Gain vs. Proportional Band

Transcription

1 Gain vs. Prprtinal Band The end result f the analysis f a typial lp tuning predure, whether pen lp r lsed lp, is a set f parameters with whih t adjust the ntrller. One f these parameters is ntrller gain. But what if yur ntrller has its gain slider labeled and alibrated as perent prprtinal band? Nt a prblem. Just take the reipral f gain and multiply by 100, right? Nt neessarily. The fllwing relatinship between gain and perent prprtinal band is well knwn. 100 %PB = Gain Hwever, what is nt well knwn is the fat this relatinship is based upn the assumptin the input and utput ranges f the ntrller are equal. In ther wrds, assume yu have an eletrni ntrller with an input range f 4-20 and an utput range f Further assume the ntrller is driving an eletrni atuatr with a full strke that urs with an input signal (t the atuatr) f In suh a ase, the abve relatinship hlds true. But what abut the fllwing ases: An eletrni ntrller driving an eletrni atuatr where the signal neessary t d s is nly a perentage f the utput range f the ntrller. An eletrni ntrller driving a pneuti atuatr thrugh an I/EP valve A pneuti ntrl system In these ases, the gain and perent prprtinal band are nt neessarily reiprals as generally stated in the typial textbk. We will address these situatins by example later. Fr nw, let's determine hw t nvert frm gain t perent prprtinal band in the general ase. T d s, we need t review the definitins f gain, prprtinal band, and perent prprtinal band. Gain: The rati f the hange in utput signal t the hange in input signal defines ntrller gain. As an example, suppse yu have a ntrller that aepts a 4-20 urrent signal and prvides a 4-20 utput signal. Further assume yu apply a step hange f 2 t the input terminals f the ntrller and yu measure a hange f 5 at the utput terminals. The ntrller gain is then: 5 K = = 2.5 2

2 Prprtinal Band: The amunt f hange in the ntrlled variable, expressed in engineering units, required t mve the atuatr frm ne end f its strke t the ther. This is als referred t as thrttling range. %PB: Perent prprtinal band is the prprtinal band expressed as a perentage f the sensr span. It is smetimes alled perent thrttling range (%TR). Fr example, if yu had a rm temperature press with a thrttling range f 5 F and a sensr with a range f 60 t 85 F, then the perent prprtinal band wuld be: 5 F 100% % PB = = 20% F ( 85 60) Using these basi definitins, let's nsider three separate ntrllers. Eah ntrller aepts a 4-20 input signal. Hwever, ne has an utput apability f 4-20, anther utputs 4-16, while a third utputs Input Cntrller Output Sensr Cntrller A Cntrller B Cntrller C Figure 1 Assume eah ntrller has a perent prprtinal band slide and this slide is set t 100% n eah ntrller. By definitin, a 100% prprtinal band means the thrttling range equals the sensr span. Sine the entire sensr span is als the thrttling range, it fllws that as the input signal is stepped by 100%, the ntrller utput will als hange 100%. Nte that in eah ase, even thugh the %PB is the same in eah ase, the hange in utput is quite different. This is beause eah has a different utput range. The gain fr eah ntrller is als quite different. The bserved gain fr eah ntrller is as fllws: Cntrller A: K = = 1.0 Cntrller B: K ( 16 4) = = 0.75

3 Cntrller C: K ( 12 4) = = 0.50 Obviusly, nly the first value f gain is the reipral f the ntrller s perent prprtinal band setting while the ther tw are nt. In rder t determine the prper prprtinal band setting frm the value f gain fr ntrllers B and C, we must nrlize the ntrller utput t the ntrller input as fllws: 100% Atuatr Span % PB = K Input Span S we an nw alulate the %PB fr eah f the abve three ntrllers as fllws: Cntrller A: Cntrller B: Cntrller C: 100% % PB = = 100% ( 16 4) 100% % PB = = 100% ( 12 4) 100% % PB = = 100% Fr illustratin, the abve examples assumed the atual utput f the ntrller was limited t smething less than Of urse, the typial eletrni ntrller always has an utput range equal t its input range, bth f whih are standardized t sme standardized press signal (i.e.: 4-20, 0-5 vlt, 0-50 mv, et.) Hwever, when 16 Open Cntrller TR=20 0 SP= F T Output Signal N.C. 6 Clsed Input Signal Figure 2 Cntrl lp and ntrl diagram fr example prblem

4 an end-devie requires an input urrent (r vltage) range less than the utput apability f the ntrller, the result is the same as desribed abve. Fr example, shwn belw is a single lp eletrni ntrller reeiving a signal frm a 70 t 150 F temperature sensr. The sensr utputs 4-20 ver its sensing range. Althugh the ntrller is apable f an utput f 4-20, the atuatr strkes the nrlly lsed heating valve full lsed t full pen with a 6-16 input signal. Using the fundamental definitin f gain, we an define ntrller gain by expressing the entire prprtinal band (ntrller input) in terms f urrent and the ntrller utput as 6 t 16. Then: Gain = ( 16 6) ( 14 10) Realizing the input and utput ranges are nt equal, we an alulate the %PB as fllws: ( 16 6) 100% % PB = = 25% The abve example assumed an eletrni atuatr with an input range less than that f the ntrller utput range. What is mre mmn is the use f an I/P r E/P valve driving a pneuti atuatr. In mst ases, the I/P r E/P transduer will utput a 3-15 psi signal with a 1-5 v, a 2-10 v, r a 4-20 signal. Hwever, the I/P (E/P) generally drives an atuatr with a spring range less than the ximum utput range f the I/P (E/P). In suh a ase, the effetive utput f the ntrller is redued. This results in an analysis virtually idential t the abve analysis. 21 IP 3-9 psi Cntrller TR=20 0 SP= F T Take, fr example, the abve system, but replae the eletrni valve atuatr with an I/P and a 3-9 psi pneuti valve atuatr. A typial I/P will utput a 3-15 psi pressure with a 4-20 input urrent. The 3-9 psi atuatr has a 6 psi span and represents 50% f the utput apability f the I/P. It is easily shwn that the rrespnding ntrller utput is This is idential t Cntrller 'C' in the abve example. In ther Figure 3 Example ntrl lp with I/P and pneuti valve wrds, the rati f the effetive ntrller utput t the ntrller input is ½. Thus, the

5 reipral f gain must be multiplied by this rati t btain a prper %PB setting. Pneuti Cntrllers Pneuti ntrllers are handled in a similar fashin, but there is ne jr differene between pneutis and eletrnis. The pneuti ntrller is pwered with a mpressed air sure with a line pressure usually smewhere between 18 and 25 psi. This mpressed air sure is als the sure f pwer fr pneuti transmitters (similar t eletrni lp pwered transmitters). It is als the sure f pwer fr atuatrs if the atuatr is equipped with a pilt psitiner. In the end, the utput apability f any pneuti ntrller will be 0 psi t line pressure. Sine line pressure is smewhat variable, the utput range f any given ntrller will als be variable. Hwever, even if line pressure was standardized suh that the utput range f the pneuti ntrller was nstant, pneuti atuatrs are available with varying spring ranges. Thus the effetive utput f any ntrller is dependent upn the seletin f the atuatr. The adjustment f mst pneuti ntrllers is via a slider r a rtary knb alibrated in perent prprtinal band. Remember that prprtinal band is defined as: "The amunt f hange in the ntrlled variable..." This is a temperature, pressure, r humidity range, in engineering units, ver whih we wish t ntrl. But this y be expressed as a pressure hange in sensr utput rather than engineering units. In ther wrds, a hange in [ntrller] input pressure. "...required t run the atuatr ver its full strke." In ther wrds, ver the atuatr spring range expressed in units f pressure. This means a hange in [ntrller] utput pressure. This means the utput range f all pneuti ntrllers wuld have t be standardized s the nufaturer an prvide a alibrated prprtinal band sale indexed t this standard utput. Herein lies the prblem; nufaturers never agreed upn a single standard ntrller utput. Every nufaturer alibrates their ntrller based upn their idea f what this shuld be. Table 1 lists standard utputs adpted by sme nufaturers fr sme f their ntrller mdels. Hwever, if we knw what this standard utput range is, we an use it t rewrite the equatin fr perent prprtinal band by indexing the sensr t bth the ntrller utput range and the atuatr range as fllws:

6 Prprtinal Band Std. Cntrller Output % PB = 100% Sensr Span Atuatr Spring Range MANUFACTURER Pwers Hneywell Barber Cln Rbertshaw Kreuter STANDARD OUTPUT 5 psi 10 psi 10 psi 12 psi 12 psi Table 1 Standard Cntrller Outputs If we use the previus example, we nte the sensr has a range f 70 F F (80 F span). The thrttling range is 20 F and the atuatr has a 6 psi spring span. We an determine the value f ntrller gain as fllws. ( 15 3) psi psi Sensr Sensitivity = = F F psi Prprtinal Band ( in psi) = F = 3 psi ( Cntrller input) F Cntrller Output = Spring Range = 9 3= 6psi 6 psi Cntrller Gain = = 2 3psi This value f gain is rret regardless f the ntrller being used. Hwever, we must nw nvert this t a prprtinal band setting fr ur partiular ntrller. Using the abve equatin fr %PB, as develped fr pneuti ntrllers, we an determine the rret value f %PB t whih we must set eah ntrller in rder t btain the desired value f gain. Using the standard utputs listed in Table 1. (Pwers) (Hneywell) (Barber Cln) (Krueter) (Rbertshaw) 20 F 5 psi % PB = % 80 F 6 psi = = 20 F 10 psi % PB = % 80 F 6 psi = = 20 F 12 psi % PB = % 80 F 6 psi = = Nte the reipral f the perent prprtinal band thes the gain alulatin nly in the last ase when the standard ntrller utput is equal t the input span.