By Michael L. Luyben, William L. Luyben
This article features a very functional engineering orientation with many real-world commercial regulate examples and difficulties. insurance comprises plantwide regulate and the interactions among steady-state layout and dynamic controllability. MATLAB is used as a computer-aided research instrument. also, many examples and an intensive collection of difficulties are integrated.
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Additional resources for Essentials of Process Control
46)], setting the time derivative dCA/dt equal to zero. 49) = m Is this reasonable? A to C,O will be smaller) the bigger k and T are. This certainly makes good chemical engineering sense. , will be equal to the feed concentration CAo, as it should be. 4 Step response of order system. I:K z Time Domain Dynamics 30 state value. Thus. rhc predictions 01‘ the solution stem to check with the real physical world. ~f~~f~ pritz of the process K,,. 50) These steady-state gains will be cxtrcmely important in our dynamic studies and in controller design.
2 Temperature Control of a Three-Tank Process As a second simple example that demonstrates some very important and far-reaching principles, let us consider the control of temperature in a single tank and then in a series of two and three tanks. The dynamic model for three heated tanks in series is given in Eqs. ( I. IO) to ( I. 12). Constant holdup and constant physical properties are assumed. The, FORTRAN program used to simulate the process is given in Appendix A. The temperature in one of the tanks (TI, 7’2, or Tj) is controlled by a proportional temperature controller that manipulates the heat input Ql to the first tank.
46) are identical, except one is in terms of total variables and the other is in terms of perturbations. Whenever the original ODE is already linear, either total or perturbation variables can be used. Initial conditions will. of course. differ bv the steadv-state values of all variables. 7. 55) ~~AO(,, = Kf where K is a constant. C,, is initially xro. Rearranging Eq. 5 I) gives *. tllIL!! E, tl! 56) The solution, according to Eq. 57) The integral in Eq. 57) can be looked up in mathematics tables or found by integrating by parts.