Download e-book for iPad: Advances in Control: Highlights of ECC’99 by K. J. Åström (auth.), Paul M. Frank (eds.)
By K. J. Åström (auth.), Paul M. Frank (eds.)
Advances in Control comprises keynote contributions and educational fabric from the 5th ecu keep watch over convention, held in Germany in September 1999. the themes lined are of specific relevance to all lecturers and practitioners within the box of contemporary keep watch over engineering. those contain:
- smooth keep watch over concept
- Fault Tolerant keep an eye on platforms
- Linear Descriptor platforms
- universal strong regulate layout
- Verification of Hybrid platforms
- New business views
- Nonlinear procedure id
- Multi-Modal Telepresence structures
- complicated techniques for strategy regulate
- Nonlinear Predictive keep an eye on
- good judgment Controllers of continuing vegetation
- Two-dimensional Linear structures.
This very important choice of paintings is brought by means of Professor P.M. Frank who has virtually 40 years of expertise within the box of automated regulate. cutting-edge examine, specialist evaluations and destiny advancements up to the mark conception and its commercial purposes, mix to make this an important quantity for all these occupied with keep an eye on engineering.
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Additional info for Advances in Control: Highlights of ECC’99
3. Pitchfork bifurcation The pitchfork bifurcation locus in the bifurcation diagram is given by c + da = 0, see equation (21) with e = O. For c + da < 0 the origin is a saddle. The other two equilibria are described by (aYe,Ye,y~/o-) with y~ = -a(c/a + d). Their local stability is determined from the location of the roots of (23): ,\3 1 + -(ao- + a 2 a C),\2 0a + -(-2(ad + c) - c + a2),\ - 20-(ad + c) (25) These equilibria are stable when a2 - c > max(ao-, -2(ad + c)), and (a 2 - c)(a 2 + ao- - c) - 2(ad + c)(ao- - c) > 0 unstable otherwise.
It ... ;. ... )I )I ...... > ... ~--- )I ... A' o. , } ~ f· , f , , } " . ' ... ~ \ ... \ ~ .... If " ~ A ~ ~ \ ~ .... ~ ~- ~ ...... - Figure 4: Phase portrait for bifurcation diagram region I in Fig. 3 In the regions II, after the saddle-node bifurcation, three equilibria coexist. A saddle and unstable focus come into existing through the SaddleNode bifurcation. It appears from the phase portrait in Figure 5 that apart from the stable manifold of the saddle, all solutions converge to the stable focus.
4] (see also the Appendix I): Ax + by, -ex - dy + guo (1) Here u is the input, y the output and (x,y) E lRn x lR is the state of the linear system (1). A E lRnxn is a matrix whose eigenvalues have negative real part. The eigenvalues of the matrix A are precisely the zeroes of the transfer function of the system (1). We assume that g > 0, g is the high frequency gain from input to output. We assume that the original system (1) is controllable. As a consequence, see Appendix I, the pair (A, b) is controllable.
Advances in Control: Highlights of ECC’99 by K. J. Åström (auth.), Paul M. Frank (eds.)