Dissipative Systems Analysis and Control: Theory and - download pdf or read online

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By Bernard Brogliato

ISBN-10: 1447136683

ISBN-13: 9781447136682

ISBN-10: 1447136705

ISBN-13: 9781447136705

This moment version of Dissipative platforms research and regulate has been considerably reorganized to deal with new fabric and increase its pedagogical positive aspects. It examines linear and nonlinear platforms with examples of either in every one bankruptcy. additionally integrated are a few infinite-dimensional and nonsmooth examples. all through, emphasis is put on using the dissipative homes of a approach for the layout of solid suggestions regulate laws.

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As h(s) has no poles in Re [s] < 0 by assumption, it follows that the system is passive if and only if Re[h(jw)] ~ 0 for all w. 56) CHAPTER 2. POSITIVE REAL SYSTEMS 22 where all the poles are on the imaginary axis. 4 is satisfied. 58) w w02 -w 2 so that also condition 2 holds in view of Re[ h1 (jw) 1 = Re[h2 (jw) 1 = 0 for all w so that jw is not a pole in h (s). 4 the system with transfer function h2(s) is passive, while h1(s) is passive whenever a< wo. Example 2. 62) The transfer function has no poles in Re [s1 > 0, and Re[h(jw)1 ~ 0 for all w =f.

Consider the following special cases: 1. Impedance matching can be achieved with a restriction at the outlet satisfying p2 (8)=zo which gives ZL = zo. 158) which means that all wave energy is dissipated in the restriction. 2. 160) In this case the wave is reflected from the load with a change of sign. 3. 161) while the scattering function is 91(8) = exp(-2T8) This shows that the wave is reflected from the load. 14. 1 Motor and load with elastic transmission An interesting and important type of system is a motor that is connected to a load with an elastic transmission.

The power supplied from the inlet is q1p1 . 147) where d is the power dissipated in the system. Because it is assumed that there is no energy-generating component in the system it follows that loT d(t)dt ~ 0 for all T passive. 148) 0. 150) V1f7P where c = is the speed of sound and z0 = pcfA is the characteristic impedance of the pipeline. 153 CHAPTER 2. 154) is the wave propagation time along the pipeline. A scattering formulation is obtained by introducing a; = p; + zoq; and b = p;- zoq; fori E {1, 2}.

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Dissipative Systems Analysis and Control: Theory and Applications by Bernard Brogliato

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