By J.E. Normey-Rico, E.F. Camacho,

ISBN-10: 1846288282

ISBN-13: 9781846288289

ISBN-10: 1846288290

ISBN-13: 9781846288296

This article introduces the elemental ideas for controlling dead-time approaches from uncomplicated monovariable to complicated multivariable situations. Dead-time-process-control difficulties are studied utilizing classical proportional-integral-differential (PID) keep watch over for the better examples and dead-time-compensator (DTC) and version predictive keep an eye on (MPC) equipment for a growing number of complicated ones. Downloadable MATLAB® code makes the examples and ideas less difficult and easier.

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15. Normalised step response of the lag approximation (dashed line) and the Pad´e approximation (solid line). 6 rad. The analysis can be performed in the time domain using the process response to a unitary step test and, for instance, the integral of the square error (ISE) between the approximate response and the real one can be used to compare the different models. 22. 15 shows the step response of G1 and P11 for a unitary dead time. The step input is applied at t = 1. Furthermore, as can be seen from the figure, P11 presents nonminimal phase behaviour.

As can be seen, the differences between the responses of the model and the process are very small. In this case any small error in the estimation of the value of L could cause larger errors than the ones shown in Fig. 18. These errors are normally related to the use of linear low-order models to represent the nonnecessary linear high-order dynamics of the process and also to measurement errors produced by noise. These issues are analysed later in this chapter and in Chap. 3. 4 State-space Representation of Dead-time Systems A state-space representation equivalent to the input−output representation given by the transfer function of a dead-time-free process (G(s)) can be obtained using different realisations [71].

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. The state-space representation of the dead-time system is used in several works to analyse stability and other properties (see the Further Reading section for references).

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