zn open loop method - TechTeach

1 Article:Ziegler-Nichols open -Loop MethodFinn HaugenTechTeach17. July 20101 IntroductionZiegler and Nichols published in 1942 a paper [1] where they described twomethods for tuning the parameters of P-, PI- and PID controllers. Thesetwo methods are theZiegler-Nichols closed loop method1, and theZiegler-Nichols open loop method2. The present article describes theopen-loop method , while the closed-loop method is described in anotherarticle (available at ).Ziegler and Nichols [1] used the following definition of acceptable stabilityas a basis for their contoller tuning rules: The ratio of the amplitudes ofsubsequent peaks in the same direction (due to a step change of thedisturbance or a step change of the setpoint in the control loop) isapproximately 1/4, see Figure 1.

2 A2A1=14(1)However, there is no guaranty that the actual amplitude ratio of a givencontrol system becomes 1/4 after tuning with one of the Ziegler andNichols methods , but it should not be very different from 1 that the Ziegler-Nichols closed loop method can be applied only toprocesses where it is possible to read off an apparant time delay in thestep-response of the process to be The Ziegler-Nichols PID tuning procedureThe Ziegler-Nichols open loop method is based on theprocess stepresponse. The PID parameters are calculated from the response in the1 Also denoted theUltimate gain theProcess reaction curve method1yyrA1A2ttvFigure 1:IfA2/A1 1/4the stability of the system is ok, according to Zieglerand Nicholsprocess measurementymafter a step with heightUin the control variableu, see Figure 2.

3 The term process here means all blocks in thecontrolexcept the controller. The step response experiment is executed on theuncontrolled process, so the control loop is open (no feedback).Processincludingsensor andscalingProcessmeasure-mentuu0u0+Uutty mymym0 ControlsignalFigure 2:The Ziegler-Nichols open loop method is based on the step responseof the uncontrolled processThe method is as If the control loop is closed ( feedback), the loop must be can be done by setting the controller in manual Bring the process to the operation point by adjusting the controlvariable manually. This is done by adjustingu0in Figure Excite the process via a step of amplitudeUin the control variableu.

4 The step should be small so that the process is not broughttoofar from the operation point, but of course the step must largeenough to give an observable response in process measurementym. Astep amplitude ofU= 10%can be a reasonable value, but theamplitude must be chosen individually in each Read off the following characteristic parameters from thestepresponse inym: Equivalent dead-time or lagL Rate or slopeRFigure 3 which shows the relevant part of a typical step response. Inthe figure the time axis starts at the step time. The annotation along the y-axis corresponds toym0in Figure the time fromthe step time to the point of intersection between the -line andthe steepest the slope of the steepest 3:Ziegler-Nichols open loop method : The equivalent dead-timeLandrateRread off from the process step response.

5 (The figure is a reprint from[1] with permission.)5. Calculate the controller parameters according to Table After the controller parameters have been calculated andentered intothe PID controller, the control loop is closed (by setting thecontroller in automatic mode).Eksempel 1 Controller tuning using Ziegler-Nichols open loopmethod3 KpTiTdP controller1LR/U 0PI 1:Ziegler-Nichols open loop method : Formulas for the controller have tried the Ziegler-Nichols closed loop method on a level controlsystem for a wood-chip tank with feed screw and conveyor beltwhich runswith constant speed, see Figure 4 The purpose of the control system isto keep the chip level of the tank equal to the actual, measured level control system works as follows.

6 The controller tries to keep themeasured level equal to the level setpoint by adjusting the rotational speedof the feed screw as a function of the control error (which is the differencebetween the level setpoint and the measured level).The step in the control variable isU= 10%fromu0= 45%to55%. Figure5 shows the response in the level measurement. We read offL= (2)Rcan be calculated from the slope of the level response. From Figure 5 wewill find that the level increases during 10min, givinga slope ofR1= = However, the slopeRmust beexpressed in unit %/min. The level sensor transforms0 15m to0 100%,corresponding to a measurement gain ofKm= Therefore,R=R1Km= (3)Using these values forLandRin Table 1 gives the following PIDparameters:Kp= ;Ti= 504s;Td= 126s(4)Figure 6 shows simulated responses with the PID controller with theseabove parameters.

7 There is a step in the setpoint and a step inthedisturbance (the outflow). The stability of the control system is on thelimit of being acceptable, but this is to be expected with this tuningmethod.[End of Example 1]3 This example is based on an existing system in the paper pulp factory S dra Cell Toftein Norway. The tank with conveyor belt is in the beginning of the paper pulp simulator of the system is available at [m]Wood chipWood chip tankud[kg/min]LTLCFeed screwProcess(tank with belt and screw)Sensor(LevelTransmitter- LT )ySPuePID controllerydBlock diagram:Process & Instrumentation (P &I) Diagram:Level controllerSensor (Level transmitter)ControlvariableProcessoutput variableProcess disturbance(environmental variable)ControlerrorProcess measure-mentymProcessmeasure -mentymnMeasurement noiseReferenceorSetpointControlvariableP rocess output variableLevel controller (LC)ControlloopMeasure-mentfilterym,fFil teredmeasure-mentConveyor beltReferenceorSetpointySPMeasurement noisenProcess (tank with belt and screw)Process disturbance(environmental variable)Figure 4:P&I (Process and Instrumentation) diagram and block diagram of alevel control system for a wood-chip tank in a pulp factoryReferences[1] J.

8 G. Ziegler and N. B. Nichols:Optimum Settings for AutomaticControllers,Trans. ASME, Vol. 64, 1942, s. 759-7685 Figure 5:Example 1: Ziegler-Nichols open -loop method applied to the wood-chip tank6 Figure 6:Example 1: Time responses with PID parameters tuned using theZiegler-Nichols open loop method7