INTERNAL MODEL CONTROL (IMC) AND IMC BASED PID
INTERNAL MODEL CONTROL (IMC)AND IMC BASED PID CONTROLLERA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFBachelor of Technology inElectronics and Instrumentation EngineeringByANKIT PORWALROLL NUMBER: 10607001&VIPIN VYASROLL NUMBER: 10607009Department of Electronics & Communication EngineeringNational Institute of TechnologyRourkela2009-20101 Page
INTERNAL MODEL CONTROL (IMC)AND IMC BASED PID CONTROLLERA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFBachelor of Technology inElectronics and Instrumentation EngineeringUnder the Guidance ofProf. T K DANBYANKIT PORWAL (10607001)&VIPIN VYAS (10607009)Department of Electronics & Communication EngineeringNational Institute of TechnologyRourkela2009-20102 Page
NATIONAL INSTITUTE OF TECHNOLOGYROURKELACERTIFICATEThis is to certify that the project report titled “INTERNAL MODEL CONTROL(IMC) AND IMC BASED PID CONTROLLER ” submitted by Ankit Porwal(Roll No: 10607001) and Vipin Vyas ( Roll No: 10607009) in the partialfulfillment of the requirements for the award of Bachelor of Technology Degree inElectronicsNationalandInstituteInstrumentation Engineering duringofsession2006-2010atTechnology, Rourkela (Deemed University) and is anauthentic work carried out by them under my supervision and guidance.To the best of my knowledge, the matter embodied in the thesis has not been submittedto any other university/institute for the award of any Degree or Diploma.Prof. T K DANDate:Department of E.C.ENational Institute of TechnologyRourkela-7690083 Page
ACKNOWLEDGEMENTWe would like to take this opportunity to express my gratitude and sincerethanks to our respected supervisor Prof. T K DAN for his guidance, insight, andsupport he has provided throughout the course of this work.We are also grateful to our respected Prof. U C PATI. Under the guidance ofrespected professors we learned about the great role of self-learning and theconstant drive for understanding emerging technologies, and a passion for knowledge.We would like to thank all faculty members and staff of the Department ofElectronics and Communication Engineering, N.I.T. Rourkela for their extreme helpthroughout course.ANKIT PORWAL (10607001)VIPIN VYAS (10607009)4 Page
CONTENTSAbstract8List of Figures10List of tables101. Introduction to IMC111.1 IMC background121.2 IMC basic structure131.3 IMC parameters141.4 IMC strategy162. Analysis of IMC using SISO Design Tool192.1 Brief Introduction202.2 Steps of using SISO tool for IMC simulation225 Page2.2.1 Control architecture232.2.2 Loading system data242.2.3 Automated tuning252.2.4 Analysis plots26
3. IMC Design Procedure313.1 Introduction323.2 IMC design procedure333.2.1Factorization333.2.2 Ideal IMC controller333.2.3 Adding filter343.2.4 Low pass filter343.3 IMC design for 1st order system3.3.1 Simulation3.4 IMC design for 2nd order system3.4.1 Simulation4. IMC Based PID35363738394.1 Introduction404.2 IMC based PID structure404.3 IMC based PID design procedure426 Page4.3.1 Factorization424.3.2 Ideal IMC Controller434.3.3 Adding filter434.3.4 Low pass filter43
4.3.5 Equivalent standard feedback444.3.6 Comparison with standard PID controller444.4 IMC based PID for 1st order system4.4.1 Simulation result4.5 IMC based PID for 2nd order system4.5.1 Simulation result45464748SIMULATION RESULTSSim1: SISO simulation for IMC 1stst order (tau 1.5)Sim2: SISO simulation for IMC 1st order (tau 2.5)Sim3: SISO simulation for IMC 1nd order (tau 3.5)Sim4: SISO simulation for IMC 2nd order (tau 1)Sim5: SISO simulation for IMC 2nd order (tau 2)Sim6: SISO simulation for IMC 2 order st(tau 3)Sim7:Output variable response for IMC 1 ordersystemstSim8:Manipulated variable response for IMC1ordersystemSim9:Output variable response for IMC 2nd orderndsystemSim10:Manipulated variable response for IMC 2 ordersystemSim11:Output variable response for IMC based PID 1stnd order systemSim12:Output variable response for IMC based PID 2 order system272728292930363638384648Applications of IMC49Conclusion and Future Work50References517 Page
ABSTRACTInternal Model Control (IMC) is a commonly used technique that provides atransparent mode for the design and tuning of various types of control. The ability ofproportional-integral (PI) and proportional-integral-derivative (PID) controllers to meetmost of the control objectives has led to their widespread acceptance in the controlindustry. The Internal Model Control (IMC)-based approach for controller design is oneof them using IMC and its equivalent IMC based PID to be used in control applications inindustries. It is because, for practical applications or an actual process in industries PIDcontroller algorithm is simple and robust to handle the model inaccuracies and henceusing IMC-PID tuning method a clear trade-off between closed-loop performance androbustness to model inaccuracies is achieved with a single tuning parameter.Also the IMC-PID controller allows good set-point tracking but sulky disturbanceresponse especially for the process with a small time-delay/time-constant ratio. But, formany process control applications, disturbance rejection for the unstable processes ismuch more important than set point tracking. Hence, controller design that emphasizesdisturbance rejection rather than set point tracking is an important design problem thathas to be taken into consideration.In this thesis, we propose an optimum IMC filter to design an IMC-PID controller forbetter set-point tracking of unstable processes. The proposed controller works fordifferent values of the filter tuning parameters to achieve the desired response As the IMCapproach is based on pole zero cancellation, methods which comprise IMC designprinciples result in a good set point responses. However, the IMC results in a longsettling time for the load disturbances for lag dominant processes which are notdesirable in the control industry.In our study we have taken several transfer functions for the model of the actual processor plant as we have exactly little or no knowledge of the actual process whichincorporates within it the effect of model uncertainties and disturbances entering into theprocess. Also, the parameters of the physical system vary with operating conditions andtime and hence, it is essential to design a control system that shows robust performancein the case of the above mentioned situations. Then we tried to tune our IMC controllerfor different values of the filter tuning factor.8 Page
Since all the IMC-PID approaches involve some kind of model reduction techniques toconvert the IMC controller to the PID controller so approximation error usually occurs.This error becomes severe for the process with time delay. For this we have taken sometransfer functions with significant time delay or with non invertible portions i.e.containing RHP poles or the zeroes. Here we have used different techniques likefactorization to get rid off these error containing stuffs. It is because if these errors are notremoved then even if IMC filter gives best IMC performance but structurally causes amajor error in conversion to the PID controller, then the resulting PID controller couldhave poor control performance.Thus in our approach to IMC and IMC based PID controller to be used in industrialprocess control applications, there exists the optimum filter structure for each specificprocess model to give the best PID performance. For a given filter structure, as λdecreases, the inconsistency between the ideal and the PID controller increases while thenominal IMC performance improves. It indicates that an optimum λ value also existwhich compromises these two effects to give the best performance. Thus what we meanby the best filter structure is the filter that gives the best PID performance for theoptimum λ value.9 Page
List of FiguresFig 1.1Open loop control strategy12Fig 1.2 IMC basic structure14Fig 1.3 IMC strategy16Fig 2.1Line diagram of system in SISO TOOL20Fig 2.2GUI SISO design tool21Fig 3.1 IMC design strategy32Fig 4.1 IMC based PID design41Fig 4.241Inner loop of rearranged IMC structureFig 4.3 Equivalent IMC rearranged structure42List of tablesTable 1 Effect of time constant (tau) on settling time for 1st order system28Table 2 Effect of time constant (tau) on settling time for 2nd order system3010 P a g e
Chapter 1INTRODUCTION TOINTERNAL MODEL CONTROL (IMC)11 P a g e
CHAPTER 11.1 IMC BackgroundIn process control applications, model based control systems are often used to track setpoints and reject low disturbances. The internal model control (IMC) philosophy relies onthe internal model principle which states that if any control system contains within it,implicitly or explicitly, some representation of the process to be controlled then a perfectcontrol is easily achieved. In particular, if the control scheme has been developed basedon the exact model of the process then perfect control is theoretically possible.For above open loop control system:Output Gc . Gp . Set-point (multiplication of all three parameters)Gc controller of processGp actual process or plantGp* model of the actual process or plant12 P a g e
A controller Gc is used to control the process Gp. Suppose Gp* is the model of Gp thenby setting:Gc inverse of Gp* (inverse of model of the actual process)And ifGp Gp* (the model is the exact representation of the actual process)Now it is clear that for these two conditions the output will always be equal to the setpoint.It show that if we have complete knowledge about the process (as encapsulated in theprocess model) being controlled, we can achieve perfect control.This ideal control performance is achieved without feedback which signifies thatfeedback control is necessary only when knowledge about the process is inaccurate orincomplete.Although the IMC design procedure is identical to the open loop control designprocedure, the implementation of IMC results in a feedback system. Thus, IMC is able tocompensate for disturbances and model uncertainty while open loop control is not. AlsoIMC must be detuned to assure stability if there is model uncertainty.1.2 IMC basic structureThe distinguishing characteristic of IMC structure is the incorporation of the processmodel which is in parallel with the actual process or the plant. Also we consider that „*‟is generally used to represent signals associated with the model.13 P a g e
1.3 IMC parametersThe various parameters used in the IMC basic structure shown above are as follows:Qc IMC controllerGp actual process or plantGp* process or plant modelr set point14 P a g e
R‟ modified set point (corrects for model error and disturbances)u manipulated input (controller output)d disturbanced* estimated disturbancey measured process outputy* process model outputFeedback signal:d* (Gp - Gp*)u dSignal to the controller:R‟ r- d* r- (Gp - Gp*) u – dNow we consider a limiting casePerfect model with no disturbance:We will say a model to be perfect ifProcess model is same as actual processi.e. Gp Gp*no disturbance meansd 0Thus we get a relationship between the set point r and the output y asy Gp . Qc .rThis relationship is same for as we got for open loop system design. Thus if the controllerQc is stable and the process Gp is stable the closed loop system will be stable.But in practical cases always the disturbances and the uncertainties do exist hence actualprocess or plant is always different from the model of the process.15 P a g e
1.4 IMC StrategyAs stated above that that actual process differs from the model of the process i.e. processmodel mismatch is common due to unknown disturbances entering into the system. Dueto which open loop control system is difficult to implement so we require a controlstrategy through which we can achieve a perfect control. Thus the control strategy whichwe shall apply to achieve perfect control is known as INTERNAL MODEL CONTROL(IMC) strategy.In the above figure, d(s) is the unknown disturbance affecting the system. Themanipulated input u(s) is introduced to both the process and its model. The processoutput, y(s), is compared with the output of the model resulting in the signal d*(s). Hencethe feedback signal send to the controller isd*(s) [Gp(s) – Gp*(s)].u(s) d(s)16 P a g e
In case d(s) is zero then feedback signal will depend upon the difference between theactual process and its model.If actual process is same as process model i.e Gp(s) Gp*(s) then feedback signal d*(s)is equal to the unknown disturbance.So for this case d*(s) may be regarded as information that is missing in the modelsignifies and can be therefore used to improve control for the process. This is done bysending an error signal to the controller.The error signal R’(s) incorporates the model mismatch and the disturbances and helps toachieve the set-point by comparing these three parameters. It is send as control signal tothe controller and is given byR’(s) r(s) – d*(s)(input to the controller)And output of the controller is the manipulated input u(s). It is send to both process andits model.u(s) R‟(s) . Gc(s) [r(s) – d*(s)] Gc(s) [ r(s) – {[Gp(s) – Gp*(s)].u(s) d(s)} ] . Gc(s)u(s) [ [r(s) – d(s)] Gc(s) ] / [ 1 { Gp(s) – Gp*(s) } Gc(s) ]Buty(s) Gp(s) . u(s) d(s)Hence, closed loop transfer function for IMC scheme isy(s) {Gc(s) . Gp(s) . r(s) [1 – Gc(s) . Gp* (s)] . d(s)} / { 1 [Gp(s) – Gp* (s)] Gc(s) }Now if Gc(s) is equal to the inverse of the process model and if Gp(s) Gp*(s) thenperfect set point tracking and disturbance rejection can be achieved.17 P a g e
Also to improve the robustness of the system the effect of model mismatch should beminimized. Since mismatch between the actual process and the model usually occur athigh frequency end of the systems frequency response, a low pass filter Gf(s) is usuallyadded to attenuate the effects of process model mismatch.Thus the internal model controller is usually designed as the inverse of the processmodel in series with the low pass filter i.eGimc(s) Gc(s). Gf(s)Where order of the filter is usually chosen so that the controller is proper and to preventexcessive differential control action. The resulting closed loop then becomesy(s) {Gimc(s) . Gp(s) . r(s) [1 – Gimc(s) . Gp* (s)] . d(s)} / { 1 [Gp(s) – Gp* (s)]Gimc(s) }18 P a g e
Chapter 2ANALYSIS OF IMC USINGSISO DESIGN TOOL19 P a g e
CHAPTER 22.1 Brief introductionSISO TOOL is a Graphical User Interface (GUI) which lets us design single-input/singleoutput (SISO) compensators by graphically interacting with the root locus, Bode plots ofthe open-loop system. To insert the plant data into the SISO Tool, select the Import itemfrom the File menu. By default, the control system configuration isr -- [ F ]-- O--- [ C ]--- [ G ]----- --- y- --------- [H] ---------- Fig 2.1 Line diagram of a system in SISO TOOLwhere C and F are tunable compensators.SISOTOOL (G) specifies the plant model G to be used in the SISO Tool.SISOTOOL (G, C) and SISOTOOL (G, C, H, F) further specify values for thefeedback compensator C, sensor H, and pre-filter F.By default C, H, and F are all unit gains. Using the SISO Design Tool, we cangraphically tune the gains and dynamics of the compensator (C) and pre-filter (F) using amix of root locus and loop shaping techniques.For example, we can use the root locus view to stabilize the feedback loop and enforcesome minimum damping, and use the Bode diagrams to adjust the bandwidth, check thegain and phase margins, or add a notch filter for disturbance rejection.20 P a g e
Fig 2.2 GUI SISO design toolThe SISO Design Tool is designed to work closely with the LTI Viewer, allowing us torapidly iterate on your design and immediately see the results in the LTI Viewer. Whenwe make a change in your compensator, the LTI Viewer associated with our SISODesign Tool automatically updates the response plots that we have chosen. By default,the SISO Design Tool displays the root locus and open-loop Bode diagrams for ourimported systems. We can also bring up an open-loop Nichols view or pre-filter Bodediagram by selecting these items in the View menu.Imported systems can include any of elements of the feedback structure diagram locatedto the right of the Current Compensator panel. We cannot change imported plant (G) orsensor (H) models, but we can use the SISO Design Tool for designing a new (ormodifying an existing) pre-filter (F) or compensator (C) for your imported plant andsensor configuration.21 P a g e
2.2 Using SISO TOOL for IMC implementationIMC Design with Automatic TuningWe will now design the compensator in an IMC structure in SISO Design Tool.Open SISO Design ToolAt the MATLAB command prompt, type SISOTOOL and the Controls and EstimationTools Manager opens.22 P a g e
2.2.1 Control architecture Click on the “Control Architecture” button on control tool and estimation manager. Select Configuration 5 for IMC structure from the panel in the Control Architecturedialog box.23 P a g e
2.2.2 Loading system dataFirst we create the following LTI models in MATLAB command prompt:Considering for 1st order systems tf('s');G1 1 / (7 * s 3);G2 G1;Gd 5 / (3 * s 1);Considering for 2nd order systems tf('s');G1 16/ (s 2 2 * s 16);G2 G1;Gd 5 / (3 * s 1);24 P a g e
Note: G1 is the real plant used; G2 is an approximation of the real plant and it is used asthe plant model in the IMC structure.G1 G2 means that there is no model mismatch.Gd is the disturbance model.Now we load the system data into the Controls and Estimation Tools Manager byclicking on the System Data button. The System Data Dialog is given the abovementioned values.2.2.3 Automated tuningTo tune the IMC compensator, we will click on the Automated Tuning on the Controlsand Estimation Tools Manager and select Internal Model Control (IMC) Tuning as thedesign method.25 P a g e
Here we have taken controller of second order and now we will vary the time constantand compare different output responses for both first order and second order system.Now we take 3 different values of time constant2.2.4 Analysis plotsTo look at the closed loop response, click on the Analysis Plots on the Controls andEstimation Tools Manager, select Step as the plot type for Plot 1 and make Closed Loopr to y as the content of Plot 1:26 P a g e
First order plotsSimulation1: For tau 1.5Simulation2: For tau 2.527 P a g e
Simulation3: For tau 3.5We have taken the first order transfer function as:G 1 / (7*s 3)Effect of time constant (tau) on settling time for 1st order system:S. NoValues of time constant (tau)Settling time (in sec)11.5922.51533.525Table 128 P a g e
For 2nd order systemSimulation4: For tau 1Simulation5: For tau 229 P a g e
Simulation6: For tau 3We have taken the second order transfer function as:G 16 / (s 2 2*s 16)Effect of time constant (tau) on settling time for 2nd order system:S. NoValues of time constant (tau)Settling time (in sec)11822163325Table 230 P a g e
Chapter 3IMC DESIGNPROCEDURE31 P a g e
CHAPTER 33.1IntroductionThe IMC design procedure is exactly the same as the open loop control design procedure.Unlike open loop control, the IMC structure compensates for disturbances n modeluncertainties. The IMC tuning (filter) factor “lem” is used to detune for modeluncertainty. It should be noted that the standard IMC design procedure is focused on setpoint responses but good set point responses do not guarantee good disturbance rejection,particularly for the disturbances that occur at the process inputs. A modification of thedesign procedure is developed to improve input disturbance rejection.32 P a g e
Tolerance of model uncertainty is called robustness. Like open loop control thedisadvantage compared with standard feedback control is that IMC doesn‟t handleintegrating or open loop unstable systems.3.2 IMC design procedureConsider a process model Gp*(s) for an actual process or plant Gp(s). The controllerQc(s) is used to control the process in which the disturbances d(s) enter into the system.The various steps in the Internal Model Control (IMC) system design procedure are:3.2.1 FACTORIZATIONIt means factoring a transfer function into invertible (good stuff) and non invertible(bad stuff) portions. The factor containing right hand plane (RHP) or zeros or timedelays become the poles in the inverts of the process model when designing thecontroller. So this is non invertible portion which has to be removed from the system.Mathematically it is given asGp*(s) Gp*( )(s) Gp*(-)(s)WhereGp*( )(s) is non-invertible portionGp*(-)(s) is invertible portionUsually we use all pass factorization3.2.2 IDEAL IMC CONTROLLERThe ideal IMC controller is the inverse of the invertible portion of the process model.It is given asQc*(s) inv [ Gp*(-)(s)]33 P a g e
3.2.3 ADDING FILTERNow we add a filter to make our controller proper.A transfer function is said to be proper if the order of the denominator is at least asgreat as the order of the numerator. If they are exactly of the same order the transferfunction is said to be semi-proper.If the order of the denominator is greater than the order of the numerator the transferfunctions is strictly proper.Thus a controller can be physically implemented if it is proper.So to make the controller proper mathematically it is given asQc(s) Qc*(s) f(s) inv [ Gp*(-)(s)] f(s)Wheref(s) is a low pass filter3.2.4 LOW PASS FILTER f(s)In order to improve the robustness of the system the effect of model mismatch shouldbe minimized. Since mismatch between the actual process and the model usuallyoccur at high frequency end of the systems frequency response, a low pass filter f(s) isusually added to attenuate the effects of process model mismatch.Thus the internal model controller is usually designed as the inverse of the processmodel in series with the low pass filter i.eQc(s) Qc*(s) f(s) inv [ Gp*(-)(s)] f(s)Wheref(s) 1/( lem* s 1) nWhere lem is the filter tuning parameter to vary the speed of the response ofclosed loop system.Now the low pass filter can be of three types:34 P a g e
a) If we focus on setpoint changes, the form of filter used isf(s) 1/( lem* s 1) nhere n is the order of the process.b) If we focus on good tracking of ramp set point changes the filter of the formused isf(s) (n. lem. s 1)/ (lem* s 1) nc) If we focus on good rejection of step input load disturbances the filter of theform use isf ( gamma.s 1)/( lem* s 1) nwhere gamma is any constant.3.3 IMC design for 1st order systemNow we apply the above IMC design procedure for a first order system with a givenprocess model. Given process model for 1st order system : Gp*(s) Kp*/[Tp*(s) 1] Gp*(s) Gp*( )(s) . Gp*(-) (s) 1 . Kp*/[Tp*(s) 1] Qc*(s) inv[Gp*(-) (s) ] [Tp*(s) 1] / Kp* Qc(s) Qc*(s). f(s) [Tp*(s) 1] / [ Kp*. (lem(s) 1)] f(s) 1 / (lem. s 1) y(s) Qc(s). Gp(s).r(s) Gp*( )(s) . f(s). r(s){PERFECT MODEL} Output variable:y(s) r(s)/(lem. s 1) Manipulated variable:u(s) Qc(s) . r(s) [Tp*(s) 1].r(s)/ [ Kp. (lem. s 1)35 P a g e
3.3.1Simulation plot for IMC 1st order systema) Output variable responseSim7: Simulation of output variable responseb) Manipulated variable responseSim8: Simulation of manipulated variable response36 P a g e
3.4 IMC design for 2st order system Given process model for 2nd order system: Gp*(s) [-9s 1] / [ (15s 1) (3s 1)] Gp*(s) Gp*( )(s) . Gp*(-) (s) (-9s 1 )/(9s 1) . [9s 1] / [ (15s 1) (3s 1)] Qc*(s) inv[Gp*(-) (s) ] [ (15s 1) (3s 1)] / ( 9s 1) Qc(s) Qc*(s). f(s) [ (15s 1) (3s 1) / ( 9s 1) ] . [ 1 / (lem . s 1) ] f(s) 1 / (lem . s 1) y(s) Qc(s). Gp(s).r(s) Gp*( )(s) . f(s). r(s){PERFECT MODEL} Output variable:y(s) [-9s 1] / [ (15s 1) (3s 1)] . r(s) [-9s 1] / [ 9 lem s 2 (9 lem ) s 1] Manipulated variable:u(s) Qc(s) . r(s) [ (15s 1) (3s 1) / ( 9s 1)(lem . s 1) ] . r(s) [(45 s 2 18 s 1)/ ( 9 lem s 2 (9 lem ) s 1)] . r(s)37 P a g e
3.4.1 Simulation plot for IMC 2st order systema) Output variable responseSim9: Simulation of output variable responseb) Manipulated variable responseSim10: Simulation of manipulated variable response38 P a g e
Chapter 4IMC BASED PID39 P a g e
CHAPTER 44.1IntroductionThe IMC structure can be rearranged to form a standard feedback control system that caneasily handle open loop unstable system as not the case with IMC. This modification ofthe IMC design procedure is developed to improve the input disturbance rejection. TheIMC based PID structure which uses a standard feedback structure uses the processmodel in an implicit manner i.e. PID tuning parameters are often adjusted based on thetransfer function model but it is not always clear how the process model affects thetuning decision. In the IMC procedure the controller Qc(s) is directly based on the goodpart of the process transfer function. Also the IMC formulation generally results in onlyone tuning parameter, the close loop time constant (filter tuning factor). The IMC basedPID tuning parameters are then the function of this time constant. The selection of theclosed loop time constant is directly related to the robustness (sensitivity to the modularof the closed loop system). Also, for open loop unstable processes it is necessary tiimplement the IMC strategy in standard feedback form, because the IMC suffers frominternal stability problems. Though the IMC based PID controller will not give the sameperformance when there are process time delays because the IMC based PID proceduresuses an approximation for the dead time. But if the process has no time delays and theinputs do not hit a constraint then the IMC based PID controller give the sameperformance as does the IMC.4.2 IMC based PID structureIn the IMC structure the point of comparison between the process and the model outputcan be moved as shown in the figure below to form a standard feedback structure whichis nothing but another equivalent feedback form of IMC structure know n as IMC basedPID structure.40 P a g e
41 P a g e
4.3 IMC based PID design procedureConsider a process model Gp*(s) for an actual process or plant Gp(s). The controllerQc(s) is used to control the process in which the disturbances d(s) enter into the system.The various steps in the Internal Model Control (IMC) system design procedure are:4.3.1FACTORIZATIONIt means factoring a transfer function into invertible (good stuff) and non invertible(bad stuff) portions. The factor containing right hand plane (RHP) or zeros or timedelays become the poles in the inverts of the process model when designing thecontroller. So this is non invertible portion which has to be removed from the system.Mathematically it is given asGp*(s) Gp*( )(s) Gp*(-)(s)WhereGp*( )(s) is non-invertible portionGp*(-)(s) is invertible portionUsually we use all pass factorization42 P a g e
4.3.2IDEAL IMC CONTROLLERThe ideal IMC controller is the inverse of the invertible portion of the process model.It is given asQc*(s) inv [ Gp*(-)(s)]4.3.3 ADDING FILTERNow we add a filter to make our controller proper.A transfer function is said to be proper if the order of the denominator is at least asgreat as the order of the numerator. If they are exactly of the same order the transferfunction is said to be semi-proper.If the order of the denominator is greater than the order of the numerator the transferfunctions is strictly proper.Thus a controller can be physically implemented if it is proper.So to make the controller proper mathematically it is given asQc(s) Qc*(s) f(s) inv [ Gp*(-)(s)] f(s)where f(s) is a low pass filter4.3.4 LOW PASS FILTER [f(s)]In order to improve the robustness of the system the effect of model mismatch shouldbe minimized. Since mismatch between the actual process and the model usuallyoccur at high frequency end of the systems frequency response, a low pass filter f(s) isusually added to attenuate the effects of process model mismatch.Thus the internal model controller is usually designed as the inverse of the processmodel in series with the low pass filter i.eQc(s) Qc*(s) f(s) inv [ Gp*(-)(s)] f(s)43 P a g e
Wheref(s) 1/( lem* s 1) nWhere lem is the filter tuning parameter to vary the speed of the response ofclosed loop system.Now the low pass filter can be of three types:a) If we focus on setpoint changes, the form of filter used isf(s) 1/( lem* s 1) nhere n is the order of the process.b) If we focus on good tracking of ramp set point changes the filter of the formused isf(s) (n. lem. s 1)/ (lem* s 1) nc) If we focus on good rejection of step input load disturbances the filter of theform use isf ( gamma.s 1)/( lem* s 1) nwhere gamma is any constant.4.3.5 Equivalent standard feedback controllerBy rearranging the IMC we obtain equivalent standard feedback controller usingtransformation.Gc Qc/(1-Qc Gp*)We write this expression in the form of a ratio between two polynomials.4.3.6 Comparison with standard PID controllerNow we compare with PID Controller transfer functionFor first order :Gc(s) [Kc . (Ti .s 1)]/ (Ti . s)And find Kc and Ti ( PI tuning parameters)44 P a g e
Similarly for 2nd order we compare with the standard PID controller transfer functiongiven by :Gc(s) Kc . [(Ti . Td . s 2 Ti . s 1)/Ti . s]. [ 1/ Tf . s 1]WhereT Tau (any constant)Ti integral time constantTd derivative time constantTf filter tuning factorKc controller gainNow we perform closed loop simulations for above procedure and adjust lem (lemda)considering a trade off between performance and robustness (sensitivity to modelerror).4.4 IMC based PID for 1st order systemNow we apply the above IMC based PID design procedure for a first order systemwith a given process model. Given proc
constant drive for understanding emerging technologies, and a passion for knowledge. We would like to thank all faculty members and staff of the Department of Electronics and Communication Engineering, N.I.T. Rourkela for their extreme help through
17716.4.3 IMC 121 Motion Control System Programming Manual 17716.5.65 IMC 121 Handheld Pendant Operator’s Manual 17716.4.2 IMC 121 AMP Reference Manual 17716.2.3 IMC 123 Motion Control System Installation Manual 1771H3DOC 17716.4.1 IMC 123 Motion Control System Programming Manual 17716.5.60 IMC 123 Handheld Pendant Operator’s Manual 17716.7 .
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imc CANSAS is the ideal tool for achieving cost effec-tive, high precision decentralized measurements and control. High channel count, centralized systems also benefit from the imc CANSAS design: rack mountable, par-allel acquisition and easy module interchangeability are key features which make imc CANSAS popular for
imc STUDIO - the modular software for measurement, control and automation Whether you want to use your imc imc CRONOSflex in a "black box" configuration for easy data acquisition, or you want to set up Live-Monitoring on hundreds of channels during prototype testing, or you want to create a
Integrated marketing communications (IMC) has been studied and used in the global market for the past 20 years and still today, there are many different definitions and/or perceptions of IMC. Many practitioners accepted IMC as a valid new marketing tool and others have contradicted the idea of IMC as a misunderstanding (Cornelissen & lock, 2000 .
in VMC and an ILS in simulated IMC. The advanced operational concept was an IMC maneuver that used the same flight path flown for the conventional VFR traffic pattern approach; however, this "VMC-like" approach was flown in simulated IMC. Figure 5 shows a gods-eye-view of the evaluation maneuvers. The VFR traffic pattern incorporated a
Step 4: All standard IMC shipments must be shipped on the specified IMC Overseas Block Pallet 960mm x 1140mm (38" x 45"). In case that the IMC carton size exceeds the dimensions of the standard pallet then a special pallet with same foot print size of the carton used is required .This special pallet must follow the same construction
