ISA                                                                                                                TRANSAC...
438                  Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450                       ...
Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450                            439estimations s...
440                    Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450                     ...
Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450                441                         ...
442   Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450           Fig. 5. Performance of the ...
Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450   443     Fig. 7. Performance of the self-t...
444   Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450           Fig. 9. Performance of the ...
Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450            445                             ...
446               Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450      Fig. 12. Performance...
Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450             447                            ...
448                  Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450                       ...
Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450                      449                   ...
450                      Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450 ͓3͔ Olsson, H. and...
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Self tuning adaptive control for an industrial weigh belt feeder


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Self tuning adaptive control for an industrial weigh belt feeder

  1. 1. ISA TRANSACTIONS® ISA Transactions 42 ͑2003͒ 437–450 Self-tuning adaptive control for an industrial weigh belt feeder 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 2002͒Abstract An industrial weigh belt feeder is used to transport solid materials into a manufacturing process at a constantfeedrate. It exhibits nonlinear behavior because of motor friction, saturation, and quantization noise in the measurementsensors. To overcome the nonlinearities, a simple yet effective method of controller autotuning, an indirect self-tuningregulator, was designed and implemented for an industrial weigh belt feeder. Implementation issues are discussed andexperimental results show the effectiveness of the adaptive controller for several different reference inputs. Also, theperformance of the indirect self-tuning regulator is compared with that of a fuzzy logic controller for the sameapplication. © 2003 ISA—The Instrumentation, Systems, and Automation Society.Keywords: Adaptive control; Recursive least-squares method; Pole placement; Self-tuning regulator; Weigh belt feeder1. Introduction trol signal is restricted to lie in the interval ͓0,10͔ V. The motor also has significant friction. In addi- An industrial weigh belt feeder ͑see Fig. 1͒ is tion, the sensors ͑which include an optical encoderdesigned to transport solid materials into a manu- and a strain gauge load cell͒ exhibit significantfacturing process at a constant feedrate, usually in quantization noise. Hence the weigh belt feederkilograms or pounds per second. The weigh belt exhibits nonlinear behavior in the parameters ͓1͔.feeder used in this research was designed and To demonstrate this nonlinearity, the step re-manufactured by Merrick Industries, Inc. of Lynn sponses of the closed-loop system with a PI con-Haven, Florida and is a process feeder that is typi- troller, H ( z ) ϭK p ϩK i ( T/2)( zϩ1)/(zϪ1 ) withcally used in a food, chemical, or plastics manu- K p ϭ1.4, K i ϭ1.2 and sampling period Tfacturing process. To ensure a constant feedrate in ϭ0.01 sec, are given for setpoints of 1,2, . . . ,5 Vindustrial operation, a PI control law is designed ͑1 V corresponds to a belt speed of 1 ft/min͒, re-and implemented in the Merrick controller. In cur- spectively. It is clearly shown in Fig. 2͑a͒ that withrent practice the PI tuning process is performed a fixed PI controller, the damping characteristicsmanually by an engineering technician. However, of the closed-loop system change with the set-for better and more consistent quality, it is desired point. For setpoints greater than 2, this nonlinearto use automated PI tuning ͓1͔. response leads to significant overshoot, as seen in The dynamics of the weigh belt feeder are domi- Fig. 2͑b͒. Also, because of the sensor noise, thenated by the motor. To protect the motor, the con- output signals shown in the Fig. 2 are not smooth. In addition, actuator saturation occurs in the sys- *E-mail address: tem for setpoints above 4 V. † E-mail address: Transient performance of the weigh belt feeder ‡ E-mail address: affects both the quality of the manufactured prod-0019-0578/2003/$ - see front matter © 2003 ISA—The Instrumentation, Systems, and Automation Society.
  2. 2. 438 Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450 lecting a friction model and adding a feedforward friction observer in the loop. The control signal is then composed of both the signal for the linear system which results from neglecting the friction and the signal to remove the friction ͓2,3͔. The performance of this kind of model-based compen- sation relies on the accuracy of the friction mod- eling. In reality, friction force characteristics are not perfectly known and vary due to a variety of Fig. 1. The Merrick weigh belt feeder. factors. Adaptive friction compensation methods provide a mechanism for adjusting friction model parameters to cope with this uncertainty ͓2͔.uct and the efficiency of the manufacturing pro- Instead of using a model-based friction compen-cess. For example, large overshoot can be a disas- sation method, non-model-based control ap-ter when a weigh belt feeder is used to produce a proaches were chosen to control the feedrate forlime slaker. A lime slaker takes pebble lime and the weigh belt feeder. This avoids the substantialmixes it with water to make a lime paste. The effort needed for system modeling. Fuzzy logic PIpaste is used for pH control in water treatment. controllers were previously designed for the weighOvershoot causes too much lime to be present in belt feeder ͓4͔. This paper considers the design ofthe lime slaker and the paste becomes concrete. a simple self-tuning regulator, which is less com-Settling time is also an important issue when feed- putationally expensive than a fuzzy PI materials into boxes since a longer settling ͑Off-line tuning of a PI controller using unfalsifiedtime requires the material in the initial boxes to be control design is described in Ref. ͓1͔.͒discarded or reprocessed. The self-tuning regulator has received consider- A traditional and simple way to overcome the able attention because it is flexible, easy to under-motor friction is to use a dither signal, such that a stand, and easy to implement with microproces-high frequency signal is added to the control sig- sors ͓5–9͔. This method has also been studied innal ͓2͔. But, the improved performance of the sys- several industrial applications ͓10–13͔. In this pa-tem is at the expense of reduced product life. Also, per, the designed self-tuning regulator is a combi-for the weigh belt feeder, the added signal in- nation of the recursive least-squares method andcreases the chance of motor saturation. Currently, pole placement design. No specific recursive pa-most friction compensation methods use an rameter estimator is uniformly the best. Least-observer-based friction scheme which requires se- squares estimation is one of the simplest recursive Fig. 2. Nonlinear performance of the weigh belt feeder.
  3. 3. Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450 439estimations schemes ͓7,14͔. In addition, pole ⑀ ͑ k ͒ ϭy ͑ k ͒ Ϫ ␸ T ͑ k ͒ ␪ ͑ kϪ1 ͒ , ˆ ͑7͒placement is one of the most popular design meth-ods in adaptive control due to its simplicity and L ͑ k ͒ ϭ P ͑ kϪ1 ͒ ␸ ͑ k ͒the implications of the solution on the stability andtime response of the system ͓15,16͔. ϫ ͓ 1ϩ ␸ T ͑ k ͒ P ͑ kϪ1 ͒ ␸ ͑ k ͔͒ Ϫ1 , ͑8͒ The remainder of this paper is organized as fol- P ͑ k ͒ ϭ ͓ IϪL ͑ k ͒ ␸ T ͑ k ͔͒ P ͑ kϪ1 ͒ . ͑9͒lows. Section 2 discusses indirect self-tuning regu-lator design. Section 3 describes the experimental For implementation of the RLS algorithm, the ini-system. Section 4 presents implementation results tial conditions of the parameter estimate vector ␪ˆfor the weigh belt feeder. Section 5 compares the and the covariance matrix P must be provided.indirect self-tuning regulator with a fuzzy logic A general linear controller can be described bycontroller. Finally, Section 6 gives some conclu-sions. R ͑ q ͒ u ͑ k ͒ ϭT ͑ q ͒ r ͑ k ͒ ϪS ͑ q ͒ y ͑ k ͒ , ͑10͒ where r is the setpoint, and R ( q ) , S ( q ) , and T ( q ) are polynomials. ͑Below, for simplicity of notation2. Indirect self-tuning regulator the indice q is omitted.͒ To obtain expressions for R, S, and T, the minimum-degree pole placement In this section, the indirect self-tuning regulator ͑MDPP͒ algorithm is used; see Refs. ͓7,15͔ fordesign algorithm is briefly introduced. It is a com- details. A reference model is needed for the algo-bination of a recursive least-squares on-line esti- rithm which can be represented by the followingmation algorithm and a pole placement control de- form:sign method. Suppose a process is described by the single- B m͑ q ͒input, single-output ͑SISO͒ system, y m͑ k ͒ ϭ r͑ k ͒. ͑11͒ A m͑ q ͒ A ͑ q ͒ y ͑ k ͒ ϭB ͑ q ͒ u ͑ k ͒ , ͑1͒ 3. Experimental systemwhere y is the output, u is the control input, and Aand B are polynomials in the forward shift opera- The weigh belt feeder used in this research is ator q. This model can be expressed as typical process feeder that can be used in a food, y ͑ k ͒ ϭϪa 1 y ͑ kϪ1 ͒ Ϫa 2 y ͑ kϪ2 ͒ chemical, or plastics manufacturing process. There are two sensors used to measure the system fee- Ϫ ¯ Ϫa n y ͑ kϪn ͒ ϩb 0 u ͑ kϪd 0 ͒ drate. One of them is a 1000-pulse-per-revolution optical encoder. It is mounted on the tail pulley of ϩ ¯ ϩb m u ͑ kϪd 0 Ϫm ͒ , ͑2͒ the feeder and is used to measure the distance thewhere d 0 is the pole excess which represents the belt has travelled. By taking the first derivative ofinteger part of the ratio of the time delay and sam- the belt travel, the belt speed in m/sec is obtained.pling period. The corresponding regression model The second sensor is a weigh deck mounted on ais given by precision strain gauge load cell to weigh the ma- terial. This directly gives a belt load that is mea- y ͑ k ͒ ϭ ␸ T͑ k ͒ ␪ , ͑3͒ sured in kg/m. The feedrate is calculated by mul- tiplying the belt speed and the material load on thewhere belt. This product provides a feedrate in kg/sec. In ␪ Tϭ ͓ a 1 a 2 ¯ a n b 0 ¯ b m͔ , ͑4͒ this research, all of the experiments were con- ducted under a constant belt load. Thus in the fol- ␸ T ͑ k ͒ ϭ ͓ Ϫy ͑ kϪ1 ͒ ¯ Ϫy ͑ kϪn ͒ lowing sections, only control of the belt speed is considered. u ͑ kϪd 0 ͒ ¯ u ͑ kϪd 0 Ϫm ͔͒ . ͑5͒ The data measured from the sensors are pro- The recursive least-squares ͑RLS͒ algorithm for cessed first through an M C 3 controller ͓17͔ beforethe estimation of ␪ is given by ͓7͔ they are sent to the computer. The M C 3 controller is a product of Merrick Inc. developed for the con- ␪ ͑ k ͒ ϭ ␪ ͑ kϪ1 ͒ ϩL ͑ k ͒ ⑀ ͑ k ͒ , ˆ ˆ ͑6͒ trol of process weighing equipment. In this experi-
  4. 4. 440 Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450 preferred to reduce the on-line parameter estima- tion effort. The open-loop step response was tested and a representative step response is shown in Fig. 4. First-order system can reasonably approximate the observed step responses. ͑The significant delay is caused by the friction.͒ Thus the plant model isFig. 3. Feedback loop for the simulation of the digitally assumed to be of the form ͑1͒ withimplemented controller. A ͑ q ͒ ϭqϩa 1 , B ͑ q ͒ ϭb 0 . ͑12͒ment we only used it to preprocess the sampled Then, ␪ ϭ ͓ a 1 b 0 ͔ T is the parameter vector to bedata while the control algorithm was implemented estimated.using a PC. Inside the M C 3 controller the mea- For simplicity, the reference model was chosensured data are filtered by a built-in IIR ͑infinite as the first-order model,impulse response͒ filter mechanism. b m0 To control the feedrate, the feeder has a shunt- H͑ q ͒ϭ . ͑13͒wound dc motor and a silicon controlled rectifier qϩa m1͑SCR͒ motor controller combination. The motor is In particular the continuous-time reference modelcoupled to the head pulley of the feeder through a was chosen as H ( s ) ϭ 1/( 0.03sϩ1 ) , correspond-reducer and chain drive combination. The belt ing to a time constant of 0.03 sec which is a fastspeed and hence the overall system feedrate is response for the weigh belt feeder. By discretizingcontrolled by varying the rotational rate of the mo- this model at a sample period Tϭ0.01 sec, thetor. The plant in Fig. 3 presents a schematic de- discretized model is H ( q ) ϭ 0.2835/ ( qscription of the feeder. Ϫ0.7165) . Hence a m1 ϭϪ0.7165 and b m0 To run the hardware-in-the-loop experiment, ϭ0.2835 in Eq. ͑13͒.REALoop, a software and hardware kit from Based on the MDPP algorithm for the case inXANALOG Corp. ͓18͔ was used. REALoop hard- which all process zeros are canceled, in Eq. ͑10͒ware includes D/A and A/D I/O boards for the Rϭ1, Sϭ ( a m1 Ϫa 1 ) /b 0 and Tϭb m0 /b 0 . Hencecomputer ISA bus. Its software is a single the control law becomesSIMULINK ͓19͔ block with its own dialog box,which can be dragged into any SIMULINK block T S b m0 a m1 Ϫa 1model. In this dialog box the user may define the uϭ rϪ yϭ rϪ y. ͑14͒ R R b0 b0real-time sample time and indicate the number ofPC A/D and D/A board channels to communicate 4.2. Initial values of the estimated parameters ␪with the real world. A SIMULINK S-function was and the covariance matrix Pbuilt to implement the self-tuning regulator algo-rithm. Fig. 3 illustrates the feedback loop for Before the above MDPP algorithm can besimulation of the self-tuning regulator. implemented for the weigh belt feeder the initial values of ␪ and P need to be selected. The initial ˆ4. Implementation for the weigh belt feeder value of ␪ affects the transient performance of the ˆ In this section the adaptive control algorithm closed-loop system. For the case of the weigh beltproposed above is implemented for the weigh belt feeder, unsuitable initial values of ␪ can even lead ˆfeeder. Several implementation issues are dis- to motor saturation. The initial value of P affectscussed and experimental results are presented. the convergence of the estimated parameters and thus also affects the transient performance of the4.1. Proposed self-tuning controller weigh belt feeder. To achieve better transient per- formance and to protect the motor from saturation The dynamics of the weigh belt feeder are domi- both the initial values of ␪ and P must be chosen ˆnated by the dc motor. The order of the dynamic carefully.model of the weigh belt feeder must be determined Controllers were designed for setpoints of 1,2,to use pole placement design. A simple model is . . . ,5 V, where 1 V corresponds to a belt speed of
  5. 5. Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450 441 Fig. 4. Open-loop response of the weigh belt feeder.5.08ϫ10Ϫ3 m/sec ͑1 ft/min͒, and 5 V is the maxi- very small number, and thus either caused motormum possible value of the reference command. saturation or large overshoot. Smaller initial val-Due to the nonlinearity of the feeder, these initial ues of P led to a slower system response. Sincevalues will be different for different setpoints. In the dc gain of the plant b 0 / ( 1ϩa 1 ) is proportionalparticular, ␪ 0 ϭ ͓ a 0 b 0 ͔ T where a 0 ϭa m1 and b 0 ˆ to b 0 , the indicated choices of P restricted the 1 0 1 0ϭ ( sp/ ␳ ) b m0 ; here ␳ ϭ2.1ϩ0.1͚ kϭ1 ( 6Ϫsp ) sp estimated dc gain to suitable values.and sp stands for the setpoint. Considering thelinear control law described by Eq. ͑14͒, these 4.3. Experimental resultschoices of ␪ 0 set the initial control signal u ( 0 ) to ˆ2.6, 3, 3.3, 3.5, and 3.6 V, respectively at the five In this subsection, the experimental performancedifferent setpoints. This choice is needed for two of the proposed self-tuning regulator is first shownreasons: first, the control signal should be big for five different setpoints. Next, the experimentalenough to overcome the friction of the motor, performance with a variable magnitude pulse inputwhich can lead to a significant time delay in the is shown.closed-loop system response; second, a suitableinitial control signal is needed to obtain good tran- 4.3.1. Step inputsient performance. Figs. 5–9 show the experimental results of the The initial value of P was chosen as P controller at the five different setpoints. It is seenϭ0.000 12* I 2 at each setpoint, where I 2 stands that in each case, the controller performed veryfor the two-by-two identity matrix. These choices well. Each of the responses have small overshoot,were made to achieve transient responses with fast fast response and no steady state error.rise times and small overshoot and to avoid motor Figs. 10 and 11 show the parameters estimationsaturation. Larger initial values of P were tried, of a 1 and b 0 at the setpoints 1 and 5 V. The valuesbut they led to large initial transients in the esti- of the converged estimated parameters obtained atmate of the parameter of b 0 such that b 0 became a five different setpoints are listed in Table 1. Even
  6. 6. 442 Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450 Fig. 5. Performance of the self-tuning regulator at setpointϭ1 V. Fig. 6. Performance of the self-tuning regulator at setpointϭ2 V.
  7. 7. Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450 443 Fig. 7. Performance of the self-tuning regulator at setpointϭ3 V. Fig. 8. Performance of the self-tuning regulator at setpointϭ4 V.
  8. 8. 444 Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450 Fig. 9. Performance of the self-tuning regulator at setpointϭ5 V. Fig. 10. Estimation of the plant model parameters at setpointϭ1 V.
  9. 9. Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450 445 Fig. 11. Estimation of the plant model parameters at setpointϭ5 V.though the estimated values of the parameters are able pulse magnitude of 2, 4, 1, and 3 V sequen-not necessarily the true values, these values still tially. ͑See the reference signals in Figs. 12 andrepresent the trend of the parameter changes. It is 13.͒seen that at different setpoints the estimated values Due to the nonlinearity of the weigh belt feeder,of a 1 and b 0 both increased as the setpoint in- the plant model parameters change abruptly withcreased. An increase in a 1 , which was always an abrupt change in the reference magnitude.negative, indicates a faster response, while the When the self-tuning regulator was used for suchcombined effects of increasing a 1 and b 0 indicates cases, the on-line parameter estimation took con-an increase in the plant dc gain. siderable time to estimate the new model param- eters. As illustrated in Fig. 12, this lead to poor4.3.2. Pulse input transient performance such as large overshoot and To show the performance of the self-tuning motor saturation, which is undesirable. Thus theregulator design, a pulse input was also tested for initial values of the estimated parameters ␪ and thethe weigh belt feeder. The pulse input had a period covariance matrix P were reset when the referenceof 40 sec, a duty cycle of 80% period, and a vari- jumps from zero to a new magnitude level. Fig. 13 shows the performance of the adaptive controller when ␪ and P were reset to the corresponding val-Table 1 ues at different magnitudes.The estimated parameters for different setpoints. Setpoint a1 b0 dc gain 4.3.3. Load disturbances 1 Ϫ0.7160 0.0949 0.3342 Variations in the open-loop system response un- 2 Ϫ0.7086 0.1434 0.4921 der various step inputs were observed as the load 3 Ϫ0.6980 0.1754 0.5808 was increased to four times the weight of the nor- 4 Ϫ0.6868 0.1991 0.6357 mal load. As illustrated by Fig. 14, the step re- 5 Ϫ0.6714 0.2207 0.6716 sponses varied very little even when the weight of
  10. 10. 446 Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450 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.
  11. 11. Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450 447 Fig. 14. Open-loop disturbance test for the weigh belt feeder.the load was quadrupled, which indicates that the Neither of the two methods is uniformly bettersystem is robust to load disturbances. This is ba- than the other. In the following, the two methodssically because of the nature of a shunt-wound dc are compared based on on-line computational ef-motor. The characteristics of a shunt-wound motor fort, controller development effort, transient per-give it very good speed regulation, even though formance, and the ability to handle motor satura-the speed does slightly decrease as the load is in- tion.creased ͓20͔. The ultimate result is that the con-trollers designed for different setpoints were inher-ently robust with respect to load disturbances. 5.1. On-line computational effort The self-tuning regulator requires less on-line5. Discussion computational time. The recursive least-squares method that was used for on-line plant parameter In previous research fuzzy PI control design ͓4͔ estimation is one of the simplest identificationwas also used to develop and implement control- methods, and the pole placement method in thelers for the weigh belt feeder. The fuzzy logic PI case of all process zeros cancellation is also verycontrol solution and the self-tuning adaptive con- simple ͑and particularly simple in our case due totrol solution have two common aspects. First, both the use of a first-order reference model͒. Thus, thisof the methods can be categorized as adaptive con- method can be easily implemented with micropro-trol methods. ͑Fuzzy logic control can be classi- cessors.fied as adaptive control, because its control effort In contrast, the fuzzy logic controller design re-is tuned on-line at each sample period to improve quires more on-line computational effort. At eachthe performance of the system.͒ Second, neither sample period the control signal will be updatedmethod needs an explicit plant model. However, in according to the reasoning of the proposed fuzzyeach method experimental experience with the rule-bases, which requires significant computa-plant is required in the design process. tions.
  12. 12. 448 Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450 Fig. 15. Performance comparison at setpointϭ3 V.5.2. Controller development effort 5.3. Transient performance Fuzzy logic controller design required less con- In fuzzy logic control, the control signal wastroller development efforts. In our research, fuzzy generated on-line based on the error and change ofPI controllers were designed for the setpoint track- error at each sample period. The fuzzy rulesing problem. The control rules based on the char- yielded good transient performance.acteristics of step response are well known and Due to the difficulty of on-line parameter esti-generally applicable in most cases. However, ex- mation, the self-tuning regulator may suffer fromperience is needed to verify the control rules, and poor transient performance. In this research de-select or tune the membership functions and scal- sired transient performance was achieved by care- fully choosing the initial values of the estimateding factors. parameter vector and covariance matrix to keep Many implementation issues were encountered the system operating within a bounded the self-tuning regulator design. For this Figs. 15 and 16 show the performance comparisonmethod the control signal is generated based on of a fuzzy PI controller and self-tuning regulator atthe on-line estimated plant parameter vector, but setpoints of 3 and 5 V. It is seen that fuzzy logic PIunsuitably estimated parameters may lead to mo- controller yields faster response, but larger over-tor saturation and controller failure. Thus the ini- shoot.tial values of the estimated parameters and cova-riance matrix were carefully chosen for different 5.4. Motor saturationreference levels in the controller design. Much de-sign effort was invested in choosing the initial val- In our experiments, motor saturation never oc-ues to keep the system away from saturation while curred when implementing a fuzzy PI controller.achieving satisfactory performance. In practice, the maximum allowed setpoint is 5 V.
  13. 13. Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450 449 Fig. 16. Performance comparison at setpointϭ5 V.With this bounded setpoint, if an acceptable over- initial values of the estimated plant parameter vec-shoot of the output signal is achieved, the con- tor ␪ and the algorithm matrix P affect the tran-struction of the fuzzy controller is experimentally sient performance of the closed-loop system andseen to always keep the control signal less than 10 may possibly lead to motor saturation. Hence theyV, i.e., motor saturation does not occur. must be chosen carefully. Experimental results Self-tuning regulator design sometimes suffered demonstrate the effectiveness and robustness offrom motor saturation because of the shortcom- the algorithm for several different reference in-ings of the on-line parameter identification. With puts. Also, the indirect self-tuning regulator wasthis method it is more difficult to guard against compared with a fuzzy logic control approach tomotor saturation when the reference signal is show its strengths and weaknesses.changed. Acknowledgment6. Conclusions This research was supported in part by the Na- The industrial weigh belt feeder has high non- tional Science Foundation under Grant CMS-linearity due to motor saturation, friction, and sen- 9802197sor noise. A self-tuning regulator was designed forthe feeder which bounded the motor away from Referencessaturation while maintaining a constant feedrate. ͓1͔ Collins, E. G., Jr., Zhao, Y., and Millett, R., A geneticThis paper introduced the experimental system search approach to unfalsified PI control design for aand the indirect self-tuning regulator design algo- weigh belt feeder. Int. J. Adapt. Control Signal Pro-rithm, which is a combination of the on-line recur- cess. 15, 519–534 ͑2001͒. ͓2͔ Olsson, H., Astrom, K. J., Canudas de Wit, C.,sive least-squares method and pole placement con- Gafvert, M., and Lischinsky, P., Friction models andtroller design. The adaptive algorithm was friction ompensation. Eur. J. Control 4, 176 –195implemented to control the weigh belt feeder. The ͑1998͒.
  14. 14. 450 Y. Zhao, E. G. Collins, Jr., D. A. Cartes / ISA Transactions 42 (2003) 437–450 ͓3͔ Olsson, H. and Astrom, K. J., Observer-based friction compensation. In Proceedings of the 35th Conference Yanan Zhao received the B.S. on Decision and Control, Kobe, Japan, 1996, pp. and the M.S. degrees from Beijing Institute of Technol- 4345– 4350. ogy, Beijing, China in 1987 ͓4͔ Zhao, Y. and Collins, E. G., Jr., Fuzzy PI control of an and 1990, respectively. She re- industrial weigh belt feeder. In Proceedings of Ameri- ceived a Ph.D. in mechanical can Control Conference, Anchorage, AK, 2002, pp. engineering from the Florida 3534 –3539. State University in 2001. She ͓5͔ Astrom, K. J., Theory and applications of adaptive was an Engineer in the Minis- try of Aerospace Industry of control—A survey. Automatica 19, 471– 486 ͑1983͒. China and then a faculty mem- ͓6͔ McDermott, P. E., Mellichamp, D. A., and Rinker, R. ber of Beijing Institute of G., Pole-placement self-tuning control of a fixed-bed Technology from 1990 to autothermal reactor. Part I: Single variable control. 1998. Her professional inter- AIChE J. 32, 1004 –1014 ͑1986͒. ests include intelligent control systems for autonomous vehicles, auto- ͓7͔ Astrom, K. J. and Wittenmark, B., Adaptive Control, mated controller tuning, system identification, numerical optimization, and modeling, simulation and analysis of dynamic system. 2nd ed. Addison-Wesley Publishing Company, Read- ing, MA, 1995. ͓8͔ Astrom, K. J., Tuning and adaptation. In Proceedings of the 13th World Congress of IFAC, Vol. K, San Francisco, CA, 1996, pp. 1–18. Emmanuel G. Collins, Jr. re- ceived the Ph.D. degree in ͓9͔ Narendra, K. S. and Annaswamy, A. M., Stable Adap- aeronautics and astronautics tive Systems. Prentice-Hall, Englewood Cliffs, NJ, from Purdue University in 1989. 1987. He worked for seven͓10͔ Yang, T. C., Yang, J. C. S., and Kudva, P., Load- years in the Controls Technol- adaptive control of a single-link flexible manipulator. ogy Group at Harris Corpora- IEEE Trans. Syst. Man Cybern. 22, 85–91 ͑1992͒. tion, Melbourne, FL before joining the Department of Me-͓11͔ Ji, J. K. and Sul, S. K., DSP-based self-tuning IP speed chanical Engineering at the controller with load torque compensation for rolling Florida A&M University- mill DC drive. IEEE Trans. Ind. Electron. 42, 382– Florida State University Col- 386 ͑1995͒. lege of Engineering, Tallahas-͓12͔ Tsai, C. C. and Lu, C. H., Multivariable self-tuning see, FL, where he currently temperature control for plastic injection molding pro- serves as professor. His current research interests include intelligent control systems for autonomous vehicles, robust fault detection and cess. IEEE Trans. Ind. Appl. 34, 310–318 ͑1998͒. isolation, control in manufacturing, automated controller tuning, auto-͓13͔ Yang, Y. and Gao, F. R., Adaptive control of the filling mated weight selection in modern control, and fluidic thrust vector velocity of thermoplastics injection molding. Control control. Eng. Pract. 8, 1285–1296 ͑2000͒.͓14͔ Ljung, L., System Identification: Theory for the User. 2nd ed. Prentice-Hall, Upper Saddle River, NJ, 1999.͓15͔ Astrom, K. J. and Wittenmark, B., Self-tuning control- David A. Cartes received the lers based on pole-zero placement. IEE Proc.-D: Con- Ph.D. in engineering science trol Theory Appl. 127, 120–130 ͑1980͒. from Dartmouth College in͓16͔ Youlal, Y., Najim, K., and Najim, M., Regularized 2001. He subsequently joined pole placement adaptive control. In Proceedings of the the Mechanical Engineering IFAC Workshop, Newcastle, Australia, 1988, pp. 73– Department at the Florida A&M University-Florida State 77. University College of Engi-͓17͔ Merrick Industries, Inc., M C 3 Controller: Operation neering, Tallahassee, FL, and Maintenance Manual for the 24.96.EX Belt where he teaches courses in in- Feeder. Lynn Haven, FL, 1997. telligent and evolutionary con-͓18͔ XANALOG Corporation, REALoop User Manual. trol systems, dynamics, and North Reading, MA, 1998. acoustics. His research inter- ests include advanced power͓19͔ The MathWorks Inc., Simulink, Dynamic System systems control and active control of sound and vibration. In 1994, Dr. Simulation for MATLAB. Natick, MA, 1998. Cartes completed a 20-year career in the U.S. Navy, where he special-͓20͔ Krishnan, R., Electric Motor Drives. Prentice-Hall, ized in the repair of nuclear powered ships, and managed the conver- Upper Saddle River, NJ, 2001. sion, overhaul, and repair of complex marine propulsion systems.