By Howard Kaufman
Suitable both as a reference for training engineers or as a textual content for a graduate path in adaptive keep an eye on structures, this ebook is a self -contained compendium of effectively implementable adaptive keep an eye on algorithms which have been constructed and utilized by way of the authors for over fifteen years. those algorithms, which don't require the person to spot the method parameters explicitly, were effectively utilized to a large choice of engineering difficulties together with versatile constitution keep an eye on, blood strain keep watch over, and robotics; they're appropriate for a large choice of a number of input-output keep watch over structures with uncertainity and exterior disturbances. The textual content is meant to permit a person with wisdom of uncomplicated linear multivariable platforms to evolve the algorithms to difficulties in a large choice of disciplines. therefore, as well as constructing the theoretical info of the algorithms awarded, the textual content provides massive emphasis to layout of algorithms and to consultant purposes in flight regulate, versatile constitution keep watch over, robotics, and drug-infusion keep watch over. Engineers can hence use and try those algorithms in useful difficulties. This moment version has been corrected and up-to-date all through. It uses MATLAB courses for the various illustrative examples; those courses are defined within the textual content and will be got from the MathWorks dossier server.
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Extra info for Direct Adaptive Control Algorithms: Theory and Applications
3 Stability and Positivity Concepts 39 stabilizing effect, and the state is driven toward the equilibrium x(t) = O. Finally, the state reaches x(t) = 0, and the adaptive gain reaches some fixed value in the admissible stabilizing region. 127) is sufficient to guarantee stability of the closed-loop system. The rigorous proof of this simple theorem is rather elaborate and can be found in Bar-Kana [82). The upper bound for the admissible control gains is merely a measure of caution, rather than real knowledge.
16), Cpx;(t) = Cmxm(t), and therefore, Cpxp = Cmx m , which is the desired result. timately bounded. 5), are together a special case of the command generator tracker when the state vector is available, and it is assumed that x;(t) = xm(t). Since x;(t) = 8uxm(t) + 8 12 U m , the PMF conditions imply that 8 11 = I and 8 12 = o. 37) These equations have a solution when the column vectors of the difference matrix Am - Ap and of the matrix Brn are linearly dependent on the column vectors of the matrix Bp.
Although various direct adjustment algorithms have been proposed, model reference adaptive control is very appealing for the following reasons: • It provides (continuously or at each sample) a measure of system performance. • It is not difficult to design a reference model that incorporates the desired response specifications. • It lends itself to elegant stability analysis. Thus, taking into account the large body of theory and successful applications of the simple direct model reference adaptive control algorithm discussed in the previous sections, this text, with the designer in mind, covers the relevant theory and design procedures.