Lecture_03(CP1).pdf

Li HongguangAutomation DepartmentBeijing University of Chemical TechnologyChapter 1Process Control EngineeringProcess Control Engineering03SingleSingle-loop Feedback Control Systemloop Feedback Control System1.1 Structure and Elements1.1 Structure and Elements1.2 Controlled Variable1.2 Controlled Variable1.3 Process Analysis&Manipulated Variables1.3 Process Analysis&Manipulated Variables1.4 Control Valve1.4 Control Valve1.5 Measurement Device1.5 Measurement Device1.6 Controller1.6 Controller1.7 Loop Interaction1.7 Loop Interaction1.8 Implementation and Tuning1.8 Implementation and TuningLab Work:Implementation,Tuning and Disturbance AnalysisLab Work:Implementation,Tuning and Disturbance AnalysisChapter Chapter 1 11.5 1.5 Measurement DeviceMeasurement DeviceImpact of measurement delayImpact of measurement delay LagLagMeasurement device can be viewed as an one order lag Measurement device can be viewed as an one order lag dynamic system,the lag of that is characterized by a time dynamic system,the lag of that is characterized by a time constant.constant.Nowadays,measurement device is possibly manufactured Nowadays,measurement device is possibly manufactured with small time constant,which ensures quick response with small time constant,which ensures quick response for measurements.for measurements.DelayDelayUsually,longUsually,long-distance signal transmission accounts for distance signal transmission accounts for the time delay.the time delay.We know of that time delay involved in a control loop We know of that time delay involved in a control loop is significantly disadvantageous to the control is significantly disadvantageous to the control performance.Therefore,measurement delay should be performance.Therefore,measurement delay should be avoided as possible as we can.avoided as possible as we can.1.5 1.5 Measurement DeviceMeasurement DeviceMeasurements delay:Measurements delay:Transmitter(filed)Transmitter(filed)Controller(console cabinet)Controller(console cabinet)Control delay:Control delay:Controller(console cabinet)Controller(console cabinet)Valve(filed)Valve(filed)The problems may become relatively severe in the case The problems may become relatively severe in the case of utilization of pneumatic instrumentation.of utilization of pneumatic instrumentation.1.5 1.5 Measurement DeviceMeasurement DeviceSingleSingle-loop Feedback Control Systemloop Feedback Control System1.1 Structure and Elements1.1 Structure and Elements1.2 Controlled Variable1.2 Controlled Variable1.3 Process Analysis&Manipulated Variables1.3 Process Analysis&Manipulated Variables1.4 Control Valve1.4 Control Valve1.5 Measurement Device1.5 Measurement Device1.6 Controller1.6 Controller1.7 Loop Interaction1.7 Loop Interaction1.8 Implementation and Tuning1.8 Implementation and TuningLab Work:Implementation,Tuning and Disturbance AnalysisLab Work:Implementation,Tuning and Disturbance AnalysisChapter Chapter 1 11.6 Controller1.6 ControllerControl PerformancesStabilitySteady-state offsetDynamic errorPID Three-term ControllerPID：Proportional Integral Derivative()()()()+=tedtdTdeTteKtudtip01The I,P,D parts can be interpreted as control actions based onthe past,the present and the future.Kpe(t)Proportional term,Kp,Proportional gain Integral term,Ti,Integral time()tideT01 Derivative term,d,Derivative time()tedtdTdThree tuning parameters of PID controller:Three tuning parameters of PID controller:Proportional gain(P);P);Integral time(I);I);Derivative time(D)D)Transfer function：+=sTsTKsEsUsGdipc11)()()(1.6 Controller1.6 ControllerThe PID controller is the most common form of feedback.In process control today,more than 95%of the control loops are of PID type.The family of PID controller includes P,PI,PD,PID controllers.Each has its own merits and limitations,and therefore its preferred range of applications.PID algorithm is not only suitable for model based control systems,but also eligible for those industrial plants whose behaviors are hardly to be accurately modeled.PID controller is readily to be tuned.1.6 Controller1.6 Controller1.6.11.6.1 Effect of PID parameters on steady state errorEffect of PID parameters on steady state errorR(s)E(s)Gc(s)Go(s)F(s)P35 Fig.1P35 Fig.1-2929F(s)Go(s)E(s)Gc(s)+=)12()1()12()1()(2222sTsTsTssTsTsTKsGjjivllkoossF/1)(=)(1lim)(lim)(lim00sGsEtecsst=P35 1P35 1-5858()111)(+=+=sTsTKsTKsGiiciccSummaryThe steady state error is in reverse ratio to the gain of the controller which conducts purely P action,i.e.,the increase of P leads to the decrease of the error.The integral action is beneficial to eliminating steady state error,while the derivative action is of no relevance.1.6.11.6.1 Effect of PID parameters on steady state errorEffect of PID parameters on steady state error1.6.21.6.2 Effect of PID parameters on dynamic performanceEffect of PID parameters on dynamic performance(1)Effect of(1)Effect of KcKcKcKc?0 implies the control loop is forced open.0 implies the control loop is forced open.KcKcresults in improvement of control performance(decrease results in improvement of control performance(decrease of dynamic offset)but deterioration of stability.of dynamic offset)but deterioration of stability.Conflicting!Conflicting!P controller is eligible to the process of high stability.P controller is eligible to the process of high stability.0ueKuc+=0ty(t)KcKc increaseincreaseP36 Fig.1P36 Fig.1-3131P controllerP controller(2)Effect of Ti(2)Effect of TiThe contribution from the integral term is proportional to both The contribution from the integral term is proportional to both the the magnitude of the error and the duration of the error.magnitude of the error and the duration of the error.The strength of integral action increases with decreasing integral time Ti,which Ti,which enhances the power of eliminating steady state error.enhances the power of eliminating steady state error.Theoretically,the steady state error disappears when integral action is used,while oscillation becomes severely with the decrease of Ti.PI controller PI controller 01uedtTeKuic+=0ty(t)Ti decreaseTi decreaseP25 Fig.1P25 Fig.1-28281.6.21.6.2 Effect of PID parameters on dynamic performanceEffect of PID parameters on dynamic performance(3)Effect of Td(3)Effect of TdThe differential element is proportional to the change slope of the process error,which is only responsive during transient conditions.“LeadLead”tuningtuningLarge Td indicates a strong derivative action,leading to an Large Td indicates a strong derivative action,leading to an active control action.active control action.However,However,the period of oscillation increases when derivative time is increased.0udtdeTeKuDc+=PD controller PD controller 1.6.21.6.2 Effect of PID parameters on dynamic performanceEffect of PID parameters on dynamic performance1.6.31.6.3 Choice of controllerChoice of controller(1)P controller is used in the process which is not much(1)P controller is used in the process which is not much concerned with the steady state error of the controlled concerned with the steady state error of the controlled variable.variable.(2)PD controller is suitable for the process with large lag(2)PD controller is suitable for the process with large lag process but little demands for steady state accuracy.process but little demands for steady state accuracy.(3)PI controller is eligible for the process which prefers(3)PI controller is eligible for the process which prefers relatively higher steady state accuracy.relatively higher steady state accuracy.(4)In regard to key process parameter which demands both(4)In regard to key process parameter which demands both superior dynamic and steady state performances,PID superior dynamic and steady state performances,PID controller is strongly recommended.controller is strongly recommended.Typical controllers include P,PI,PD,PID Typical controllers include P,PI,PD,PID Supplement 03Supplement 03Some industrial controllers use proportional band,rather Some industrial controllers use proportional band,rather than proportional gain.than proportional gain.The proportional band is the range of error that causes the The proportional band is the range of error that causes the controller output(manipulated input)to change over its full controller output(manipulated input)to change over its full range.range.Proportional Band Proportional Band ckPB100=ckPB100=ckPB100=ckPB100=ckPB100=ckPB100=ckPB100=PBckPB100=ckPB100=ckPB100=ckPB100=SingleSingle-loop Feedback Control Systemloop Feedback Control System1.1 Structure and Elements1.1 Structure and Elements1.2 Controlled Variable1.2 Controlled Variable1.3 Process Analysis&Manipulated Variables1.3 Process Analysis&Manipulated Variables1.4 Control Valve1.4 Control Valve1.5 Measurement Device1.5 Measurement Device1.6 Controller1.6 Controller1.7 Loop Interaction1.7 Loop Interaction1.8 Implementation and Tuning1.8 Implementation and TuningLab Work:Implementation,Tuning and Disturbance AnalysisLab Work:Implementation,Tuning and Disturbance AnalysisChapter Chapter 1 11.7 Loop interactions1.7 Loop interactionsConsider an example in real life.A couple of faucets are Consider an example in real life.A couple of faucets are located on a water main,where flow interactions may happen located on a water main,where flow interactions may happen among the individual faucets.among the individual faucets.Process variables are correlated(Multivariable system)Process variables are correlated(Multivariable system)TCLCThe interactions between TC and LC consisting in a distillation columnIt reveals that there really exists loop interactions.It reveals that there really exists loop interactions.Loop interaction must be considered when developing a control strategy.If it is not,it may be difficult to run the unit under closed loop control,creating many operational problems.1.7.11.7.1 Effect of loop interactionsEffect of loop interactionsSteam valve opens Steam valve opens steam flow increases steam flow increases temperature temperature rises;rises;Evaporation increases Evaporation increases level falls.level falls.Level valve opens Level valve opens outlet flow increase outlet flow increase level falls;level falls;Liquid heated decreases Liquid heated decreases temperature rises.temperature rises.1.7.21.7.2 Analysis methodsAnalysis methodsRelative Gain MethodRelative Gain MethodGc1(s)Gcn(s)R1(s)nnRn(s)Y1(s)Yn(s)u1(s)un(s)jiState-of-the-art calculations:Initially,calculate the gain with respect to a changes of Initially,calculate the gain with respect to a changes of jthjthmanipulated variable(the others maintains unchanged);manipulated variable(the others maintains unchanged);Then,calculate the gain of the close loop.Then,calculate the gain of the close loop.Finally,the relative gain in terms of j Finally,the relative gain in terms of j i path is attained asi path is attained as：The definitionThe definitionInteraction degreeyuyuuyjijiij=yuyuuyjiji=1.7.21.7.2 Analysis methodsAnalysis methods(1)(1)ij=1 indicates there is no interaction with other control indicates there is no interaction with other control loops.loops.(2)(2)ij1 indicates that loop interactions exist,which indicates that loop interactions exist,which additionally lead to a decrease of its gain(negative interactiadditionally lead to a decrease of its gain(negative interaction).on).The interaction degree increases with The interaction degree increases with ij ij growing.growing.(3)(3)ij1，indicates that loop interactions exist,which indicates that loop interactions exist,which additionally lead to a decrease of its gain(positive interactiadditionally lead to a decrease of its gain(positive interaction).on).The interaction degree increases with The interaction degree increases with ij ij falling.falling.1.7.21.7.2 Analysis methodsAnalysis methods(4)ij=0 indicates manipulated input,i,has no affect on output,j.1.7.31.7.3 Solutions of the interaction problemSolutions of the interaction problemFrom the From the univariateunivariate control point of view,loop interactions are undesirable.How do you minimize the effect of loop interaction?How do you minimize the effect of loop interaction?Relative gain based analysis:Relative gain based analysis:(1)When the values of(1)When the values of lie in the vicinity of 1 lie in the vicinity of 1(interactions are not severe),the controllers may be tuned to(interactions are not severe),the controllers may be tuned to attenuate loop interactions;attenuate loop interactions;(2)When the values of(2)When the values of go far beyond 1(interactions are go far beyond 1(interactions are significant),designificant),de-couple strategies have to be employed;couple strategies have to be employed;ExampleExampleControl systems associated with the centrifugal pumpControl systems associated with the centrifugal pumpPCFCInteractions exist between flow loop and pressure loop.Interactions exist between flow loop and pressure loop.In practice,the working frequencies of the two individual In practice,the working frequencies of the two individual control systems should be kept apart to ensure them to work control systems should be kept apart to ensure them to work independently.Controller tuning methods are alternatives to independently.Controller tuning methods are alternatives to treat such problems.treat such problems.1.7.31.7.3 Solutions of the interaction problemSolutions of the interaction problemExercise 3P54 1.3 Optional:Try to use SIMULINK to reproduce the analysis of a PID controller.