Dissipative Systems Analysis and Control: Theory and by Bernard Brogliato

By Bernard Brogliato

This moment variation of Dissipative platforms research and regulate has been considerably reorganized to house new fabric and increase its pedagogical beneficial properties. It examines linear and nonlinear structures with examples of either in every one bankruptcy. additionally incorporated are a few infinite-dimensional and nonsmooth examples. all through, emphasis is put on using the dissipative houses of a process for the layout of reliable suggestions regulate laws.

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Dissipative Systems Analysis and Control: Theory and Applications

This moment variation of Dissipative structures research and keep an eye on has been considerably reorganized to house new fabric and improve its pedagogical positive factors. It examines linear and nonlinear platforms with examples of either in each one bankruptcy. additionally integrated are a few infinite-dimensional and nonsmooth examples.

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It is not even necessary to know the order of the system dynamics, as the result holds for an arbitrary n. 19. The motors have inertias Jmi, angle Qmi and motor torque Tmi where i E {1, 2}. Motor 1 is connected to the inertia h 1 with a spring with stiffness K 11 and a damper Dn. Motor 2 is connected to the inertia h 2 with a spring with stiffness K22 and a damper D22· Inertia JLi has angle QLi· The two inertias are connected with a spring with stiffness K 12 and a damper D 12 . The total energy of the system is CHAPTER 2.

138) zo is the scattering function corresponding to the transfer function zL(s)/ zo. Because zL(s) is positive real, it follows that 9L(s) is bounded real. 139) -(s) = exp [-2Ts] gL(s) a1 which is a time delay of 2T which is the wave propagation time from x = 0 to x =land back, in series with the load scattering function. It is seen that ~(s) is bounded real as it is the product of two bounded real functions. 137). We consider the following three important cases: 1. First consider impedance matching for the transmission line, which is achieved with ZL(s) = zo.

We note that tanhs = sinhs/ coshs, where sinhs = ~(e 8 - e- 8 ) and coshs = Hes + e- 8 ). First we investigate if h(s) is analytic in the right half plane. The singularities are given by sinhs = 0 => e 8 - e-s = 0 => e 8 (1- e- 28 ) = 0 Here leal ~ 1 for Re[s] > 0, while es(l- e-28) = 0 => e-2s = 1 Therefore the singularities are found to be Bk = jk1r, k E {0, ±1, ±2 ... 126) which are on the imaginary axis. This means that h(s) is analytic in Re[s] > 0. Obviously, h(s) is real for real s > 0. Finally we check if Re [h(s)] is positive in Re[s] > 0.

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