By Cornelius T. Leondes

ISBN-10: 012012727X

ISBN-13: 9780120127276

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Extra info for Advances in Theory and Applications : System Identification and Adaptive Control, Pt 3 of 3

Example text

However, to A NEW APPROACH TO ADAPTIVE CONTROL 27 avoid loss of ( Z a , Z) observability these polynomial modes should not be duplicated in any common element of [δΑ]χ and FHz in (13). V. SOME WORKED EXAMPLES USING THE NEW ADAPTIVE CONTROLLER, (47) AND (50) The simplicity and systematic nature of the design procedure for the new adaptive controller (47) and (50), and the degree of adaptive performance which that controller can achieve, are best demonstrated by the study and simulation of specific numerical examples.

0 [ °0 #j7 20 ^ 25 Fig. 3. Simulation results for the first-order example of Section V,A. The plant (55a) with linear adaptive controller (70) and (71) installed (with a M = a N = - 1 and / = - 5 ) was simulated on a digital computer and exercised with a variety of plant-parameter perturbations 5a, setpoint values y s p, and "constant" disturbances w(t). Some representative plots of the closed-loop plant response y(t) are shown in Fig. 3, where it can be seen that y(t) closely mimics the idealmodel response over a wide range of plant parameter perturbations Ôa (including large "destabilizing" values of 6a) and external disturbances w(t).

GENERALIZATION OF THE NEW APPROACH: CONSIDERATION OF NONZERO [δΒ], [ δ η , [ÖC] The adaptive controller (47) and (50) was derived under the assumptions 7 [δΒ] = 0, [δί ] = 0, [5C] = 0 in (9). However, as stated earlier, the controller (47), (50) will, in fact, tolerate a moderate range of [OF], [δΒ]. In this section we will show how the same DAC techniques used to derive (47) and (50) can be generalized to accommodate the cases of nonzero [δΒ], [OF], In the case of [δΒ] this will require a mild nonlinearity (multiplier) in the controller.

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Advances in Theory and Applications : System Identification and Adaptive Control, Pt 3 of 3 by Cornelius T. Leondes

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