By J.E. Normey-Rico, E.F. Camacho,
This article introduces the basic ideas for controlling dead-time tactics from uncomplicated monovariable to complicated multivariable situations. Dead-time-process-control difficulties are studied utilizing classical proportional-integral-differential (PID) regulate for the better examples and dead-time-compensator (DTC) and version predictive keep watch over (MPC) tools for an increasing number of advanced ones. Downloadable MATLAB® code makes the examples and ideas less complicated and less complicated.
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Extra resources for Control of Dead-time Processes (Advanced Textbooks in Control and Signal Processing)
SL)i i! , that is an i-order truncation of expression e−Ls = lim i→∞ • 1 , (1 + Ls/i)i a Pad´e representation of ij-order. 2 Dynamic Behaviour of Dead-time Systems 23 0 magnitude 10 Padé Lag −1 10 −2 −1 10 0 10 10 0 phase −20 −40 Padé Lag Dead time −60 −2 10 −1 0 10 normalised frequency 10 Fig. 14. Normalised frequency response of G1 (dashed lines) and P11 (solid lines). The phase of the real dead time is by dotted line P11 (s) = 1− 1+ L 2s , L 2s P22 (s) = 1− 1+ L 2s L 2s + + L2 2 12 s . L2 2 12 s For control purposes, when simple models are necessary to compute controllers such as the PID analysed in Chap.
0 ⎥ ⎢0⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎥ x(t) + ⎢ ... ⎥ u(t), . . . . . . . . . . . . x(t + 1) = ⎢ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 0 0 0 ... 0 ... 0 ⎥ ⎢0⎥ 1 ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ 0 0 0 . . 0 −a0 . . −an−1 1 y(t) = b0 b1 . . bn−1 0 . . 0 x(t), where t ∈ Z represents the discrete time. In this case, the state description maintains the characteristics of the dead-time-free case but the dimension of the system is greatly increased. 1T, we have n = 1 and d = 50. Thus, while the dead-time-free system has a state vector of dimension 1, the dead-time system has a state vector of dimension 51.
12. (a) Phase diagram of the dead-time factor e−Ls . 2: Consider a heated tank such as the one shown in Fig. 1 repre5 sented by the model P (s) = 1+2s e−s = G(s)e−s . The frequency response is obtained by computing |P (jω)| = 5 ; 1 + (2ω)2 ϕP (jω) = −arctan(2ω) − ω. It is possible to see the effect of the dead time on the phase of the system. As can be seen in Fig. 13 the effect of dead time on the phase decreases the phase margin (PM) of the system. In this particular case, the phase margin of the system without dead time is positive while that with dead time is negative, which shows the important negative effect of dead time on stability.