DESIGN OF PSO-PID CONTROLLER FOR A NONLINEAR

VOL. 11, NO. 2, JANUARY 2016ARPN Journal of Engineering and Applied SciencesISSN 1819-6608 2006-2016 Asian Research Publishing Network (ARPN). All rights reserved.www.arpnjournals.comDESIGN OF PSO-PID CONTROLLER FOR A NONLINEAR CONICALTANK PROCESS USED IN CHEMICAL INDUSTRIES1DepartmentD. Mercy1 and S. M. Girirajkumar2of EEE, St. Joseph’s College of Engineering & Technology, Elupatti, Thanjavur, Tamilnadu, Indiaof ICE, Saranathan College of Engineering, Panjappur, Trichy, Tamilnadu, IndiaE-Mail: mercyprabhu06@gmail.com2DepartmentABSTRACTConical tank process has become increasingly popular in many industrial sectors like Chemical Industries,Paramedical Industries, Fermentation Industries, Drugs Manufacturing Industries, etc. Conical tank plays a vital role inchemical industries for chemical mixing, chemical storage & waste product draining. It is very difficult to control the levelof the conical tank as it has a non-linear property of varying diameter and volume. Hence, it needs a sophisticated methodto control the process and the most reliable one is using the PID controller. The PID controller is the generic feedbackcontrol technology and it makes up 90% of automatic controllers in process industries and is also the cornerstone for manyadvance control algorithms and strategies. For regulating the PID Controller, many tuning rules have been enclosed.Though, it provides proper tuning of the PID and it does not provide optimal tuning. In this paper we proposed theconventional tuning, internal model controller tuning and Particle Swarm Optimization (PSO) tuning. The three results arecompared based on the tuning values, time domain specifications and error criteria and the best tuning method is identifiedfor a nonlinear conical tank system.Keywords: PID controller, non-linear system, PSO-particle swarm optimization.INTRODUCTIONConical tank process is a tough control problemdue to their nonlinear dynamic behavior, uncertain andtime varying parameter values, constraint on themanipulated variables, interaction between the manipulatedand the controlled variables, unmeasured and frequentdisturbances, dead time on input and measurements.Because of the inherent nonlinearity, most of the chemicalindustries are in need of optimized control techniques.Conical tank process find wide application in gas plants,cement plants, Petroleum industries, FermentationIndustries and so on. Control of a level in a conical tank isimportant, because the change in shape gives rise to thenonlinearity. Due to the nonlinearity of the conical tanksystem, adaptive control techniques are widely used. It isconsidered as an adaptive servo system where the desiredperformance can be expressed in terms of the referencemodel, which gives the desired response to a commandsignal. The nonlinearity arises due to the plant transferfunction that varies with the height of the liquid in a tankand the controller output to be adaptive and robust for thesechanges. The primary job of the controller is to maintainthe process under stable condition even at different kinds ofunknown disturbances [10].In Chemical Industries, Conical tanks are used forchemical mixing, chemical storage and the settlement ofraw sewage can also be used for the secondary treatment ofsewage, have been used in the Water Utilities, commercialor industrial waste water solutions. The industrial conicalbottom tank is fast moving and a leading choice inindustrial storage. Conical Bottom Tanks are suitable whena complete drain out of the stored liquid is required (i.e.)for total evacuation of liquids. Suitable for both indoor andoutdoor installations. The tanks require stands to supportthe conical bottoms. The conical tank should offertreatment for various flow rates and solid loadings. Theycan be used in a wide variety of applications wheresettlement of wastewater is required either in conjunctionwith existing processes or as part of a ‘modular’ packageplant installation. Conical tanks are manufactured frommedium- or high-density polyethylene with U.V. inhibitorsand designed for containment of liquids of up to 1.7specific gravity. Tank walls are translucent for levelviewing and equipped with gallon indicators [26, 27, 28].PROBLEM FORMULATIONIn this section the controller equations areformulated as well as the assumed process model structureand the optimization problem that is proposed in order totune the PID controller. Optimization is a powerful tool fordesign of controllers. The important step beforeformulating a controller is to calculate the mathematicalrelationship or the governing dynamics between the inputand the output of the system. The fundamental principleand knowledge of the system should be investigated torealize the incidence of nonlinearity in the systemdynamics. Recently, the interest in Particle SwarmOptimization Algorithm is growing due to their differencefrom ordinary optimization tools [21].There are wide collections of control techniquesthat can be useful to encounter the control objective of thesystem and these depend on the factors of which thesuggested design objective might depend on. There areissues such as tracking, reducing the effects of opposingconditions and uncertainty, behaviors in terms of timeresponse (e.g., delay time, rise-time, peak overshoot, andsteady state error) and lastly engineering goals such as costand consistency which is vital in industrial standpoint.Superiority of controller scheme primarily depends on the1147

VOL. 11, NO. 2, JANUARY 2016ARPN Journal of Engineering and Applied SciencesISSN 1819-6608 2006-2016 Asian Research Publishing Network (ARPN). All rights reserved.www.arpnjournals.comdegree of how the nonlinearity can be endured andassumed using the linearization theory.Moreover, apart from nonlinearities, there may bea consequence of unknown parameters which hinders theobjective to obtain a complete detail model of a processavailable for control purpose. The factors that abstainedmany researchers to use conventional control theory andtechniques can be listed as follows: Systems are nonlinear and may contain unknownparameters. That unknown parameters may not beestimated accurately if reliable experimental data isabsent. The delays present in the process of system (conicaltank system specifically) might complicate achievinghigh performance control. There are several cases such as that of conical tank inindustry where the process or disturbancecharacteristics are changing continuously. Thisrequires simultaneous regulation of various variablesin order to maintain the desired liquid level. Thus, amodel must account for all of the most significantvariables of the process.Due to the above mentioned factors, it might bedifficult to formulate a control strategy based on theanalytical model because the mathematical model isusually linearized to FOPTD in account for complexity andnonlinearity which are inevitable in a complicated system.PID (proportional-integral-DERIVATIVE) control is oneof a kind of control scheme that uses the approach oflinearized model. However, the PID controller might notcapable to satisfy the control objectives or requirement atall times as it need to be regularly tuned due to the varyingsystem dynamics. Hence, it is desirable to have a robustand reliable control technique for modeling the complexand nonlinear system that prevails in all industrial process.Adaptive control is chosen as the conical tank’s controlscheme. The requirement to choose either two or threecontroller parameters has meant that the use of tuning rulesto determine these parameters is popular. It is regarded as anovel approach in parameter adjustment for a system whereprocess dynamics are nonlinear [23].PID TUNING METHODS“PID” is an acronym for “proportional, integral,and derivative”. A PID controller is a controller thatincludes elements with those three functions. Theconventional linear PID controller is combined by thefollowing three terms linearly, the control error, theintegral of the error, and the derivative of the error. Manyresearches and practices show that it is helpful to thecontrol results when the three terms are constructed insome kind of nonlinear function forms. There areconsiderable papers present different ways to designnonlinear PID controller. Among them, those methods thatmodify linear PID controller using some kind of specialnonlinear function are of more attractive to theengineering application [24].Astrom and Hagglund Tuning MethodIn 1984, Karl Astrom and Tore Hagglund of theLund (Sweden) Institute of Technology proposed a lessrisky alternative to the Ziegler-Nichols open-loop test.Their relay method generates a sustained oscillation of theprocess variable but with the amplitude of thoseoscillations restricted to a safe range. The AstromHagglund method works by forcing the process variableinto a limit cycle as shown in the "relay test" graphic. Withall three PID terms temporarily disabled, the controller usesan on/off relay to apply a step-like control effort to theprocess. It then holds the control effort constant and waitsfor the process variable to exceed the set point. At thatpoint, it applies a negative step and waits for the processvariable to drop back below the set point. Repeating thisprocedure each time the process variable passes the setpoint in either direction forces the process variable tooscillate out of synchronization with the control effort butat the same frequency [24].PID Parameters for Astrom and Hagglund MethodProportional constant:Kc 5Tm/6(Km τm) 0.73Integral constant:Ti 1.5 τm 0.06Derivative constant:Td 0.25 τm 1.54Internal Model ControlInternal model control is model based controllerstructure that provides a suitable framework for satisfyingour objectives. The IMC structure which makes use of aprocess model to infer the effect of immeasurabledisturbance on the process output and then counteracts thateffect. The controller consists of an inverse of the processmode. IMC design procedure depends exclusively on twofactors: the complexity of the model and the performancerequirements. The IMC based PID controller algorithm isrobust and simple to handle the uncertainty in model. Thismethod seems to be a useful trade-off for the performanceof the closed loop system. It achieves robustness to modelinaccuracies with a single tuning parameter. The IMCdesign procedure can be used to solve quite a few criticalproblems especially at the industrial level (using theconcept of designing a model of the actual plant process). Italso gives good solutions to processes having a significanttime delay which actually happens when working in a realtime environment. For tuning the controller the filter tuningparameter λ value is varied. According to that variouseffects of discrepancies enter in the system thus, bestperformance is achieved. Hence, a good filter structure isone for which the optimum λ value gives the best PIDperformance [3, 24].1148