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A robust version of the self-tuning regulator is developed. The regulator, which requires relatively little knowledge of system characteristics (estimated order of transfer function polynomials and an upper bound for transportation delays), has been shown to yield stable control and convergence for linear, time-invariant systems. Simulations and practical tests on a large pilot-scale process have shown that the inclusion of a variable forgetting factor and an "extended horizon" control criterion provides the regulator with a sufficient degree of robustness and flexibility to perform well in a nonlinear time-varying environment. The regulator makes use of intuitively easy-to-understand concepts and leaves few degrees of freedom for the potential user. Furthermore, extensive experiments and simulation studies have shown it to be insensitive to choice of initial conditions and dynamic characteristics set by the user. SCOPEThe idea of the self-tuning regulator was developed (ktrom and Wittenmark, 1973) to cope with the problem of controlling linear, time-invariant systems with unknown or uncertain models, and which were subject to stochastic disturbances-a situation which is not common in the chemical industry. There have been subsequent attempts to modify the basic concepts to obtain algorithms which can deal with the more typical chemical engineering problem-the control of processes with nonlinear, uncertain, nonconstant dynamics and with long and variable transportation delays.In order to deal with this more complex problem it is necessary to incorporate some adaptive mechanism into the part of the algorithm which estimates a model for the process being controlled. It is also necessary to "detune" the control action in an appropriate way to prevent severe overshoot and potential instability of the real nonlinear process. Finally, it is important to reduce the sensitivity of the algorithm to any remaining parameters which must be specified a priori by the operator or control engineer.Only if all the above are achieved is the resulting control algorithm likely to be robust enough to be generally useful in the control of process plants. CONCLUSIONS AND SIGNIFICANCEIt is likely that some form of self-tuning controller will find significant application in the control of time-dependent nonlinear processes within the chemical industry. These controllers have the advantages of simplicity, flexibility, and cornpatability with microcomputer technology, as well as an intuitively satisfying basis.The results of this study have shown that the basic self-tuning algorithm can be modified to produce a version far more robust than the early formulations. The algorithm has been shown to Correspondence concerning this paper should be addressed to L. S. Kershenbaum. B. E. Y&e is presently at Chemical Engineering Department, University of Marsachuset6Amherst. MA 01003.be stable and convergent for linear, time-invariant systems, and requires only a few parameters to be supplied by the operator. Moreover, for a wide range of simulati...

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A method was devised to yield chemical reaction kinetic parameters from nonisothermal, nonisobaric flow experiments. The system studied was the pyrolysis of propane a t high temperatures (800" to 1,OOO"C.). A t these temperatures the rates of the various reactions are so high that a batch or even an isothermal flow experiment is impossible. To keep the conversions low so that the initial stages of decomposition could be studied, the feed gas was diluted with varying amounts of nitrogen. Residence times in the reactor were in the millisecond range. The reactor exit gas was analyzed by mass spectrometry. The method developed in this work is not limited to simple kinetic studies, but can be useful in complicated series and parallel reactions which often require nonisothermal conditions.As reaction temperatures are raised, it becomes increasingly difficult to measure kinetic rate constants experimentally. In this work, the pyrolysis of propane was studied at 800" to 1,OOO"C. where the reactions are extremely rapid. Furthermore, the products of reaction themselves decompose under these conditions, tending to mask the primary kinetics. Conversions, therefore, were kept low through the use of a steady state flow system, where residence times can be shorter than in batch systems; the concentration of the reaction products was minimized by diluting the feed gas with nitrogen to about 5% propane.The extent of this dilution was limited however, because the higher the concentration of diluent and the lower the conversion, the more difficult becomes the exit gas analysis.Since rate constants are strongly dependent upon temperature, it would be most convenient to conduct kinetic experiments isothermally. However, because of the low residence times required and the physical limitations on heat transfer rates, a 'nonisothermal experiment results. Some previous workers have chosen an equivalent, average temperature for all or a fraction of the reactor, but this procedure leads to only partially satisfactory results. An alternative is to measure the gas temperature profile throughout the reactor and to devise some method of treating the data to yield the desired rate constants. Such was the method used in this study.Once the rate constants are obtained as functions of temperature, the kinetic model can be programmed on an analog computer; it is then possible to test the consistency of the data and to predict product distributions, conversions, etc., for any arbitrary set of conditions. This is extremely valuable if similar studies are made for the other low hydrocarbons which are products of propane pyrolysis. Then the entire series could be studied simultaneously; that is, product distributions could be predicted not only for the simple case of low conversions but also for the more complicated cases of consecutive reactions where reaction products themselves react further.There is much ublished information in the literature in general and propane in particular. While much kinetic work has been done with propane at lower temperatu...