Effect of Conversion on Openloop and Closedloop Stability

The linear model permits the use of all the linear analysis tools available to the process control engineer. For example, the poles and zeros of the openloop transfer function reveal the dynamics of the openloop system. A root locus plot shows the range of controller gains over which the system will be closedloop-stable. 

To illustrate these methods and to show quantitatively the impact of conversion on stability, we use the numerical case considered in Chapter 2. Table 2.1 gives the kinetic and process parameters and is repeated here as Table 3.1. The feed flowrate is 4.377 x 10-3 m3/s, and the reactor temperature is 350 K. 

Design conversions of 85 and 95% are considered. The corresponding reactor volumes are 26.1 and 102 m3, jacket heat transfer areas are 40.9 and 101 m2 and jacket temperatures are 309 and 330 K. 

The one zero and the three poles of the openloop transfer function (not including the two poles from the measurement lags) for the two cases are given in Table 3.2. The 85% conversion case has two complex conjugate poles with positive real parts, so it is openloop-unstable. The 95% conversion case is openloop-stable. 

Preexponential factor k0 Activation energy E Process molecular weight Process densities p0 and p Coolant density p/ 

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