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

This article introduces the basic concepts for controlling dead-time approaches from easy monovariable to advanced multivariable circumstances. Dead-time-process-control difficulties are studied utilizing classical proportional-integral-differential (PID) keep watch over for the easier examples and dead-time-compensator (DTC) and version predictive regulate (MPC) tools for increasingly more complicated ones. Downloadable MATLAB® code makes the examples and concepts less complicated and easier.

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**Extra resources for Control of Dead-time Processes (Advanced Textbooks in Control and Signal Processing)**

**Example text**

This is not the case when a discrete representation of the dead-time process is used. 10) where A(z) is monic and has degree n and B(z) has degree n − 1 A(z) = z n + an−1 z n−1 + . . + a1 z + a0 , B(s) = bn−1 z n−1 + bn−2 z n−2 + . . + b1 z + b0 . Thus, the dead time only increases the order of the model in d. Note that the new denominator A(z)z d has degree n + d A(z)z d = z d+n + an−1 z d+n−1 + . . + a1 z d+1 + a0 z d . 3 Simple Models for Typical Dead-time Systems 31 Using the canonical form to represent the system gives ⎡ ⎤ ⎡ ⎤ 0 1 0 ...

4. Behaviour of the outlet and inlet tank temperatures F 1I ............ H1 ............ H2 F 2O ...... Hn F nO Fig. 5. 0 13 14 2 Dead-time Processes dynamic behaviour of the level in each tank Hi can be modelled by a linear system A dHi = FiI − FiO , dt FiO = KHi , where A is the area of the base of the tank and K is a constant that depends on the tank characteristics. Thus, the transfer function relating the input ﬂow in tank i and its level is Hi (s) = 1/K FiI (s), Ts + 1 For tank 1 H1 (s) = T = A/K.

5 to 8. The comparison is used to introduce a new controller, the dead-time compensator generalised predictive controller DTC-GPC. This algorithm has most of the advantages of the GPC and DTC for controlling dead-time processes. The ideas of the dead-time compensators are generalised to the MIMO case in Chap. 11. The design of these MIMO-DTCs are analysed. The difﬁculties associated with tuning the fast model and primary controller of multidead-time processes are presented. Chapter 12 extends the dead-time compensator generalised predictive controller to the MIMO case, showing that the proposed controller can be used for controlling stable or unstable MIMO processes with multiple dead times.