By Cornelius T. Leondes
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Additional resources for Advances in Theory and Applications : System Identification and Adaptive Control, Pt 3 of 3
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). (77) and (78) are shown in Fig. 7, which is seen to compare closely with the previous results in Figs. 4 and 5. The similarity of Figs. 4 , 5, 7 suggests that the controller (77) and (78) might be able to accommodate a variety of different linear and nonlinear plants of general second-order form y + f(y, y) = u + w.
On the other hand, if [bC] is due entirely to sensor perturbations [bCs], then a different set of control design considerations must be invoked. In other words, one must be careful to avoid the pitfall of regulating y s e n( t ) -> y s p when, in fact, y s en is an unreliable indication of y p h y! This kind of subtlety becomes even more complicated when [bC] is due to simultaneous perturbations [δΟ ρ] and [ÖC S], or when the primary control task is to regulate a specific state variable Xj(t) which is not accessible for direct measurement.
4% + k (y + ξ) 2 sp 02 V V k ^ y + ξ) z^k^y ^2i=^22 Z22 + + ξ) k o5(y = - z 2i - 1A (77a) (77b) (77c) (77d) + %i ^ (77e) + ^ ( y + ξ)· (770 A NEW APPROACH TO ADAPTIVE CONTROL Fig. 4. Simulation results for the second-order example of Section V,B- 33 the case of constant parameter perturbations [δΑ]. 21 ο •ι " 2 0 -1 -5+ΟΜ 0 II H 4 -1 5 -5+03U 0 " 6 -1 7 cos(i) Ο ο il Ί Q -1 9 Ο -l+cos(t) ο 10 -1 il cosd) -l+cos(i) ο " lZ -1 3 Ο Fig. 5. Simulation results for the second-order example of Section V,B; the case of time-varying perturbations [6A(t)].
Advances in Theory and Applications : System Identification and Adaptive Control, Pt 3 of 3 by Cornelius T. Leondes