Direct Adaptive Control Algorithms: Theory and Applications by Howard Kaufman

By Howard Kaufman

Suitable both as a reference or as a textual content for a graduate direction in adaptive keep an eye on platforms, this ebook is a self-contained compendium of simply implementable adaptive regulate algorithms which were built and utilized by way of the authors for over 10 years. those algorithms don't require particular strategy parameter identity and feature been effectively utilized to a large choice of engineering difficulties together with versatile constitution keep an eye on, blood strain regulate and robotics. as a rule, those algorithms are compatible for a large type of a number of input-output regulate structures containing major uncertainty in addition to disturbances.

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For this general situation, perfect tracking is only an ideal target, that the actual plant might eventually reach at those times when the input signal can be followed and when no disturbances are present. In more difficult situations, perfect tracking cannot be achieved, and the designer is confined to tracking with errors. It will be shown that the adaptive control systems proposed here remain stable and that the tracking errors remain bounded, in spite of the disturbances. 51), only this time no particular assumption on the dimension of the unknown matrices Av and C v , and thus on the complexity of U m (t), is used.

Actually, it may not be even desirable to seek perfect tracking for any possible input command, such as, for example, any high frequency disturbance signals that may occasionally appear at the plant input. Therefore, the ideal trajectories are only "targets" that the plant tries to reach or at least be close to, in order to have bounded tracking errors (that hopefully are as small as possible). 51) and thus was differentiable. For the sake of generality, any particular assumptions about the input signal um(t), except for its boundedness will now be removed.

51 ) where vm(t) is the command state vector. Of course, this representation is only needed for the subsequent analysis; the matrices Av and C v are unknown, and only measurements of the input U m (t) are permitted. The commands U m (t) are thus represented as generalized Fourier terms of the form L:i j t j ea,t cos (3it. 51), its response can be written as the sum of the general and the particular solution: Xm (t) = E Vm (t) + e A",tfjo. 51) always has a solution. 53) can be guaranteed only if Am and Av have no common eigenvalues [77].

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