Presentation on theme: "Module 15: Process Control and Process Integration – Tier I"— Presentation transcript:
1 Module 15: Process Control and Process Integration – Tier I Program for North American Mobility in Higher Education (NAMP)Introducing Process Integration for Environmental Control in Engineering Curricula (PIECE)Module 15: Process Control and Process Integration – Tier ICreated atUniversidad de Guanajuato & École Polytechnique de Montréal
3 This module is divided in three essential complements, it will demonstrate the relationship between the use of PI tools to design a process and the control strategies.
4 Structure Tier one: Tier Two: Tier Three: Basic Concepts About Process ControlTier Two:Use of PI tools and especially dynamic simulation to address control strategiesTier Three:Analysis of a real process.
5 Index: Tier one: Comparison between Steady State and Dynamic State. Important Definitions about dynamic state.Dynamic Models.
6 Index:Tier two:Relationship between Process Design and Process ControlDynamic Effect on recycle Structures
8 Tier 1Objective:Understand the difference between steady state and dynamic state.Understand basic concepts about control process.Understand the advantages of Dynamic Simulation.
9 Initial conditions = Final conditions Steady StateInitial conditions = Final conditionsProcessT2T1Flow 1Flow 2INPUTOUTPUT
10 When a system is at steady state, there is no change in the process, input and output remains constant in the time.INPUTProcessOUTPUTConstantTIMEConstant
11 Initial conditions Final conditions Dynamic State:Initial conditions Final conditionsIn steady state every variable in the process remain constant while dynamic state one or some variables could change thereby affecting the processCHANGE WITH TIMEKEY PHRASE
12 And now……What does control mean?Why is it necessary?
13 Before the next part it is necessary to understand the next concepts: Manipulated VariableA variable that can be changed to maintain constant the controlled variable.Controlled VariableA variable which is desirable to control.
14 Next there is a typical example of control, everyone has needed to control the temperature when you wish to take a shower…………How ??An adequate temperature of water is desirableChanging flows of hot and cold water.
15 Let’s identify new concepts about control…. DisturbanceProcessSensorFinal Control Element
16 Variables which help to control temperature Controlled VariableTemperatureVariables which help to control temperatureFlows of cold and hot water
17 It is a feedback control loop. It is possible to observe some elements:SensorInputOutputDisturbancesFinal ControlElementProcessDesired TemperatureControllerCauseEffectIt is a feedback control loop.
18 Either flow of cold or flow of hot water In addition if it is usedEither flow of cold or flow of hot waterTemperatureSISOSingleSingleInputOutputBut if…
19 MIMO Flow of cold and flow of hot water Temperature and Total flow MultipleMultipleInputOutput
20 To ControlTo take necessary actions to maintain a system in desired conditions.
22 High Quality Manufactured Products Control SystemHigh Quality Manufactured ProductsRaw MaterialsWhat would happen if there was lower quality raw materials , what should be considered ?
23 Some aspects that should be considered: Raw materials quality and availabilityServices quality and availabilityProduct Quality and throughputPlant equipment availabilityEnvironmental conditionsProcess materials behaviorPlant equipment malfunctionControl system malfunctionLink to other plantsDrifting and decaying factors
25 Information from existing plants Steps to design a Control SystemInformation from existing plantsFormulate Control ObjectivesManagement ObjectivesPhysical and chemical principlesDevelop process modelComputer SimulationProcess Control theoryDevise Control StrategyComputer SimulationExperience with existing plantsSelect Control HardwareVendor Hardware selectionInstall control systemAdjust controller settingsFinal Control system
26 Objectives of a control process system SafetyEnvironmental ProtectionMonitoring and diagnosisControl SystemEquipmentProtectionProfitSmoothOperationProduct Quality
27 Environmental Protection SafetySafety of people in the plant and in the surrounding community is of paramount importance. Working at an industrial plant should involve less risk than any other activity in persons life.Environmental ProtectionFederal, state or local laws regulations require that the effluents of a plant satisfy certain specifications.Equipment protectionOperating conditions must be maintained within bounds to prevent damage to expensive equipmentSmooth OperationIt is desirable because it results in attenuated disturbances to all the integrated units.
28 Monitoring and Diagnosis Product QualityProcess Control contributes maintaining the operation required for excellent product quality set by the purchasers.OptimizationIt is concerned with operating the process so that the operation results in producing the highest rate of profit.Monitoring and DiagnosisBoth the controlled and manipulated variables must be monitored in order to evaluate the performance of a control system.
29 Control System Less Output Variation Higher Quality When a process control is implemented, the variability of the key parameters is reduced.xATime0.970.990.98Without controlWith controlTimexA0.9750.9850.98Control SystemLess Output VariationHigher Quality
30 MATHEMATICAL MODELS Are the models necessary? A mathematical model is a representation of a process, using mathematical relationships, an equation or a set of equations. These equations are obtained from basic conservation balances as material, energy and momentum.Basic Balance EquationsMathematical ModelProcessConstitutive RelationshipsAre the models necessary?
31 When should the reaction be stopped to have a maximum B concentration? Models allow to analyze behavior system when any change is made. It is a safe, fast and easy way.What would happen if inlet flow stop, how fast will the tank be empty?FlowLiquid Level
32 Distributed parameters Classification of Fundamental ModelsDependent variables are not function of spatial locationUses macroscopic balancesOrdinary Differential equationsLumped ParametersDependent variables are function of spatial locationUses microscopic balancesPartial differential equationsDistributed parameters
33 Dynamic state vs. Steady-State. ModelBasic EquationsNo Accumulation TermAccumulation TermAlgebraicEquationsDifferentialEquationsSteady StateDynamic State
34 Steady State Conservation Law .Steady State Conservation LawMass inMass producedMass consumedMass out-=-+Dynamic State Conservation LawRate of mass producedRate of changeRate of mass inRate of mass outRate of mass consumed-=-+
35 The dynamic model gives a relation for determining the output variable as function of time for arbitrary variations in the input.T(Energy)L(Inventory)Accumulation TermVariation with time !!CA(Species)
36 Dynamic models of chemical processes invariably consist of one or more partial or ordinary differential equations. To solve them it is possible to use the Laplace transform. It means that transient responses of the dependent variables can be found.BUT Just for linear equations !!Laplace DomainInverse LaplaceLaplaceDifferential equations ModelSolutionTime Domain
37 When a system is under control, it is located in a small region. LinearizationVery often, it is possible to find non-linear models, and linearized methods provide useful result for many process. The application is justified by the small region of a process when under control.When a system is under control, it is located in a small region.
38 For this non linear function The linear approximation about (xs,ys) can be obtained by applying a Taylor series expansion to this function truncating the second order and higher order terms.These terms are known because they are evaluated at xs and ys
40 Changes in variable from initial values or conditions. Having the model, now it desirable to make the model as GENERAL as possible in order to analyze the dynamic behavior of different processes.Subtracting the steady state equation and defining deviation variables.How?Deviation variablesChanges in variable from initial values or conditions.New conditionsInitial conditions
41 Model Deviation variables Laplace Transform Transfer Function G (s) Y (s)X (s)Transfer FunctionG (s)
42 Dynamic relation Input-Output Physical Realizability Condition (Laplace Domain)InputPhysical Realizability ConditionTransfer function is the Laplace Transform of the output variable Y(s) divided by the Laplace Transform of the input variable X(s) with all the initial conditions equal to zero.
43 Steps to obtain a transfer function LaplaceTransformLinearModelDeviation variablesTransfer FunctionLinearizationNon Linear
44 Gain represents the difference between two steady state of the system. Time constant is indicative of the speed of response of the process. It has time unitsLarge ValueSlow process responseSmall ValueFast process response
45 Transfer function of different systems. Efecto con diferente ganancia, incluir las graficas de entrada, usar las misma variables, in cluir deltaKTransfer function of different systems.Differential EquationTransfer FunctionSteady-State63%
46 Testing another transfer function Steady-StateTime
47 Degree of oscillation in a process response after a perturbation. ADD GraphicsDifferential EquationTransfer FunctionDegree of oscillation in a process response after a perturbation.OverdampedCritically DampedUnderdamped
48 Every process can be characterized in term for its values of time constant and gain.
49 Key characteristics of an underdamped second order response. Rise Time (trise)Time required to first cross the new steady state value and is given byb) Percentage overshoot(B/D*100)
50 c) Decay Ratio (C/B)d) Period of oscillation (T )e) Response timeTime required for the response to remain within a ± 5% band, based upon the steady state change in y.
53 And what is stability……? How is it possible to know if a system is stable?When is a system stable?It is necessary to analyze the poles in the general form of a transfer function
54 Poles of transfer function General FormNumerator Polynomial in s of order mDenominator polynomial of s of order nPoles of transfer functionPoles are the roots of P(s), it means the values that render P(s) zero.
55 a) Assume that P(s) can be factorized into a series of real poles Pi Inverse Laplace transformReImxp>0p=0p<0TimeIt growsto infinity.
56 Sinusoidal behavior with amplitude of c/p b) Assume that one of the factors o P(s) isThe roots areSinusoidal behavior with amplitude of c/pInverse transform LaplaceReImxTime
57 c) Assume that one of the factors of P(s) is (s2+as+b) Inverse transform LaplaceFactoringIf a2- 4b>0 apply a)If a2- 4b=0 Critically damped behavior.If a2- 4b<0 apply the next result:
59 For complex conjugated poles, the larger the magnitude of the imaginary component (further the pole is from x axis ) the more oscillatory the response.
60 Negative real roots is stable Plane Imaginary - RealReImNegative real roots is stableUnstableRegionIf there are positive real roots, even if it is a complex number, it will be unstable
61 StabilityA system is stable when bounded input changes result in bounded output, otherwise it is unstable.A variable is bounded when it does not increase in magnitude to infinity as time increases.The poles of a transfer function indicate very specifically the type of dynamic behavior that the transfer functions represent for a wide variety of inputs .
62 This is the block diagram for the system Block Diagrams.Individual elementsPhysical ModelSensorDisturbanceEvery element has a transfer function !!ProcessRepresentationGDFinal Control ElementGvGPGSThis is the block diagram for the system
63 Block Diagram AlgebraIt provides the method for combining individual transfer functions into an overall transfer function behavior.G1(s)Y (s)X (s)CauseEffectGn(s)G3(s)G2(s)G1(s)X0X2X3Xn
66 Comparison open-loop and closed-loop u (s)Y (s)G (s)StimulusResponseControl action depends the outputClosed Loop.u (s)Y (s)G (s)StimulusResponseAction
67 Feedback makes use of a output of a system to influence an input to the same system SensorInputOutputDisturbancesFinal ControlElementProcessDesired TemperatureControllerNegativeAction tends to reduce the error from desiredPositiveAction tends to increase the error from desired
68 Objectives of a feedback control Maintain safe operation.Maintain quality product.
69 StructureMeasurement ElementMeasurementError Detection ElementComparison and CalculationControl ElementCorrectionBasic ElementsBasic Actions
79 The controller does this task In a real process what is desired is to maintain the controlled variables in a given value despite the presence of disturbances. The control system does this task.Set PointThe controller does this task
80 Standard form for the PID (Proportional-Integral-Derivative) algorithm Tuning parameters of controller
81 a) ProportionalControl action is proportional to error.
82 Characteristics of Proportional Action. Proportional action does not change the order of the process.Closed Loop time constant is smaller then the open loop time constant. Proportional action makes faster the response of the process.There is an offset. (The manipulated variable will change until the error is constant)
83 b) IntegralIntegralControl action is proportional to the integral of the error.It allows to reduce the error to zero
84 Characteristics of Integral Action. All steady state corrections for disturbances or set point changes must come from integral actions.There is no offset at steady state. (The manipulated variable will change until error equal to zero)Integral action increase the order of the process dynamics by 1.Increasing the amount of integral action ( decreasing ) results in a faster responding feedback process, but increases the degree of oscillatory behavior.
85 c) Derivative Derivative Control action that is proportional to the derivative of rate of change or error
86 Characteristics of Derivative Action. It does not change the order of the processIt does not eliminate offsetDerivative action tends to reduce the oscillatory nature of feedback, however it amplifies process noise.
87 Comparison between P, PI and PID action OffsetPID
88 Tuning Criteria Eliminate deviations from set point. Good set point tracking should be minimized.Excessive variations of the manipulated variable should be avoidedThe controlled process should remain stable for major disturbances upsets.
89 Deviations from set point PerformanceDeviations from set pointPIDcontrollerReliabilityController’s ability to remain in service while handling major disturbancesTuning consists to find the best parameters for the controller to achieve the control objective.
90 Performance Assessment IAE (Integral Absolute Error)ITAE (Integral Time Absolute Error)ISE (Integral Square Error)ITSE (Integral Time Square Error)
91 ISE and ITSE penalize larger deviations more severely than IAE and ITAE ITAE and ITSE penalize deviations at long time more severely than IAE and ISE
93 Cohen and CoonIt assumes that a FOPDT model of the process is available.FOPDT (First Order plus Delay Time)
94 Ziegler-Nichols Tuning The ultimate parameters are obtained by operating a P only controller under sustained oscillations and then measuring the period of the oscillations and noting the gain of the P only controller.PPIPIDKc0.5Kcu0.45Kcu0.6 KcutI-Pu /1.2Pu /2tDPu /8KuUltimate GainPuUltimate Period
95 Direct Method Synthesis This method is based upon prescribing a desired form for the system’s response and then finding a controller strategy and parameters to give that response.This block diagramInputOutputGvGpGcYsp(s)Y(s)+-has the next closed loop equation for changes in set point:
96 This is called Synthesis Equation If the system’s response for the relation Y/Ysp, is specified. Then the controller that will give this closed loop response characteristic is that which satisfies the following equation:This is called Synthesis EquationThus, the required controller can be designed if we have a model of the process, it may have a PID form.
97 If the desired response form is ThenThe process model is required
98 If the process model is a first order process The controller strategy is:This is simply a PI controller with settingsDepending the process model, is possible to have a PID controller.
99 ADVANTAGES FEEDBACKAchieves zero steady state offset for all step-like input.Uses only one measurementAlgorithm and tunes rules available
100 DISADVANTAGESProcess output must be upset before feedback action beginFeedback control performance can be poor for some combinations of disturbance frequencies and feedback dynamicsPoor feedback can cause instability, PID does not provide the best possible control for all process.
102 There are many industrial systems which have multiple inputs and multiples outputs …..
103 Distillation ColumnsSteam and reflux affect both top and bottom product compositionsGas-liquid separatorGas and liquid product flows affect both tank level and pressure.
104 Characteristics Multi-input Multi-output (MIMO) processes Several CV’s and several MV’sThe numbers of CV’s and MV’s are not necessary same.One MV affects all or some of CV’s. ( Process interaction )CharacteristicsWhich MV will control which CV? ( Pairing )One control loop affects the other control loops (Control loop interaction)Decentralized control: Multiple SISO controllers are applied.Centralized control: All MV’s will be manipulated to all or some CV’s.
105 In contrast Single-input single-output (SISO) processes One CV and one MV: No need of pairing
108 It means that there is interaction !! MIMOAffectsOne InputTwo* OutputsU1(s)Y1(s)Y2(s)U2(s)It means that there is interaction !!A multivariable process is said to have interaction when process input (manipulated) variables affect more than one process output (controlled) variable.
109 ControllabilityThe ease with a continuous plant can be held at a specific steady state.ResiliencyMeasures the degree to which a processing system can meet its design despite external disturbances and uncertainties in its design parameters.
110 Controllability is defined for a selected set of manipulated and controlled variables, and a system may be controlled for one selection and uncontrolled for another selection.In order to control the process is necessary to know the interaction among the variables and how the variables will be pairing.
111 Commonly used controllability measures RGA (Relative Gain Array) (Bristol, 1966)Niderlinski IndexCondition NumberModel of the process necessaryResiliency measuresRelative Disturbance GainDisturbance Cost (Lewin, 1996)Disturbance Condition Number (Skogestad & Morari, 1987)Model of the process and disturbances necessary
112 11 : measure of the interaction using u1 to control y1 Relative Array GainOpen LoopClosed LoopEffecty1(s)u1 – y1G11u1(s)+K11CL=K11OLK ΔyiG21InteractionG12u2(s)y2(s)Steady stateControllerG22+11 : measure of the interaction using u1 to control y1Gain Open LoopGain Closed Loop
113 Recommendation to pairing With the other loops openRecommendation to pairingPairDo not pairAvoidAvoidDo not pair
114 Control integralNiderlinski IndexTool for input-output pairing multi-loop SISO controllers with integral action.Sufficient condition for instability if independently tuned controllers with integral action are used.NI<0Necessary condition for stability of the closed loop system in the case of independent controller tuning.NI>0
115 Singular Value Decomposition Any matrix can be decomposed as:U is matrix of output singular vectors (output directions)V is matrix of input singular vectors (input directions)Output and input signals are vectors
116 First ColumnRepresents the input direction with the largest amplification.Matrix VLast ColumnRepresents the input direction with the smallest amplification.First ColumnOutput direction where inputs are least effectiveMatrix ULast ColumnOutput direction where inputs are more effective
117 Σ is a diagonal matrix containing the singular values of G The maximum singular value represents the largest gain for any input direction, while the minimum singular value represents the smallest gain for any input direction.
118 Esquema explicativo, razon. Condition NumberIt is an indicator or directionality of the process gain. CN is obtained by calculating the ratio of the maximum singular value to the minimum singular value of the gain matrix.Gain MatrixIf CN is large (CN >10), K is ill-conditioned.If CN is one, K is perfectly conditioned.
119 The graphical representation of the condition number is showed next:
121 Simulation is the imitation of the operation of a real - world process or system over time. Simulation is used to describe and analyze the behavior of a system, ask "what if" questions about the real system, and aid in the design of real systems.In order to do a simulation is necessary to have a model of the process, and sometimes to develop the model to simulate is costly and time consuming and therefore is a hard task to carry out.
122 However to develop the model is essential part of the simulation. What if …..Dynamic simulation predicts how process variables change with time when moving from one steady-state to another or during a transient upset.
123 Optimization of plant operations Application Areas of Dynamic SimulationProcess Design AnalysisOff line systemsOn line systemsQuasi on line systemsEducation, Training/Control System DevelopmentAdvancement of plant operations /OptimizationOptimization of plant operationsThe results obtained from the dynamic simulator in the online system are feed back to the actual plant in real-time.The results obtained from the dynamic simulator are applied to simulated plantsResults obtained from the dynamic simulator in the system are not immediately applied to actual plant operations.
124 Contributions of Dynamic Simulation Process DesignThe dynamic response of the process without corrective action by a person or control system is important in the analysis of many process design. Proper use contributes to designing processes that are easily maintained near the desired operating conditions.In addition a simulation can help to ensure that all of the equipment for a new plant is consistently sized
125 What if analysisEvaluate changes to the process equipment, feed materials and operating conditions faster and lower costs trough modelling than through experimentation.Evaluate the response of the system when changes in operating conditions and equipment are made
126 Process control design A control strategy study can be as simple as determining the optimal tuning constants for a controller or as complicated as designing an advanced control strategy for the entire plant.In general to determining the effectiveness of a process control and develop a control strategy.
127 Process Control Development Strategy Determinate how disturbances propagate trough the system.Investigate the relative sensitivity of process variables to process upsets.Investigate process and control loops interactions.Determine the effect of equipment sizing or arrangements changes on disturbances rejections and overall operability.Determine the effects of ambient conditions on the process.
128 Compare the dynamic performance of alternatives control strategies. Perform control-loop tuning.Investigate star-up, shut-down, low, mid, max throughput operations.
129 TrainingThe operators need training in how to control the process. Training courses teach how to use the Control System to control "a" plant, and simulation can be used to train operators on how to operate "their" plant during a startup or emergency.
130 What if… changes to the process equipment, feed materials and operating conditions ?? Real PlantTwo optionsFasterSimulationDynamic simulation technology plays a very important role in achieving safer and optimal plant operations.
132 Control SystemA control system is a system of integrated elements whose function is to maintain a variable process at a desirable value or within a range of desired value.InputControl system input is the stimulus applied to a control system from an external source to produce a specified response from the control system.OutputControl system output is the response to the input applied.
133 Open-Loop systemAn open-loop control system is a control system in which the control action is independent of the output.Open Closed-LoopA closed-loop control system is one in which control action is dependent on the outputTime DelayIt represents the time to have a response of the system.
134 OffsetError between the new set point and the new steady state controlled variable value.Ultimate periodPeriod of oscillation of the system at the margin of stabilityUltimate GainController gain that brings the system to the margin of stability at the critical frequency
135 SpamIs the difference between the largest measurement value made by the sensor/transmitter and de lowest valueZeroIs the lowest reading available from the sensor/ transmitter.AccuracyIs the difference between the value of the measured variable indicate by the sensor and its true value.
136 Process measurement dynamic It indicates how quickly the sensor responds to changes in the value of the measured variable.CalibrationInvolves the adjustment between the sensor output and the predicted measurementRepeatabilityIs related to the difference between the sensor readings while the process conditions remains constant
137 NoiseIs the variation in a measurement of a process variable which does not reflect real changes in the process variables. It is caused by electrical interference, mechanical vibrations or fluctuations within the process.Set PointIt is the desirable value of the controllable variable
139 1.- A dynamic model is :a) A mathematical representation of a real process. which describes approximately its behavior respect to time.b) A mathematical representation of a real process which describes its behavior without consider the variation on time.
140 2.- A dynamic state differs from steady state: a) Accumulation term is not included in variation equations to built a model.b) Accumulation term is included in variation equationsc) There is no difference between them
141 3.- To control process is important because: a) To transform raw materials in manufactured products.b) To decrease the variability of key variables of the process without forget the objectives of the control system.
142 4.- A characteristic of feedback : a) It uses an input to influence the output to the system.b) It uses an output to influence the input to the system.c) It is just a process control concept
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151 Now you know different basics concepts about process control CONGRATULATIONS!Now you know different basics concepts about process control