The tuning of level controllers can be challenging becauseof the extreme variation in the process dynamics and tun-ing settings. Control systems studies have shown that themost frequent root cause of unacceptable variability in theprocess is a poorly tuned level controller. The most com-mon tuning mistake is a reset time (integral time) and gainsetting that are more than an order of magnitude too small. In this article we ﬁrst provide a fundamental understand-ing of how the speed and type of level responses varies withvolume geometry, fluid density, level measurement spanand flow measurement span for the general case of a ves-sel and the more speciﬁc case of a conical tank. Next weclarify how tuning settings change with level dynamics andloop objectives. Finally, we investigate the use of an adap-tive controller for the conical tank in a university lab anddiscuss the opportunities for all types of level applications.General Dynamics for vessel LevelThere have been a lot of good articles on level control dy-namics and tuning requirements. However, there often aredetails missing on the effect of equipment design, processconditions, transmitter calibration and valve sizing thatare important in the analysis and understanding. Here weoffer a more complete view with derivations in AppendixA, available on the ControlGlobal website (www.control-global.com/1002_LevelAppA.html). Frequently, the flows are pumped out of a vessel. If weconsider the changes in the static head at the pump suc-tion to have a negligible effect on pump flow, the dischargeflows are independent of level. A higher level does not forceout more flow, and a lower level does not force out less flow.There is no process self-regulation, and the process has an
LeveL Normally, the denominator of the integrating pro- cess gain that is the product of the density ( ), cross-sec- tional area (A) and level span (mass holdup in the control range) is so large compared to the flow rate that the rate of change of level is extremely slow. For horizontal tanks or drums and spheres, the cross-sectional area varies with level. In these vessels, the integrating process gain is low- est at the midpoint (e.g. 50% level) and highest at the op- erating constraints (e.g. low- and high-level alarm and trip points). Most people in process automation realize that a con- troller gain increased beyond the point at which oscil- lations start can cause less decay (less damping) of the oscillation amplitude. If the controller gain is further in- creased, the oscillations will grow in amplitude (the loopFigure 1. Conical Tank in MIT Anna University Lab with becomes unstable). Consequently, an oscillatory responsean industrial DCS. is addressed by decreasing the controller gain. What most don’t realize is that the opposite correction is more likelyintegrating response. There is no steady state. Any unbal- needed for integrating processes. Most level loops areance in flows in and out causes the level to ramp. When the tuned with a gain below a lower gain limit. We are fa-totals of the flows in and out are equal, the ramp stops. For miliar with the upper gain limit that causes relatively fasta setpoint change, the manipulated flow must drive past the oscillations growing in amplitude. We are not so cogni-balance point for the level to reach the new setpoint. If we zant of the oscillations with a slow period and slow decayare manipulating the feed flow to the volume, the feed flow caused by too low of a controller gain. The period andmust be driven lower than the exit flow for a decrease in decay gets slower as the controller gain is decreased. Insetpoint. The ramp rate can vary by six orders of magnitude other words, if the user sees these oscillations and thinksfrom extremely slow rates (0.000001%/sec) to exceptionally they are due to too high a controller gain, he or she mayfast rates (1%/sec). The ramp rate of level in percent per sec- decrease the controller gain, making the oscillationsond for a 1% change in flow is the integrating process gain worse (more persistent). In the section on controller tun-(%/sec/% = 1/sec). The integrating process gain (Ki ) for this ing, we will see that the product of the controller gaingeneral case of level control, as derived in Appendix A, is: and reset time must be greater than a limit determined by Ki = Fmax / [( * A) L max ] Eq. 1 Since the PID algorithm in nearly all industrial con- Conical tanktrol systems works on input and output signals in percent,the tuning settings depend upon maximums. The flowmaximum (Fmax) and level maximum (Lmax) in Equation r1 must be in consistent engineering units (e.g. meters forlevel and kg/sec for flow). The maximums are the mea- h Variable- ow pumpsurement spans for level and flow ranges that start at zero. FmaxMost of the published information on process gains doesnot take into account the effect of measurement scalesand valve capacities. The equation for the integrating Hand valveprocess gain assumes that there is a linear relationshipbetween the controller output and feed flow that can beachieved by a cascade of level to flow control or a linearinstalled flow characteristic. If the controller output goesdirectly to position a nonlinear valve, the equation should Reservoirbe multiplied by the slope at the operating point on theinstalled characteristic plotted as percent maximum ca-pacity (Fmax) versus percent stroke. Figure 2. Conical tank detail.
LeveL standards, interfaces and tools. The DCS allows graduate students and professors to explore the use of indus- try’s state-of-the-art advanced control tools. Less recognized is the oppor- tunity to use the DCS for rapid pro- totyping and deployment of leading edge advances developed from uni- versity research. The conical tank with gravity f low introduces a severe nonlinearity from the extreme changes in area. The de- pendence of discharge f low on the square root of the static head cre- ates another nonlinearity and nega- tive feedback. The process no longerFigure 3. Performance of linear PID level controller for a conical tank. has a true integrating response. In Appendix A online ( www.control- global.com/1002_LevelAppA.html),the process gain to prevent these slow must be increased to prevent slow os- the equations for the process timeoscillations. cillations. constant ( p) and process gain (K p) In some applications, exception- Adaptive level controllers can not are developed from a material bal-ally tight level control, through en- only account for the effect of ves- ance applicable to liquids or solids.forcement of a residence time or a sel geometry, but also deal with The equations are approximationsmaterial balance for a unit operation, the changes in process gain from because the head term (h) was notis needed for best product quality. changes in f luid density and non- isolated. Since the radius (r) of theThe quantity and quality of product linear valves. Even if these nonlin- cross-sectional area at the surfacefor continuous reactors and crystal- earities are not significant, the adap- is proportional to the height of thelizers depend on residence times. tive level control with proper tuning level as depicted in Figure 2, it is ex-For fed-batch operations, there may rules removes the confusion of the pected that the decrease in processbe an optimum batch level. The allowable gain window, and prevents time constant is much larger thanvariability in column temperature the situation of level loops being the decrease in process gain with athat is an inference of product con- tuned with not enough gain and too decrease in level.centration in a direct material bal- much reset action.ance control scheme depends on the * r2tightness of the overhead receiver Speciﬁc Dynamics for Conical Tank Level p = * h1/2 3*Clevel control. Since these overhead Conical tanks with gravity discharge Eq. 2receivers are often horizontal tanks, flow are used as an inexpensive way toa small change in level can represent feed slurries and solids such as lime, h1/2 * Fmax Kp =a huge change in inventory and ma- bark and coal to unit operations. The C * L maxnipulated ref lux f low. conical shape prevents the accumu- Eq. 3 In other applications, level control lation of solids on the bottom of thecan be challenging due to shrink and tank. The Madras Institute of Tech- Controller Tuning Rulesswell (e.g. boiler drums and column nology (MIT) at Anna University in The lambda controller tuning rulessumps) or because of the need for Chennai, India, has a liquid conical allow the user to provide a closed-the level to float to avoid upsetting tank controlled by a distributed con- loop time constant or arrest timethe feed to downstream units (e.g. trol system (DCS) per the latest inter- from a lambda factor ( f) for self-reg-surge tanks). If the level controller national standards for the process in- ulating and integrating processes, re-gain is decreased to reduce the reac- dustry as shown in Figure 1. The use spectively. The upper and lower con-tion to inverse response from shrink of a DCS in a university lab offers the troller gain limits are a simple fall outand swell or to allow the level to float opportunity for students to become of the equations and can be readilywithin alarm limits, the reset time proﬁcient in industrial terminology, enforced as part of the tuning rules
LeveLin an adaptive controller. An adaptive controller integrated into the DCS was used to For a self-regulating process the controller gain (Kc) and automatically identify the process dynamics (process model) forreset time (Ti) are computed as follows from the process gain the setpoint changes seen in Figure 3. The adaptive controller(K ), process time constant and process dead time ( p): employs an optimal search method with re-centering that ﬁnds the process dead time, process time constant, and process gain Ti that best ﬁts the observed response. The trigger for process iden- Kc = tiﬁcation can be a setpoint change or periodic perturbation au- Kp * ( * + ) f p p Eq. 4 tomatically introduced into the controller output or any manual change in the controller output made by the operator. Ti = p The process models are categorized into ﬁve regions as Eq. 5 indicated in Figure 4. The controller gain and reset settings computed from the lambda tuning rules are then automati- The upper gain limit to prevent fast oscillations occurs cally used as the level moves from one region to another.when the closed loop time constant equals to the dead time. This scheduling of the identiﬁed dynamics and calculated tuning settings eliminates the need for the adaptive control- p Kc < Kp * 2 * p Eq. 6 For an integrating process the controller gain (Kc) andreset time (Ti) are computed as follows from the integratingprocess gain (Ki) and process deadtime ( p): Ti Kc = Ki * [( f /Ki) + p ]2 Eq. 7 Ti = 2 * ( f /Ki ) + p Eq. 8 The upper gain limit to prevent fast oscillations occurswhen the closed loop arrest time equals the dead time: Figure 4. Process models automatically identi ed for operat- ing regions. 3 Kc < Ki * 4 * p Eq. 9 The lower gain limit to prevent slow oscillations occurswhen the product of the controller gain and reset time istoo small. 4 Kc * Ti > Ki Eq. 10Opportunities for Adaptive Control of Conical Tank LevelA linear PID controller with the ISA standard structure wastuned for tight level control at 50% level for a detailed dy-namic simulation of the conical tank. Figure 3 shows thatfor setpoints ranging from 10% to 90%, a decrease in processtime constant greater than the decrease in process gain at Figure 5. Performance of adaptive PID level controller forlow levels causes excessive oscillations. conical tank.