) can be used instead. The cost function according to eq. 23) can be easily used for the controller design in the framework of the bicriterial design method, whereas this cost function results in great computational difficulties for the approach according to eq.