By K. J. Astrom, T. Hagglund
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The transfer function is zero for aT - 2nn. 25. An interesting property of this transfer function is that arsG(ia): -+. foratT 12n. A ContinuousStirredTankReactor Consider a continuous-time stirred tank reactor where the reaction A --+ R takes place. The reaction is exothermic, and reaction heat is removed by a coolant. The system is modeled by mass and energy balances. 38) of an ideal heat exchanger. 2 Parameters of the exothermic continuous-time stirred tank reactor. 002*3 It 0 . Lm 3 1000ks l*t a kJ lkgK h6 3 x 1 0 8s - 1 q v p Tf,7, 300K EIR 8750K cS 2 kmolf m3 uA 50w/K LH -5 x t05 kJ/kmol The first term on the right-hand side represents the mass flow rate and the second term represents the rate of removal of A through the reaction.
7 How to Obtain the Models even if Tp is very short. By comparing this with the actual variance we get an assessment of the achievable performance. This is discussed in more detail in Chapter 10. There is efficient software for computing the prediction error and its variance from process data. 7 Howto Obtainthe Models In previous sections we have briefly mentioned how the models can be obtained. In this section we will give a more detailed discussion of methods for determining the models. There are two broad types of methods that can be used.
If d is the relay amplitude, the 'rst harmonic of the square wave input has amplitude 4dlx. Let a be the ,::rplitude of the process output. The process gain at aas is then given by xrao: ffi. 51) \ ,tice that the relay experiment is easily automated. '-' oscillation is proportional to the relay output, it is easy to control it by , itusting the relay output. 37 that a stable oscillation - established very quickly. The amplitude and the period can be determined 53 Chapter 2. Process Models after about 20 s only, in spite of the fact that the system is started so far from the equilibrium that it takes about 8 s to reach the correct level.
Advanced PID Control by K. J. Astrom, T. Hagglund