Direct Adaptive Control Algorithms: Theory and Applications by Howard Kaufman

By Howard Kaufman

Suitable both as a reference for training engineers or as a textual content for a graduate path in adaptive keep watch over structures, this e-book is a self -contained compendium of with ease implementable adaptive regulate algorithms which have been built and utilized through 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 wide selection of engineering difficulties together with versatile constitution regulate, blood strain keep an eye on, and robotics; they're compatible 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 structures to conform the algorithms to difficulties in a wide selection of disciplines. hence, as well as constructing the theoretical info of the algorithms offered, the textual content provides massive emphasis to layout of algorithms and to consultant purposes in flight keep an eye on, versatile constitution keep watch over, robotics, and drug-infusion keep an eye on. Engineers can therefore use and attempt those algorithms in useful difficulties. This moment variation has been corrected and up to date all through. It uses MATLAB courses for a number of the illustrative examples; those courses are defined within the textual content and will be acquired from the MathWorks dossier server.

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30), and REAL [eigenvalues (Ap - BpKCp)] < O. 1. 44) where xp(t) is the n x 1 plant state vector; up(t) is the m x 1 control vector; Yp is the m x 1 output vector; and Ap, Bp, Cp are matrices with the appropriate dimensions. 46) where Xm is the nm x 1 model state vector, U m is the m x 1 model command, and Ym is the m x 1 model output vector. The reference model is designed to meet some desired performance properties and has the same number of outputs as the plant, but is otherwise independent of the controlled plant.

8) (~ Then 0 0 X X Bp = ~ ) Ku ~ (~ - -1 Ku = Bp - Bm. 5) to have solutions are known as the perfect model-following conditions. In general, however, a PMF controller is not easily implemented because: 22 Chapter 2. Basic Theory of Simple Adaptive Control • It is usually not possible to measure all the plant states. • The PMF conditions are often not satisfied. To alleviate these problems, output model-following (rather than full state-following) controllers have been developed. These are designed such that the process output vector (which is usually of a much lower dimension than the state vector) tracks the model output vector with all states remaining bounded.

51) where vm(t) is the command state vector. Of course, this representation is needed only for the subsequent analysis; the matrices Av and C v are unknown, and only measurements of the input um(t) are permitted. The commands um(t) are thus represented as generalized Fourier terms of the form Li j t j e"'i t cos f3it. 28 Chapter 2. 51) always has a solution. 53) can be guaranteed only if Am and Av have no common eigenvalues [78]. Examples at the end of this section will better illustrate these comments.

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