Ind. Eng. Chem. Res. 1990,29, 2161-2163 Y
Figure 1. Basic SISO integral control configuration.
t"
- Re
Figure 2. Nyquist plot of a doubly integrating transfer function.
Theorem 2. Assume H(s) has all poles in C-.The rational system (I/s)H(s) is integral controllable only if Z(H(0)) E R+. Proof. The proof follows the same lines as the proof of theorem 1 except for the fact that we must consider a set of characteristic loci rather than a single Nyquist plot. As s contours the origin, the characteristic loci encircle the entire complex plane. Unless each of the loci starts at (-m,O) when s approaches the origin, a non-zero net number of encirclements of the point (-l/k,O) is unavoidable as k is made arbitrarily small. The loci will start at (-m,O) when s approaches the origin if and only if all the eigenvalues of H(0) are positive real. QED. Theorem 2 can be viewed as the equivalent of corollary 1in Grosdidier et al. (1985), for integrating MIMO systems. This new result is much more restrictive since it requires not just the determinant but all the eigenvalues of the
2161
matrix H(0) to be positive real. This condition can be satisfied, for example, when the matrix H(s) is diagonally dominant at steady state.
Nomenclature j = complex variable s = Laplace variable w = frequency variable 0 = time delay k = compensator gain Z(A) = spectrum of the matrix A E(wi) = error term of magnitude w' C - = open left-half complex plane R+ = open right-half real axis g(s)/s = process transfer function c(s)/s = compensator transfer function p ( s ) , q(s) = polynomials in s ,
Literature Cited Grosdidier, P.; Morari, M.; Holt, B. R. Ind. Eng. Chem. Fundam. 1985,24, 221-235. Morari, M. IEEE Trans. Autom. Control 1985, AC-30, 574-577.
* Author to whom correspondence should be addressed. Pierre Grosdidier* Setpoint, Znc. 14701 St. Mary's Lane Houston, Texas 77079 Manfred Morari Chemical Engineering 210-41 California Institute of Technology Pasadena, California 91 125
Receiued for reuiew December 26, 1989 Accepted June 14, 1990
A New Disinfectant Compound A new compound, 1,3-dichloro-2,2,5,5-tetramethylimidazolidin-4-one (DC), has been synthesized and evaluated in a preliminary fashion as to its potential as a disinfectant, particularly in aqueous solution. T h e compound has been shown t o be considerably more stable in aqueous solution than free chlorine, both in the laboratory and in direct sunlight. T h e compound is biocidal a t low concentration and prevents the growth of algae. Since the preparation of DC is quite inexpensive, it should be an excellent candidate for replacement of free chlorine and other materials as disinfectants for large bodies of water such as swimming pools. For several years, work in these laboratories has been 0 ,C' progressing with a primary goal being the development of a new disinfectant compound to replace current sanitizers H H3C 3c&; such as free chlorine as biocides for aqueous solution I (potable water, swimming pools, hot tubs, cooling towers, CI etc.) and hard surface applications. In pursuing this goal, DC several organic N-halamine compounds in the oxazolidiquately biocidal, while retaining the desirable feature of none and 2-imidazolidinone classes have been synthesized long-term stability in water. This communication will and tested (Worley and Williams, 1988). These comreport preliminary stability and biocidal efficacy data for pounds were very stable, persistent biocides in aqueous this new disinfectant compound, which should become a medium (Worley et al., 1987), but they suffered the limwidely employed commercial sanitizing agent. itations of rather long times required for bacterial inactivation (at least for the N-chloramines) (Williams et al., Experimental Methods 1987) and relatively expensive preparation procedures (Barnela et al., 1987). However, we have now been able Compound DC was prepared in 85% yield by reacting 2,2,5,5-tetramethylimidazolidine-4-thione in basic solution to synthesize a new N-halamine disinfectant compound, 1,3-dichloro-2,2,5,5-tetramethylimidazolidin-4-one,a t 5 "C with chlorine gas until the pH of the solution reached 7.0. The product was extracted from the aqueous henceforth termed DC, whose structure is shown below. Compound DC is inexpensive to synthesize and is adesolution using hexane and recovered as a white solid by 0888-5885/90/2629-2161$02.50/0 1990 American Chemical Society
2162 Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990
evaporation of the hexane solvent. It could also be prepared by chlorination of 2,2,5,5-tetramethylimidazolidin4-one, but the chlorination of the thione saves a synthetic step (oxidation of the thione). The thione was prepared from acetone, sodium cyanide, ammonium sulfide, and ammonium chloride in a manner similar to that described by Christian (1957). Several types of preliminary testing procedures have been employed for the new compound including a measurement of its hydrolysis equilibrium constant, its stability in aqueous solution as a function of water quality, and its efficacy against bacteria and algae in aqueous solution. The hydrolysis equilibrium constant was measured for DC in buffered (pH 7.0) chlorine-demand-free water. In this experiment, solutions of 4.44 X and 1.76 X M total chlorine (expressed as total C1') were prepared at 24 "C. After the solutions were allowed to equilibrate while stirring for 1 h, the total and free chlorine concentrations were measured by using the DPD/FAS (N,N-diethyl-pphenylenediamine/ferrous ammonium sulfate) analytical method (American Public Health Association, 1985). The molar concentration of combined DC at equilibrium was taken to be the difference between the measured molar concentrations of total and free chlorine. The decomposition products for DC in the hydrolysis equilibrium were free chlorine (HOCl) and l-chlor0-2,2,5,5-tetramethylimidazolidin-4-one, a compound previously prepared elsewhere (Toda et al., 1972) to be used as a source of amino radicals in an ESR experiment, which could be detected by 'H NMR. Stability measurements for chlorine in DC and free chlorine (Ca(OC1)J were made as described previously (Worley et al., 1987) using standard iodometric titration (American Public Health Association, 1985) to determine total chlorine concentration. The solutions studied included pH 7.0 and pH 9.5 chlorine-demand-free water at 22 "C and a pH 9.5 water at 4 "C containing controlled synthetic demand (SDW). The SDW contained 375 mg/L of each of the salts NaC1, KCl, CaCl,, and MgC1,; 50 mg/L of Bentonite clay; 30 mg/L of humic acid; 0.01% final concentration of heat-treated horse serum; and 5 X lo5 cells/mL of heat-killed Saccharomyces cerevisiae yeast cells. The combination of high-pH, low-temperature, and heavy disinfectant demand represents a worst case disinfection scenario. The solutions were held in flasks stoppered with porous, sterile cotton plugs to allow free exchange with laboratory air. Aliquots were withdrawn periodically (at least weekly for the demand-free-water flasks and frequently over a 100-h period for the SDW flasks), and the total chlorine remaining was determined as noted above. The pH 7.0 study for demand-free water was repeated for solutions of DC and free chlorine exposed to direct sunlight (Aug 1988); the temperature for this experiment was held in the range 22-24 "C. T o demonstrate that DC is indeed a biocide, the compound was tested against the bacteria Staphylococcus aureus (ATCC 25923) and Pseudomonas aeruginosa (ATCC 27853) and the algal species Oscillatoria lutea, Anabaena cylindrica, and Chlorella pyrenoidosa in demand-free water. The procedures used in these laboratories for performing the bactericidal efficacy studies have been documented previously (Williams et al., 1987). The algae studies were performed using two 10-gal aquariums containing 35 L of Bristol's solution (Starr, 1978) at pH 6.8. The aquariums (one containing DC, the other a control) were continually aerated and illuminated by 20-W Gro-lux lamps to optimize algal growth. Absorbance at
f c
W DC.pH9.5 2 0 1 0, Ca(OC1)Z. , ,pH 9.5
n $
0
4-
al
.
0
200
. , . , . , 600
400
800
1000
,
,
1200
Time (hr)
Figure 1. Comparison of the stabilities of DC and free chlorine at 22 O C and pH 7.0 and 9.5 in demand-free water.
.-F .-
100
C
fiai
80
c
6o
m 9 m
40
'5
20
E al
X
a
g -
L
0 0
20
40
60
80
100
Time (hr)
Figure 2. Comparison of the stabilities of DC and free chlorine at pH 9.5, 4 "C, in synthetic demand water.
750 nm was used as a measure of algal turbidity (American Public Health Association, 1985).
Results and Discussion Compound DC is a white crystalline solid with a melting point range of 69-71 "C. Its solubility in water ranges from 0.138 g/100 mL at 3 "C to 0.224 g/100 mL at 37 "C. Spectroscopic data include 'H NMR (CC4) 1.36 (s, 6 HI, 1.50 (s, 6 H), and IR (KBr) 1720, 2950 cm-'. The hydrolysis equilibrium constant for DC, measured by the procedure outlined above, was (2.6 f 1.0) X This value is much lower than those reported for the commercial N-halamines with dichlorodimethylhydantoin (2.54 X and trichloroisocyanuric acid (1.6 X (Nelson, 1979), and thus DC should be expected to be far more stable in aqueous solution than the latter two commercial products. The value is a factor of 10 higher than that for 3-chloro-4,4-dimethyl-2-oxazolidinone, a very stable but slow-acting disinfectant studied extensively in these laboratories (Worley and Williams, 1988). Figure 1 shows that DC is clearly more stable than free chlorine in demand-free water at both pH 7.0 and 9.5 at 22 "C. More important, Figure 2 shows that DC has exceptional stability in the water (SDW) containing heavy chlorine demand. The difference in stability of DC and free chlorine in water exposed to direct sunlight is dramatically shown in Figure 3. It would appear that DC should function as an effective disinfectant for outdoor swimming pools. The results of biocidal efficacy testing of DC showed it to be an effective biocide. For a concentration of 5 mg/L total chlorine (expressed as CP), DC provided a 6 log reduction of S. aureus at pH 7.0,22 "C, demand-free water within 30 min and at pH 9.5, 22 "C, DFW within 5 min. Although a pH of 9.5 can be deleterious to bacteria over long contact times, control samples containing no disinfectant exhibited no significant declines in cfu/mL over
Ind. Eng. Chem. Res. 1990,29, 2163-2166
2163
and a free chlorine source simultaneously.
Sunlight Exposure (hr)
Figure 3. Comparison of the stabilities of DC and free chlorine at pH 7.0, 22-24 OC, in demand-free water in the presence of direct sunlight.
the contact times employed in these experiments. DC gave a 6 log reduction of P. aeruginosa at 5 mg/L total chlorine within 5 min at pH 7.0, 22 "C, DFW. A t heavy demand (SDW, pH 9.5, 4 "C), a 6 log reduction of S. Aureus was obtained in less than 4 h for a beginning concentration of 10 mg/L total chlorine from DC. It is well-known that S. aureus is a very resistant organism to disinfection by chlorination. Prior data for other N-halamine compounds developed in these laboratories, as well as for free chlorine, under the same experimental conditions as employed in this work have been reviewed recently (Worley and Williams, 1988). The results obtained for algae were impressive. As long as any measurable DC remained in solution, the algal concentration (asdetermined by absorption measurement at 750 nm) did not increase from zero. The experiments were run for sufficient time (over 20 days) such that the control aquarium showed heavy algal growth. It was also found that the algal concentration in an aquarium already containing heavy growth was decreased by 77% within 24 h upon addition of 10 mg/L total chlorine provided by DC. Thus, it would appear that DC will be useful for preventing algal growth in swimming pools and other large water sources. Finally, recent experiments in these laboratories have shown that DC can be formed rapidly (a few seconds) in situ if a free chlorine source such as Ca(OCl), is added to water containing 2,2,5,5-tetramethylimidazolidin-4-one, a precursor to laboratory synthesis of DC. Therefore, a possible means of disinfecting a large body of water such as a swimming pool would be the addition of the precursor
Conclusions The new N-halamine compound, 1,3-dichloro-2,2,5,5tetramethylimidazolidin-4-one(DC), which can be prepared inexpensively from the readily available materials acetone, NaCN, NH4C1, (NH4).$, and chlorine, is a stable compound in water that is effective as a biocide for vegitative bacteria and algae. It has not yet been tested against viruses,protozoa, and fungi. It should be especially useful for long-term disinfection of aqueous systems such as swimming pools, hot tubs, and cooling towers but could also have application for hard surfaces. Further testing is in progress, as well as the syntheses of derivatives of DC and brominated analogues. The results of these studies will be reported in due course. Registry No. DC, 128780-87-0. Literature Cited American Public Health Association. Standard Methods for the Examination of Water and Wastewater, 16th ed.; APHA Washington, DC, 1985; pp 306-309,950-954. Barnela, S. B.; Worley, S. D.; Williams, D. E. Syntheses and Antibacterial Activity of New N-Halamine Compounds. J . Pharm. Sci. 1987, 76, 245-247. Christian, J. D. 4-Imidazolidinethiones. J . Org. Chem. 1957, 22, 396-399. Nelson, G . D. Chloramines and Bromamines. in Kirk-Othmer Encyclopedia of Chemical Technology, 3rd ed.; Wiley Interscience: New York, 1979; p 565. Starr, R. C. The Culture Collection of Algae at the University of Texas. J. Phycol. 1978, 14, 47-100. Toda, T.; Mori, E.; Horiuchi, H.; Murayama, K. Studies on Stable Free Radicals. X. Photolysis of Hindered N-Chloramines. Bull. Chem. SOC.Jpn. 1972,45, 1802-1806. Williams, D. E.; Worley, S. D.; Barnela, S. B.; Swango, L. J. The Bacterial Activities of Selected Organic N-Halamines. Appl. Environ. Microbiol. 1987, 53, 2082-2089. Worley, S. D.; Williams, D. E. Halamine Water Disinfectants. CRC Crit. Rev. Environ. Control 1988, 18, 133-175. Worley, S. D.; Williams, D. E.; Barnela, S. B. The Stabilities of New N-Halamine Water Disinfectants. Water. Res. 1987,21,983-988.
Te-Chen Tsao, Delbert E. Williams, S. Davis Worley* Department of Chemistry Auburn University Auburn University, Alabama 36849 Received for review February 14, 1990 Accepted July 10, 1990
When To Use Cascade Control A comparative study of cascade versus feedback control of single-input, single-output (SISO) systems has been made. The primary and secondary processes are represented by first-order with dead-time models. T h e results show the relative benefits due to cascade control vis-&vis feedback control for varying process parameters. They can be used to decide when t o specify cascade control. Finally, tuning charts are presented for designing the primary controller of the cascade control system. It is believed t h a t the material in the paper will be useful t o those who are interested in the design and implementation of cascade control systems.
Introduction Cascade control is used to improve the dynamic response of a feedback control loop to disturbances in the manipulated variable. It is important for the designers to know when to specify cascade control and what improvements can be expected, say, in terms of ITAE (integral of time 0888-5885/90/2629-2163$02.50/0
X absolute error), vis-&vis feedback control, since the choice of cascade control requires an additional measurement device/transmitter and an additional controller. Information in the published literature on the relative benefits of cascade control appears to be rather limited. Among the relevant works is that of Harriott (1964), who
0 1990 American Chemical Society
