Self-tuning adaptive control for an industrial weigh belt feeder

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ISATRANSACTIONS®

ISA Transactions 42~2003! 437–450

Self-tuning adaptive control for an industrial weigh belt feed

Yanan Zhao,* Emmanuel G. Collins, Jr.,† David A. Cartes‡

Department of Mechanical Engineering, Florida A&M University–Florida State University, Tallahassee, FL 32310, USA

~Received 20 December 2001; accepted 26 June 2002!

Abstract

An industrial weigh belt feeder is used to transport solid materials into a manufacturing process at a cfeedrate. It exhibits nonlinear behavior because of motor friction, saturation, and quantization noise in the meassensors. To overcome the nonlinearities, a simple yet effective method of controller autotuning, an indirect selregulator, was designed and implemented for an industrial weigh belt feeder. Implementation issues are discuexperimental results show the effectiveness of the adaptive controller for several different reference inputs. Aperformance of the indirect self-tuning regulator is compared with that of a fuzzy logic controller for theapplication. © 2003 ISA—The Instrumentation, Systems, and Automation Society.

Keywords: Adaptive control; Recursive least-squares method; Pole placement; Self-tuning regulator; Weigh belt feeder

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1. Introduction

An industrial weigh belt feeder~see Fig. 1! isdesigned to transport solid materials into a manfacturing process at a constant feedrate, usuallkilograms or pounds per second. The weigh bfeeder used in this research was designedmanufactured by Merrick Industries, Inc. of LynHaven, Florida and is a process feeder that is tycally used in a food, chemical, or plastics manfacturing process. To ensure a constant feedratindustrial operation, a PI control law is designand implemented in the Merrick controller. In curent practice the PI tuning process is performmanually by an engineering technician. Howevfor better and more consistent quality, it is desirto use automated PI tuning@1#.

The dynamics of the weigh belt feeder are domnated by the motor. To protect the motor, the co

*E-mail address: [email protected]†E-mail address: [email protected]‡E-mail address: [email protected]

0019-0578/2003/$ - see front matter © 2003 ISA—The Instru

trol signal is restricted to lie in the interval@0,10#V. The motor also has significant friction. In addtion, the sensors~which include an optical encodeand a strain gauge load cell! exhibit significantquantization noise. Hence the weigh belt feedexhibits nonlinear behavior in the parameters@1#.To demonstrate this nonlinearity, the step rsponses of the closed-loop system with a PI cotroller, H(z)5Kp1Ki (T/2)(z11)/(z21) withKp51.4, Ki51.2 and sampling period T50.01 sec,are given for setpoints of 1,2, . . . ,5 V~1 V corresponds to a belt speed of 1 ft/min!, re-spectively. It is clearly shown in Fig. 2~a! that witha fixed PI controller, the damping characteristiof the closed-loop system change with the spoint. For setpoints greater than 2, this nonlineresponse leads to significant overshoot, as seeFig. 2~b!. Also, because of the sensor noise, toutput signals shown in the Fig. 2 are not smooIn addition, actuator saturation occurs in the sytem for setpoints above 4 V.

Transient performance of the weigh belt feedaffects both the quality of the manufactured pro

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438 Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450

uct and the efficiency of the manufacturing prcess. For example, large overshoot can be a diter when a weigh belt feeder is used to produclime slaker. A lime slaker takes pebble lime amixes it with water to make a lime paste. Thpaste is used forpH control in water treatmentOvershoot causes too much lime to be presenthe lime slaker and the paste becomes concrSettling time is also an important issue when feeing materials into boxes since a longer settlitime requires the material in the initial boxes todiscarded or reprocessed.

A traditional and simple way to overcome thmotor friction is to use a dither signal, such thahigh frequency signal is added to the control snal @2#. But, the improved performance of the sytem is at the expense of reduced product life. Alfor the weigh belt feeder, the added signalcreases the chance of motor saturation. Currenmost friction compensation methods useobserver-based friction scheme which requires

Fig. 1. The Merrick weigh belt feeder.

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lecting a friction model and adding a feedforwafriction observer in the loop. The control signalthen composed of both the signal for the linesystem which results from neglecting the frictioand the signal to remove the friction@2,3#. Theperformance of this kind of model-based compesation relies on the accuracy of the friction moeling. In reality, friction force characteristics arnot perfectly known and vary due to a varietyfactors. Adaptive friction compensation methoprovide a mechanism for adjusting friction modparameters to cope with this uncertainty@2#.

Instead of using a model-based friction compesation method, non-model-based control aproaches were chosen to control the feedratethe weigh belt feeder. This avoids the substaneffort needed for system modeling. Fuzzy logiccontrollers were previously designed for the weibelt feeder@4#. This paper considers the designa simple self-tuning regulator, which is less computationally expensive than a fuzzy PI controlle~Off-line tuning of a PI controller using unfalsifiedcontrol design is described in Ref.@1#.!

The self-tuning regulator has received considable attention because it is flexible, easy to undstand, and easy to implement with microprocesors@5–9#. This method has also been studiedseveral industrial applications@10–13#. In this pa-per, the designed self-tuning regulator is a comnation of the recursive least-squares method apole placement design. No specific recursive prameter estimator is uniformly the best. Leasquares estimation is one of the simplest recurs

Fig. 2. Nonlinear performance of the weigh belt feeder.

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439Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450

estimations schemes@7,14#. In addition, poleplacement is one of the most popular design meods in adaptive control due to its simplicity anthe implications of the solution on the stability antime response of the system@15,16#.

The remainder of this paper is organized as flows. Section 2 discusses indirect self-tuning reglator design. Section 3 describes the experimesystem. Section 4 presents implementation resfor the weigh belt feeder. Section 5 comparesindirect self-tuning regulator with a fuzzy logicontroller. Finally, Section 6 gives some conclsions.

2. Indirect self-tuning regulator

In this section, the indirect self-tuning regulatdesign algorithm is briefly introduced. It is a combination of a recursive least-squares on-line emation algorithm and a pole placement control dsign method.

Suppose a process is described by the sininput, single-output~SISO! system,

A~q!y~k!5B~q!u~k!, ~1!

wherey is the output,u is the control input, andAandB are polynomials in the forward shift operator q. This model can be expressed as

y~k!52a1y~k21!2a2y~k22!

2 ¯ 2any~k2n!1b0u~k2d0!

1 ¯ 1bmu~k2d02m!, ~2!

whered0 is the pole excess which represents tinteger part of the ratio of the time delay and sapling period. The corresponding regression mois given by

y~k!5wT~k!u, ~3!

where

uT5@a1 a2 ¯ an b0 ¯ bm#, ~4!

wT~k!5@2y~k21! ¯ 2y~k2n!

u~k2d0! ¯ u~k2d02m!#. ~5!

The recursive least-squares~RLS! algorithm forthe estimation ofu is given by@7#

u~k!5 u~k21!1L~k!e~k!, ~6!

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3@11wT~k!P~k21!w~k!#21, ~8!

P~k!5@ I 2L~k!wT~k!#P~k21!. ~9!

For implementation of the RLS algorithm, the intial conditions of the parameter estimate vectoruand the covariance matrixP must be provided.

A general linear controller can be described b

R~q!u~k!5T~q!r ~k!2S~q!y~k!, ~10!

wherer is the setpoint, andR(q), S(q), andT(q)are polynomials.~Below, for simplicity of notationthe indiceq is omitted.! To obtain expressions foR, S, andT, the minimum-degree pole placeme~MDPP! algorithm is used; see Refs.@7,15# fordetails. A reference model is needed for the algrithm which can be represented by the followinform:

ym~k!5Bm~q!

Am~q!r ~k!. ~11!

3. Experimental system

The weigh belt feeder used in this research itypical process feeder that can be used in a fochemical, or plastics manufacturing process. Thare two sensors used to measure the systemdrate. One of them is a 1000-pulse-per-revolutioptical encoder. It is mounted on the tail pulleythe feeder and is used to measure the distancebelt has travelled. By taking the first derivativethe belt travel, the belt speed in m/sec is obtainThe second sensor is a weigh deck mounted oprecision strain gauge load cell to weigh the mterial. This directly gives a belt load that is mesured in kg/m. The feedrate is calculated by mtiplying the belt speed and the material load on tbelt. This product provides a feedrate in kg/sec.this research, all of the experiments were coducted under a constant belt load. Thus in the flowing sections, only control of the belt speedconsidered.

The data measured from the sensors are pcessed first through anMC3 controller@17# beforethey are sent to the computer. TheMC3 controlleris a product of Merrick Inc. developed for the cotrol of process weighing equipment. In this expe

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ment we only used it to preprocess the sampdata while the control algorithm was implementusing a PC. Inside theMC3 controller the mea-sured data are filtered by a built-in IIR~infiniteimpulse response! filter mechanism.

To control the feedrate, the feeder has a shuwound dc motor and a silicon controlled rectifi~SCR! motor controller combination. The motorcoupled to the head pulley of the feeder througreducer and chain drive combination. The bspeed and hence the overall system feedratcontrolled by varying the rotational rate of the mtor. The plant in Fig. 3 presents a schematic dscription of the feeder.

To run the hardware-in-the-loop experimenREALoop, a software and hardware kit froXANALOG Corp. @18# was used. REALoop hardware includes D/A and A/D I/O boards for thcomputer ISA bus. Its software is a singSIMULINK @19# block with its own dialog box,which can be dragged into anySIMULINK blockmodel. In this dialog box the user may define treal-time sample time and indicate the numberPC A/D and D/A board channels to communicawith the real world. ASIMULINK S-function wasbuilt to implement the self-tuning regulator algorithm. Fig. 3 illustrates the feedback loop fosimulation of the self-tuning regulator.

4. Implementation for the weigh belt feeder

In this section the adaptive control algorithproposed above is implemented for the weigh bfeeder. Several implementation issues are dcussed and experimental results are presented

4.1. Proposed self-tuning controller

The dynamics of the weigh belt feeder are domnated by the dc motor. The order of the dynammodel of the weigh belt feeder must be determinto use pole placement design. A simple mode

Fig. 3. Feedback loop for the simulation of the digitalimplemented controller.

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preferred to reduce the on-line parameter estimtion effort. The open-loop step response was tesand a representative step response is shown in4. First-order system can reasonably approximthe observed step responses.~The significant delayis caused by the friction.! Thus the plant model isassumed to be of the form~1! with

A~q!5q1a1 , B~q!5b0 . ~12!

Then, u5@a1 b0#T is the parameter vector to bestimated.

For simplicity, the reference model was chosas the first-order model,

H~q!5bm0

q1am1. ~13!

In particular the continuous-time reference modwas chosen asH(s)5 1/(0.03s11), correspond-ing to a time constant of 0.03 sec which is a faresponse for the weigh belt feeder. By discretizithis model at a sample periodT50.01 sec,thediscretized model is H(q)5 0.2835/(q20.7165). Hence am1520.7165 and bm050.2835in Eq. ~13!.

Based on the MDPP algorithm for the casewhich all process zeros are canceled, in Eq.~10!R51, S5 (am12a1)/b0 and T5bm0 /b0 . Hencethe control law becomes

u5T

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4.2. Initial values of the estimated parametersuand the covariance matrixP

Before the above MDPP algorithm can bimplemented for the weigh belt feeder the initivalues ofu andP need to be selected. The initiavalue ofu affects the transient performance of thclosed-loop system. For the case of the weigh bfeeder, unsuitable initial values ofu can even leadto motor saturation. The initial value ofP affectsthe convergence of the estimated parametersthus also affects the transient performance ofweigh belt feeder. To achieve better transient pformance and to protect the motor from saturatiboth the initial values ofu andP must be chosencarefully.

Controllers were designed for setpoints of 1. . . ,5 V, where 1 V corresponds to a belt speed


Fig. 4. Open-loop response of the weigh belt feeder.

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5.0831023 m/sec~1 ft/min!, and 5 V is the maxi-mum possible value of the reference commaDue to the nonlinearity of the feeder, these initvalues will be different for different setpoints. Iparticular, u05@a1

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and sp stands for the setpoint. Considering tlinear control law described by Eq.~14!, thesechoices ofu0 set the initial control signalu(0) to2.6, 3, 3.3, 3.5, and 3.6 V, respectively at the fidifferent setpoints. This choice is needed for twreasons: first, the control signal should be benough to overcome the friction of the motowhich can lead to a significant time delay in thclosed-loop system response; second, a suitinitial control signal is needed to obtain good trasient performance.

The initial value of P was chosen asP50.000 12* I 2 at each setpoint, whereI 2 standsfor the two-by-two identity matrix. These choicewere made to achieve transient responses withrise times and small overshoot and to avoid mosaturation. Larger initial values ofP were tried,but they led to large initial transients in the esmate of the parameter ofb0 such thatb0 became a

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very small number, and thus either caused mosaturation or large overshoot. Smaller initial vaues of P led to a slower system response. Sinthe dc gain of the plantb0 /(11a1) is proportionalto b0 , the indicated choices ofP restricted theestimated dc gain to suitable values.

4.3. Experimental results

In this subsection, the experimental performanof the proposed self-tuning regulator is first showfor five different setpoints. Next, the experimentperformance with a variable magnitude pulse inpis shown.

4.3.1. Step inputFigs. 5–9 show the experimental results of t

controller at the five different setpoints. It is seethat in each case, the controller performed vewell. Each of the responses have small overshofast response and no steady state error.

Figs. 10 and 11 show the parameters estimatof a1 andb0 at the setpoints 1 and 5 V. The valueof the converged estimated parameters obtainefive different setpoints are listed in Table 1. Eve


Fig. 5. Performance of the self-tuning regulator at setpoint51 V.







Fig. 10. Estimation of the plant model parameters at setpoint51 V.


Fig. 11. Estimation of the plant model parameters at setpoint55 V.

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though the estimated values of the parametersnot necessarily the true values, these valuesrepresent the trend of the parameter changes.seen that at different setpoints the estimated valof a1 and b0 both increased as the setpoint icreased. An increase ina1 , which was alwaysnegative, indicates a faster response, whilecombined effects of increasinga1 andb0 indicatesan increase in the plant dc gain.

4.3.2. Pulse inputTo show the performance of the self-tunin

regulator design, a pulse input was also testedthe weigh belt feeder. The pulse input had a perof 40 sec, a duty cycle of 80% period, and a va

Table 1The estimated parameters for different setpoints.

Setpoint a1 b0 dc gain

1 20.7160 0.0949 0.33422 20.7086 0.1434 0.49213 20.6980 0.1754 0.58084 20.6868 0.1991 0.63575 20.6714 0.2207 0.6716

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able pulse magnitude of 2, 4, 1, and 3 V sequetially. ~See the reference signals in Figs. 12 a13.!

Due to the nonlinearity of the weigh belt feedethe plant model parameters change abruptly wan abrupt change in the reference magnituWhen the self-tuning regulator was used for sucases, the on-line parameter estimation took csiderable time to estimate the new model paraeters. As illustrated in Fig. 12, this lead to potransient performance such as large overshootmotor saturation, which is undesirable. Thus tinitial values of the estimated parametersu and thecovariance matrixP were reset when the referencjumps from zero to a new magnitude level. Fig. 1shows the performance of the adaptive controwhenu andP were reset to the corresponding vaues at different magnitudes.

4.3.3. Load disturbancesVariations in the open-loop system response u

der various step inputs were observed as the lwas increased to four times the weight of the nmal load. As illustrated by Fig. 14, the step rsponses varied very little even when the weight


Fig. 12. Performance of the self-tuning regulator for a variable magnitude pulse input without reset.

Fig. 13. Performance of the self-tuning regulator for a variable magnitude pulse input with reset.


Fig. 14. Open-loop disturbance test for the weigh belt feeder.

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the load was quadrupled, which indicates thatsystem is robust to load disturbances. This issically because of the nature of a shunt-woundmotor. The characteristics of a shunt-wound mogive it very good speed regulation, even thouthe speed does slightly decrease as the load iscreased@20#. The ultimate result is that the controllers designed for different setpoints were inhently robust with respect to load disturbances.

5. Discussion

In previous research fuzzy PI control design@4#was also used to develop and implement contrlers for the weigh belt feeder. The fuzzy logic Pcontrol solution and the self-tuning adaptive cotrol solution have two common aspects. First, boof the methods can be categorized as adaptive ctrol methods.~Fuzzy logic control can be classfied as adaptive control, because its control effis tuned on-line at each sample period to improthe performance of the system.! Second, neithermethod needs an explicit plant model. However,each method experimental experience withplant is required in the design process.

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Neither of the two methods is uniformly bettethan the other. In the following, the two methodare compared based on on-line computationalfort, controller development effort, transient peformance, and the ability to handle motor satution.

5.1. On-line computational effort

The self-tuning regulator requires less on-lincomputational time. The recursive least-squamethod that was used for on-line plant parameestimation is one of the simplest identificatiomethods, and the pole placement method incase of all process zeros cancellation is also vsimple ~and particularly simple in our case duethe use of a first-order reference model!. Thus, thismethod can be easily implemented with microprcessors.

In contrast, the fuzzy logic controller design rquires more on-line computational effort. At eacsample period the control signal will be updateaccording to the reasoning of the proposed fuzrule-bases, which requires significant computions.


Fig. 15. Performance comparison at setpoint53 V.

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5.2. Controller development effort

Fuzzy logic controller design required less cotroller development efforts. In our research, fuzPI controllers were designed for the setpoint tracing problem. The control rules based on the chacteristics of step response are well known agenerally applicable in most cases. However,perience is needed to verify the control rules, aselect or tune the membership functions and scing factors.

Many implementation issues were encountein the self-tuning regulator design. For thmethod the control signal is generated basedthe on-line estimated plant parameter vector,unsuitably estimated parameters may lead to mtor saturation and controller failure. Thus the intial values of the estimated parameters and coriance matrix were carefully chosen for differereference levels in the controller design. Much dsign effort was invested in choosing the initial vaues to keep the system away from saturation whachieving satisfactory performance.

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5.3. Transient performance

In fuzzy logic control, the control signal wagenerated on-line based on the error and changerror at each sample period. The fuzzy rulyielded good transient performance.

Due to the difficulty of on-line parameter estmation, the self-tuning regulator may suffer fropoor transient performance. In this researchsired transient performance was achieved by cafully choosing the initial values of the estimateparameter vector and covariance matrix to kethe system operating within a bounded spaFigs. 15 and 16 show the performance comparisof a fuzzy PI controller and self-tuning regulatorsetpoints of 3 and 5 V. It is seen that fuzzy logiccontroller yields faster response, but larger ovshoot.

5.4. Motor saturation

In our experiments, motor saturation never ocurred when implementing a fuzzy PI controlleIn practice, the maximum allowed setpoint is 5


Fig. 16. Performance comparison at setpoint55 V.

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With this bounded setpoint, if an acceptable ovshoot of the output signal is achieved, the costruction of the fuzzy controller is experimentalseen to always keep the control signal less thanV, i.e., motor saturation does not occur.

Self-tuning regulator design sometimes sufferfrom motor saturation because of the shortcoings of the on-line parameter identification. Withis method it is more difficult to guard againmotor saturation when the reference signalchanged.

6. Conclusions

The industrial weigh belt feeder has high nolinearity due to motor saturation, friction, and sesor noise. A self-tuning regulator was designedthe feeder which bounded the motor away frosaturation while maintaining a constant feedraThis paper introduced the experimental systand the indirect self-tuning regulator design algrithm, which is a combination of the on-line recusive least-squares method and pole placement ctroller design. The adaptive algorithm waimplemented to control the weigh belt feeder. T

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initial values of the estimated plant parameter vetor u and the algorithm matrixP affect the tran-sient performance of the closed-loop system amay possibly lead to motor saturation. Hence thmust be chosen carefully. Experimental resudemonstrate the effectiveness and robustnessthe algorithm for several different reference iputs. Also, the indirect self-tuning regulator wacompared with a fuzzy logic control approachshow its strengths and weaknesses.

Acknowledgment

This research was supported in part by the Ntional Science Foundation under Grant CM9802197

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@2# Olsson, H., Astrom, K. J., Canudas de Wit, CGafvert, M., and Lischinsky, P., Friction models anfriction ompensation. Eur. J. Control4, 176–195~1998!.

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@4# Zhao, Y. and Collins, E. G., Jr., Fuzzy PI control of aindustrial weigh belt feeder. In Proceedings of Amecan Control Conference, Anchorage, AK, 2002, p3534–3539.

@5# Astrom, K. J., Theory and applications of adapticontrol—A survey. Automatica19, 471–486~1983!.

@6# McDermott, P. E., Mellichamp, D. A., and Rinker, RG., Pole-placement self-tuning control of a fixed-bautothermal reactor. Part I: Single variable contrAIChE J.32, 1004–1014~1986!.

@7# Astrom, K. J. and Wittenmark, B., Adaptive Contro2nd ed. Addison-Wesley Publishing Company, Reaing, MA, 1995.

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@9# Narendra, K. S. and Annaswamy, A. M., Stable Adative Systems. Prentice-Hall, Englewood Cliffs, N1989.

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@11# Ji, J. K. and Sul, S. K., DSP-based self-tuning IP specontroller with load torque compensation for rollinmill DC drive. IEEE Trans. Ind. Electron.42, 382–386 ~1995!.

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@15# Astrom, K. J. and Wittenmark, B., Self-tuning controlers based on pole-zero placement. IEE Proc.-D: Ctrol Theory Appl.127, 120–130~1980!.

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@17# Merrick Industries, Inc.,MC3 Controller: Operationand Maintenance Manual for the 24.96.EX BeFeeder. Lynn Haven, FL, 1997.

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Yanan Zhao received the B.S.and the M.S. degrees fromBeijing Institute of Technol-ogy, Beijing, China in 1987and 1990, respectively. She received a Ph.D. in mechanicaengineering from the FloridaState University in 2001. Shewas an Engineer in the Minis-try of Aerospace Industry ofChina and then a faculty member of Beijing Institute ofTechnology from 1990 to1998. Her professional inter-

ests include intelligent control systems for autonomous vehicles, amated controller tuning, system identification, numerical optimizatioand modeling, simulation and analysis of dynamic system.

Emmanuel G. Collins, Jr. re-ceived the Ph.D. degree inaeronautics and astronauticfrom Purdue University in1987. He worked for sevenyears in the Controls Technology Group at Harris Corpora-tion, Melbourne, FL beforejoining the Department of Me-chanical Engineering at theFlorida A&M University-Florida State University Col-lege of Engineering, Tallahassee, FL, where he currently

serves as professor. His current research interests include intellcontrol systems for autonomous vehicles, robust fault detectionisolation, control in manufacturing, automated controller tuning, aumated weight selection in modern control, and fluidic thrust veccontrol.

David A. Cartes received thePh.D. in engineering sciencefrom Dartmouth College in2001. He subsequently joinedthe Mechanical EngineeringDepartment at the FloridaA&M University-Florida StateUniversity College of Engi-neering, Tallahassee, FLwhere he teaches courses in intelligent and evolutionary con-trol systems, dynamics, andacoustics. His research interests include advanced powe

systems control and active control of sound and vibration. In 1994,Cartes completed a 20-year career in the U.S. Navy, where he speized in the repair of nuclear powered ships, and managed the consion, overhaul, and repair of complex marine propulsion systems.

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Self-tuning adaptive control for an industrial weigh belt feeder