By Nikolai Michailovich Filatov, Heinz Unbehauen

This monograph demonstrates how the functionality of varied recognized adaptive controllers may be superior considerably utilizing the twin impression. The adjustments to include twin regulate are discovered individually and independently of the most adaptive controller with no complicating the algorithms. a brand new bicriterial method 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 numerous real-time difficulties are provided. This monograph is the 1st e-book offering 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 regulate in addition to layout engineers in undefined.

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21). After substituting of eq. 2) into eq. 20) and taking the expectation (compare Appendix D) using eqs. 32) 40 4. BICRITERIAL SYNTHESIS METHOD FOR DUAL CONTROLLERS J ka (u c (k ) − θ (k )) − J ka (uc (k ) + θ (k )) = − pb1 (k )[u c (k ) − θ (k )]2 − 2 pbT p (k )m 0 (k )(uc (k ) − θ (k )) 1 0 + pb1 (k )[uc (k ) + θ (k )] 2 + 2 pbT p 1 0 (k )m 0 (k )(u c (k ) + θ (k )) = 4 pb1 (k )θ (k )uc (k ) + 4 pbT p (k )m 0 (k )θ (k ) . 33) Substituting eq. 31) provides the adaptive dual control law u (k ) = uc (k ) + θ (k )sgn [ pb1 (k )uc (k ) + pbT p (k )m 0 (k )] .

38). The adaptive dual GMV controller, according to eqs. 62), is applied as well as the standard adaptive GMV controller based on the CE assumption for comparison. 1052 z − 2 . The plant parameters are assumed to be unknown and constant. 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.

At first, some remarks about least-squares parameter estimation for SISO systems with timevarying parameters are given. 1. 1. Algorithms for Parameter Estimation Consider a discrete-time SISO system with time-varying parameters described by y (k + 1) = b1 (k )u (k ) + ... + bm (k )u (k − m + 1) − a1 (k ) y (k ) + ... 1) where y ( k ) is the system output and u ( k ) the control signal. , m are the unknown time-varying plant parameters. bm (k ) − a1 (k ) ... u (k − m + 1) T y (k )... y (k − n + 1)] .