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
4 are representative of those corresponding to a large subset of operating points within the adaptability domain shown in Fig. 6. Of course, as the operating point ( a l 9 a 2 ) approaches the boundary of the adaptability domain in Fig. 6, the idealness of the time-response y(t) will gradually deteriorate, exhibiting the characteristic oscillations associated with a system operating near its boundary of stability. C. A UNIVERSAL ADAPTIVE CONTROLLER' FOR A BROAD CLASS OF LINEAR AND NONLINEAR SECOND- AND FIRST-ORDER PLANTS The effectiveness of the adaptive controller (77) and (78) in accommodating unknown, unmeasurable time-varying parameter perturbations öai(t), ôa 2(t) for the linear plant (72), as illustrated in Fig.
And ν or in the face of [SC], What the designer then does with the estimates ν or Φ depends on the nature of the primary control task and on whether [SC] is caused by [SCS] or [öC p ], or both. For example, if a "compensating signal" u c(t) is added to (113a) to yield y = C N x + [8C]x + u c (t), (119) and if u c(t) is chosen as u c(t) = -v(t), (120) then the effect of [SC] on y is approximately cancelled, so that y « C Nx , for "all" [6C]. (121) Likewise, if Ψ is nonsingular and the output y(t) in (113a) is multiplied by [Ψ] -1 « Ψ to produce the "new" output Vnew^fY (122) then, by (117), y ne w ~ C Nx , for "all" [ÔC].
Simulation results for other nonlinear plants in the example of Section V,C. C. D. JOHNSON Fig. 9. Simulation results for other nonlinear plants in the example of Section V,C. A NEW APPROACH TO ADAPTIVE CONTROL Fig. 10. C. 40 C. D. JOHNSON Fig. 11. Simulation results for some first-order plants using the "universal" adaptive controller (77) and (78). A NEW APPROACH TO ADAPTIVE CONTROL 41 ~! Plant (72) [or as shown in R3S. 4S+1 Fig. 12. Transfer function interpretation of the universal adaptive controller (77) and (78).