By Jean-François Magni
Robust Modal Control covers so much classical multivariable modal keep watch over layout innovations that have been proven to be potent in perform, and likewise proposes numerous new instruments. The proposed new instruments contain: minimal strength eigenvector choice, low order observer-based keep an eye on layout, conversion to observer-based controllers, a brand new multimodel layout method, and modal research. The textual content is followed by means of a CD-ROM containing MATLAB® software program for the implementation of the proposed suggestions. The software program is in use in aeronautical and has confirmed to be potent and practical.
For extra element, please stopover at the author's web site at http://www.cert.fr/dcsd/idco/perso/Magni/booksandtb.html
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33). 4 - Set i to i + 1 if i < n or to 1 if i = n and go to Step 2. Usually, this algorithm must be completed by standard optimization. The advantage of using this algorithm before standard optimization is that, in almost all cases, optimization will not lead to a very bad local mmlmum. Extension to the output feedback case. This technique can be adapted to output feedback design. In this case, only p right eigenvectors are treated. So, Ui cannot be computed as the orthogonal to n -1 vectors as only p - 1 vectors Vi are known.
See Appendix 4, page 277. 3, it might be relevant to multiply Df = I and Bf by the matrix (I - Cfk/Bf)-I in order to normalize the steady state gain. Software I Related MATLAB-function: fLassgn. 3 with the aforementioned normalization. In addition, this function permits the user to define approximate (optimal) cancellation when the poles to be cancelled are not equal to the zeros. Example. A random stable system is considered. rand('seed',O); randn('seed',O); sys = rss(4,4,2); A feedback gain K and the equivalent dynamic feedforward gain i f are designed (elean_ev remove complex conjugate values): K = fb_prop(sys,O,[-l -2 -3+3*jJ ,'z',[l 23J); Feedforward computation zer = elean_ev(eig(sys)); ff = ff_assgn(sys,O,zer,zer,[-l -2 -3+3*jJ ,'z', [1 23J); Before comparison of feedback and feedforward controllers, the steady state gains between inputs and outputs must be rendered equal in order to have similar behavior in steady state (and, by the way, during the transient pnase that is related to eigenvectors).
See Appendix 4, page 282. 3 Summary There are two steps for designing an observer-based feedback law: observer design and then output feedback (or state feedback) design. • The observer order should be chosen as being equal to the difference between the number of dominant poles that need to be assigned and the number of measurements. See the summary of page 53. 78). See the summary of page 30. 76) can be applied to the result if the observer structure is not relevant. Software I Related MATLAB-functions: add_obs, obs2dfb, dfb_ins and dfb_proj.