The success of proportional-integral-derivative (PID) control

Transcription

1 APPLICATIONS OF CONTROL «Robut Advanced PID Control (RaPID) PID Tuning Baed on Engineering Specification JAIRO J. ESPINOSA OVIEDO, TOM BOELEN, and PETER VAN OVERSCHEE The ucce of proportional-integral-derivative (PID) control in the proce indutry i baed on the ability to tabilize and control around 9% of exiting procee []. Thi importance i overhadowed, however, by a lack of performance in ome application. It ha been reported that a ignificant percentage of intalled PID are operated in manual mode and that 65% of the loop operating in automatic mode generate greater variance in cloed-loop operation than in open-loop operation [], [2]. Thi lack of performance i, in many cae, the reult of a poorly tuned et of parameter due to» lack of knowledge among operator and commiioning peronnel» generic tuning method baed on ad hoc criteria that do not match pecific proce need» the large variety of PID tructure, which lead to error during application of tuning rule. Thee challenge motivated our development of the oftware package Robut Advanced PID Control (RaPID) for tuning PID controller. RaPID i an intuitive tool with multiple level of complexity that can be acceed according to the knowledge of the peron commiioning the loop. Thi article decribe the method and algorithm ued by RaPID for tuning PID loop. PROJECT DESCRIPTION In the project decription, the uer provide information about the control loop, uch a ampling time, range, unit, name, and decription of the etpoint, the controlled variable, and the manipulated variable. Thee definition are needed to interpret ampled data and define the limit of variable. The limit provide aturation contraint a well a appropriate caling of variable. In thi phae of the project, the uer define the objective that mut be achieved once the PID i tuned (either diturbance rejection or etpoint tracking) a well a the template of the controller. The template of the controller contain the parameter format, which can be elected for everal different commercial PID controller a tand-alone unit or integrated in ditributed control ytem (DCS) unit. The template are baed on the decription provided by the manufacturer, which include Siemen, Emeron, Omron, Honeywell, and other. The template provide two benefit: ) exact knowledge of the controller tructure to maximize the performance of the controller hardware and 2) elimination of the need for manual converion of the controller parameter from the traditional Kp, Ti, and Td to the manufacturer format. Thi converion reduce error due to caling and entering parameter. The interface alo allow the uer to employ engineering unit rather than caled value. COLLECTION OF PROCESS DATA Once the element of a project have been decided, RaPID ue an input-output experiment to identify the dynamic of the plant. Experiment are cotly becaue they interrupt normal plant operation. To minimize the impact of experiment, RaPID determine a et of input that can be choen according to the preent condition and the feature of the proce by adjuting parameter uch a amplitude and dc content. The available predefined input ignal include teplike (tep, block, polynomial tep, and aturated ramp), impule, ine wave (including ingle ine, wept ine, and multiine), and noiy input, namely, random Gauian and peudorandom binary noie equence (PRBNS). Uer can alo create cutom input ignal. Signal generated during the experiment can be loaded into the program by mean of file or by uing an object linking and embedding for proce control (OPC) connection to the proce computer. The OPC connection provide a reading and writing connection by which the manipulated variable (input) ignal for the experiment can be deigned in RaPID and ent to the DCS through OPC. The controlled variable ignal i then read back and ued for the identification. IDENTIFICATION RaPID include a ytem-identification algorithm that combine ubpace identification and prediction error method [3], [4], complemented by an intuitive uer interface (ee Figure ). Once the ignal from the experiment are acquired, RaPID weep over a et of tructure to tet model with different delay and number of pole and zero. The model with the bet fit i automatically elected. The algorithm detect integral effect and applie automatic preproceing to remove ignal offet. Advanced option include ignal filtering uing lowpa, highpa, bandpa, and bandtop filter. Thee filter can be configured by electing the cutoff frequencie and the dynamic order. All change can be previewed prior to being applied. The uer can alo et the maximum delay and the maximum number of pole and zero. In many cae, the operator ha a good idea of the dc gain of the proce. Thi prior knowledge can be ued by limiting the dc gain of the model. During identification, the uer can retrict the 66-33X/6/$2. 26IEEE FEBRUARY 26 «IEEE CONTROL SYSTEMS MAGAZINE 5

2 Although all model are identified a dicrete-time ytem, the reult are hown in a continuou repreentation, which i more intuitive to the uer. FIGURE Identification panel of RaPID. The dark green ignal i the meaured ignal (output), the light green ignal i the identified model output, and the red line i the manipulated variable (input). The tool calculate a et of model with different tructure in term of pole, zero, and delay and automatically elect the model tructure with the bet performance. The uer can elect option by combining thi reult with prior knowledge about the proce. preence of reonant pole a well a imaginary and righthalf plane zero. The uer can tet different model with a ingle click, and the model can be evaluated graphically by comparing the imulated repone with the real repone or numerically by calculating an error index, which meaure the portion of the output ignal that are not correctly explained by the model. CONTROL DESIGN PID controller have traditionally been tuned by precribing the hape of the cloed-loop tep repone (Ziegler- Nichol, Chien-Hrone-Rewick, and Cohen-Coon [], [2]). After the parameter are found according to the method, a trial-and-error approach i ued to achieve the deired repone, often acrificing the robutne provided by the original parameter. For controller deign, RaPID ue contrained optimization to obtain the deired time repone while guaranteeing robutne. Three element mut be defined: control objective and control tructure, cot function, and contraint. Selection of the optimization criterion (cot function), control objective, and contraint can be done through the uer interface a hown in Figure 2 and 3. The uer interface allow interactive deign of the controller, including reformulation of the objective and contraint. Thee element are decribed in the following ection. Control Objective and Control Structure The control objective i choen by the uer according to the application. Objective that can be purued with RaPID include» tracking, that i, following a pretored or real-time reference ignal (ervomechanim problem)» variance control, that i, keeping the output of the ytem at a etpoint while recovering a quickly a poible from diturbance (regulator problem). To achieve thee objective, RaPID optimize the PID parameter K P, K I, K D, and K DD, a well a the parameter α, β, and γ of the feedforward action, where the controller i repreented by FIGURE 2 Uer interface for controller optimization. Propertie allow the uer to define contraint on noie enitivity (HF gain) and robutne. The calculated controller i preented according to the definition of the PID controller template. The reulting robutne and noie enitivity are hown. The uer can define the condition of the tet, uch a etpoint, diturbance, and load change. FIGURE 3 Uer interface for controller optimization. Thi window define the control objective, cot function, and overhoot contraint. The origin of the variance change i defined by etting the ource either a a load or a an output diturbance. The nominal operating point i decribed in the entrie Nominal CV (controlled variable) and Nominal MV (manipulated variable). The cot function can be elected a either IAE, ITAE, or energy. 6 IEEE CONTROL SYSTEMS MAGAZINE» FEBRUARY 26

3 U() = K P (αr() Y()) + K I (R() Y()) 2 + K D (βr()y()) + K DD + P d ( + P d ) 2(γ R() Y()) + manual reet. () A block diagram of the controller () i hown in Figure 4. Table outline the function of each controller element for the different control objective. For intance, when the control objective i tracking, the feedback and feedforward parameter are both optimized. On the other hand, when the objective i to imultaneouly achieve tracking and variance control, the feedback parameter are employed for variance control while the feedforward parameter are targeted to the tracking objective. R () PD U FF () Man ual Reet E () PID + Sytem U FB () FIGURE 4 PID control with feedforward PD action and manual reet. The feedforward action i ued only for tracking application. The manual reet i a contant value added to the control action to guarantee bumple tranfer of the controller from manual to automatic. Optimization Criteria Once the control objective and the tructure (template) of the controller have been elected, the next tep in tuning i to elect criteria to evaluate the controller during optimization. For optimization, RaPID ue timedefined criteria and overall error criteria. For a time-defined criterion, the optimization minimize the time needed to reach a given point of the tep repone. RaPID include both ettling time and rie time a time-defined criteria. Alternatively, an overall error criterion evaluate the error ignal over a period of time (N ample) in repone to a tep reference (ee Figure 5). The idea i to capture in a ingle number the total deviation between the reference and the output of the ytem. The overall error criteria ued by RaPID are ) integral of abolute error (IAE) IAE = 2) energy E = e k k= k= 3) integral of time multiplied by the abolute value of error (ITAE) ITAE = e 2 k k e k. k= Optimization Contraint Optimizing the parameter of the controller baed only on the optimization criteria often reult in a controller with le than atifactory behavior. RaPID thu include variou contraint. TABLE Controller function for achieving the control objective. When the control objective i tracking, the feedback and feedforward parameter are both optimized. On the other hand, when the objective i to achieve both tracking and variance control, the feedback parameter focu on the variance while the feedforward parameter aim at the tracking objective. Controller Objective Controller Section Tracking Variance Variance + Tracking Feedback Tracking mode Variance mode Variance mode Feedforward Tracking mode Tracking mode Ref v Out E rror IAE Energy ITAE FIGURE 5 Error-baed optimization criteria. The top plot how a reference ignal and the controlled variable of the ytem. The error plot how the tracking error from the reference, calculated a the difference between the reference and the output. The lat three plot how intantaneou value of the ignal ued to calculate the performance of the controller. Oberve that the IAE criterion penalize proportionally to the abolute value of the error, the energy criterion penalize according to the quare of the error (large error are trongly penalized compared with mall error), and the ITAE criterion penalize late error. FEBRUARY 26 «IEEE CONTROL SYSTEMS MAGAZINE 7

4 Imaginary Axi Parabolic Approximation Nyquit Curve +j Real Axi Robutne Circle FIGURE 6 Nyquit plot and the parabolic robutne contraint. During controller optimization, the robutne contraint (black) i approximated by a parabola (magenta), which pae through the interection point of the robutne circle with the real axi. Thi contraint guarantee robutne and tability of the ytem with the optimized PID controller. Overhoot Thi contraint allow the uer to pecify the maximum permiible overhoot. Thi contraint can be invoked only for the tracking control objective. Saturation The aturation contraint retrict the action of the controller to the actuator phyical limit, thu avoiding integrator windup, which can reult in poor performance or intability. High-Frequency Gain Thi contraint on the controller gain limit the effect of the high-frequency meaurement noie on the actuator. Selecting the maximum high-frequency gain (HF-Gain) provide a trade-off between the peed of the controller and it enitivity to noie. When HF-Gain i elected to be too mall, the controller react lowly in tracking and variance control. Robutne RaPID can guarantee robut tability and performance of the optimized PID value through a robutne contraint. Specifically, RaPID ue a parabolic contraint to prevent the Nyquit curve from encircling the - point. Figure 6 illutrate the parabolic contraint, while Figure 7 compare the performance of an initial PID controller with a PID controller optimized by RaPID. CONCLUSIONS RaPID ha been applied to hundred of PID loop ranging from mechanical ytem to proce control loop and embedded application. Power plant, refinerie, chemical plant, and food and beverage plant are jut a few of the application that have benefited from thi methodology. RaPID enhance tability and afety in plant operation while improving productivity. We believe that the robutne of the controller i the mot likely explanation for the ucce of RaPID. Reduction in down time due to actuator failure ha alo been oberved Thi reduction can be explained by the limitation of the influence of enor noie on the control action, thank to the contraint on the HF-Gain of the controller made poible by optimization. Energy aving and increaed production have alo been reported; thee improvement are likely due to better tuning for variance control. FIGURE 7 Uer interface for controller comparion. The uer interface how the cloed-loop imulation repone of the controller with the original PID etting (black) and the PID etting obtained with RaPID (green). The upper figure how the controlled variable and the reference while the lower plot how the manipulated variable and the load diturbance. The figure how a tet in which the etpoint (blue) i changed at time 6 ; once the plant ha reached thi etpoint a load diturbance i applied (yellow). The table provide a numerical comparion of variou performance meaure for the controller. AUTHOR INFORMATION Jairo J. Epinoa Oviedo (Jairo.Epinoa@ipco.be) obtained hi electronic engineering degree from the Univeridad Ditrital de Bogotá, Colombia, and mater (cum laude) and Ph.D. (magna cum laude) degree in electrical engineering from the Katholieke Univeriteit Leuven, Belgium. He i currently a reearch and development engineer for IPCOS N.V. in Leuven, Belgium. He combine hi work at IPCOS with teaching aignment at the Univeridad de Ibagué in Colombia. He i the author of Fuzzy Logic, Identification and Predictive Control. 8 IEEE CONTROL SYSTEMS MAGAZINE» FEBRUARY 26

5 Tom Boelen received hi M.Sc. in agricultural engineering in 997 from the Katholieke Univeriteit Leuven. He wa a reearcher in the field of biological proce technology at the ame univerity. He joined ISMC in 998 and i currently a project engineer for project in the chemical and petrochemical indutry. Peter Van Overchee received hi M.Sc. degree in applied cience in 989 at the Katholieke Univeriteit Leuven, Belgium. In 99 he received hi M.Sc. degree in electrical engineering at Stanford Univerity, California. In 996 he received the Automatica Bet Paper Award. He i preident of IPCOS Belgium and i reponible for project in the oil indutry. REFERENCES [] A. O Dwyer, Handbook of PI and PID Controller Tuning Rule. London: Imperial College Pre, 23. [2] K. Atröm and T. Hagglund, PID Controller: Theory, Deign and Tuning. Reearch Triangle Park, NC: Intrum. Soc. Amer., 995. [3] L. Ljung, Sytem Identification Theory for the Uer. Englewood Cliff, NJ: Prentice-Hall, 999. [4] P. Van Overchee and B. De Moor, Subpace Identification for Linear Sytem. Norwell, MA: Kluwer, 996. [5] Rapid, Robut advanced PID control. Coure Control Theory Hand on Tuning and Application, Leuven: IPCOS N.V., 24. [6] G.F. Franklin, J.D. Powell, and M.L. Workman, Digital Control of Dynamic Sytem. Reading, MA: Addion-Weley, 99. [7] F.G. Shinkey, Proce Control Sytem, Application, Deign and Tuning. New York: McGraw-Hill, 996. [8] P.B. Dehpande, Multivariable Proce Control. Reearch Triangle Park, NC: Intrum. Soc. Amer., 989. [9] P. Friedman, Economic of Control Improvement. Reearch Triangle Park, NC: Intrum. Soc. Amer., 995. [] M. Morari and E. Zafiriou, Robut Proce Control. Englewood Cliff, NJ: Prentice Hall, 999. Preciion Timing Control for Radioatronomy Maintaining Femtoecond Synchronization in the Atacama Large Millimeter Array JEAN-FRANÇOIS CLICHE and BILL SHILLUE The Atacama Large Millimeter Array (ALMA) (ee Figure ) i an international radio atronomical facility currently under contruction in Chile through the collaboration of intitution in the United State, Canada, Europe, and Japan []. When completed, the facility will conit of an array of up to 64 2-m parabolic antenna that can detect millimeter and ubmillimeter wavelength radio wave in the frequency band between 3 95 GHz. The antenna will be located at an elevation of 5, m on the Chajnantor plain in the ditrict of San Pedro de Atacama. At thee wavelength, the radiotelecope array will be able to reveal the tructure of the cold region of the univere, otherwie dark at viible wavelength, with unprecedented enitivity and a reolution of milliarcecond. Thi reolution i an order of magnitude better than the Hubble telecope or the very large array operating in New Mexico. ALMA achieve it exceptional reolution and enitivity by linking all of the 64 antenna into an interferometer array. In thi etup, the exact intant at which a radio wave reache each of the antenna i preciely recorded. Since the relative poition of each antenna i well known, the ource of the wave can be accurately pinpointed by comparing the timing (or phae) of the wave arriving at any one antenna relative to the other antenna uing real-time correlator ytem. The ditance between two antenna i known a the baeline. A large baeline caue ignal to arrive at the antenna with a large differential delay, and thu accurate angular reolution can be achieved. The ALMA antenna can be moved into different configuration like che piece uing a pecially deigned truck to achieve different combination of reolution and enitivity. The maximum reolution i obtained with baeline up to 8 km. To accurately meaure the phae of the ky ignal over the entire array or ubarray, every antenna mut receive a highly table common reference ignal known a the local ocillator (LO) reference. For ALMA, thi LO reference ignal i compoed of two optical wave ent through a ingle optical fiber [2]. Both wave have a wavelength around.556 µm to allow tranmiion through conventional telecommunication optical fiber with little lo. One optical wave i generated by a mater laer (ML), while the other i generated by phae-locking a lave laer at a given frequency offet from the mater. Both FIGURE Artit rendition of the ALMA radiotelecope, which will conit of up to 64 2-meter parabolic antenna pread over 8 km. The array will receive comic ignal from 3 95 GHz. Image courtey of NRAO/AUI and computer graphic by ESO X/6/$2. 26IEEE FEBRUARY 26 «IEEE CONTROL SYSTEMS MAGAZINE 9