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Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process.

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Presentation on theme: "Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal Module 15: Process."— Presentation transcript:

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2 Tier 1Module 15PIECE Process Control and Process Integration 1 Created at Universidad de Guanajuato & École Polytechnique de Montréal 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)

3 Tier 1Module 15PIECE Process Control and Process Integration 2

4 Tier 1Module 15PIECE Process Control and Process Integration 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.

5 Tier 1Module 15PIECE Process Control and Process Integration 4  Tier one: Basic Concepts About Process Control  Tier Two: Use of PI tools and especially dynamic simulation to address control strategies  Tier Three: Analysis of a real process. Structure

6 Tier 1Module 15PIECE Process Control and Process Integration 5 Index:  Tier one: Comparison between Steady State and Dynamic State. Important Definitions about dynamic state. Dynamic Models.

7 Tier 1Module 15PIECE Process Control and Process Integration 6 Index:  Tier two: Relationship between Process Design and Process Control Dynamic Effect on recycle Structures

8 Tier 1Module 15PIECE Process Control and Process Integration 7 Tier 1

9 Tier 1Module 15PIECE Process Control and Process Integration 8 Objective:  Understand the difference between steady state and dynamic state.  Understand basic concepts about control process.  Understand the advantages of Dynamic Simulation. Tier 1

10 Tier 1Module 15PIECE Process Control and Process Integration 9 Steady State Initial conditions = Final conditions Process T2T2 T1T1 Flow 1 Flow 2 Process T2T2 T1T1 Flow 1 Flow 2 INPUTINPUT OUTPUTOUTPUT

11 Tier 1Module 15PIECE Process Control and Process Integration 10 When a system is at steady state, there is no change in the process, input and output remains constant in the time. Process INPUTOUTPUT TIME Constant

12 Tier 1Module 15PIECE Process Control and Process Integration 11 Dynamic State: Initial conditions Final conditions In steady state every variable in the process remain constant while dynamic state one or some variables could change thereby affecting the process KEY PHRASE CHANGE WITH TIME

13 Tier 1Module 15PIECE Process Control and Process Integration 12 And now…… What does control mean? Why is it necessary?

14 Tier 1Module 15PIECE Process Control and Process Integration 13 Before the next part it is necessary to understand the next concepts: Manipulated Variable A v ariable that can be changed to maintain constant the controlled variable. Controlled Variable A v ariable which is desirable to control.

15 Tier 1Module 15PIECE Process Control and Process Integration 14 How ?? Changing flows of hot and cold water. An adequate temperature of water is desirable Next there is a typical example of control, everyone has needed to control the temperature when you wish to take a shower…………

16 Tier 1Module 15PIECE Process Control and Process Integration 15 Let’s identify new concepts about control…. Process Final Control Element Sensor Disturbance

17 Tier 1Module 15PIECE Process Control and Process Integration 16 Temperature Flows of cold and hot water Controlled Variable Variables which help to control temperature

18 Tier 1Module 15PIECE Process Control and Process Integration 17 It is possible to observe some elements: It is a feedback control loop. CauseEffect Sensor Input Output Disturbances Final Control Element Process Desired Temperature Controller

19 Tier 1Module 15PIECE Process Control and Process Integration 18 Temperature Either flow of cold or flow of hot water Input Output Single But if… In addition if it is used

20 Tier 1Module 15PIECE Process Control and Process Integration 19 Temperature and Total flow Flow of cold and flow of hot water Input Output Multiple

21 Tier 1Module 15PIECE Process Control and Process Integration 20 To Control To take necessary actions to maintain a system in desired conditions.

22 Tier 1Module 15PIECE Process Control and Process Integration 21 Why is important to control processes ?

23 Tier 1Module 15PIECE Process Control and Process Integration 22 Raw Materials High Quality Manufacture d Products What would happen if there was lower quality raw materials, what should be considered ?

24 Tier 1Module 15PIECE Process Control and Process Integration 23  Raw materials quality and availability  Services quality and availability  Product Quality and throughput  Plant equipment availability  Environmental conditions  Process materials behavior  Plant equipment malfunction  Control system malfunction  Link to other plants  Drifting and decaying factors Some aspects that should be considered:

25 Tier 1Module 15PIECE Process Control and Process Integration 24 How is a Control System designed?

26 Tier 1Module 15PIECE Process Control and Process Integration 25 Information from existing plants Physical and chemical principles Management Objectives Process Control theory Vendor Hardware selection Experience with existing plants Formulate Control Objectives Computer Simulation Develop process model Devise Control Strategy Select Control Hardware Install control system Adjust controller settings Final Control system Steps to design a Control System

27 Tier 1Module 15PIECE Process Control and Process Integration 26 Control System Safety Equipment Protection Smooth Operation Environmental Protection ProfitProduct Quality Monitoring and diagnosis Objectives of a control process system

28 Tier 1Module 15PIECE Process Control and Process Integration 27 Safety Safety 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 Protection Federal, state or local laws regulations require that the effluents of a plant satisfy certain specifications. Equipment protection Operating conditions must be maintained within bounds to prevent damage to expensive equipment Smooth Operation It is desirable because it results in attenuated disturbances to all the integrated units.

29 Tier 1Module 15PIECE Process Control and Process Integration 28 Product Quality Process Control contributes maintaining the operation required for excellent product quality set by the purchasers. Optimization It is concerned with operating the process so that the operation results in producing the highest rate of profit. Monitoring and Diagnosis Both the controlled and manipulated variables must be monitored in order to evaluate the performance of a control system.

30 Tier 1Module 15PIECE Process Control and Process Integration 29 When a process control is implemented, the variability of the key parameters is reduced. Control System Less Output Variation Higher Quality xAxA Time 0.97 0.99 0.98 Without control With control Time xAxA 0.975 0.985 0.98

31 Tier 1Module 15PIECE Process Control and Process Integration 30 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. MATHEMATICAL MODELS Process Mathematical Model Constitutive Relationships Basic Balance Equations Are the models necessary?

32 Tier 1Module 15PIECE Process Control and Process Integration 31 When should the reaction be stopped to have a maximum B concentration? What would happen if inlet flow stop, how fast will the tank be empty? Flow Liquid Level Models allow to analyze behavior system when any change is made. It is a safe, fast and easy way.

33 Tier 1Module 15PIECE Process Control and Process Integration 32 Lumped Parameters  Dependent variables are not function of spatial location  Uses macroscopic balances  Ordinary Differential equations Distributed parameters  Dependent variables are function of spatial location  Uses microscopic balances  Partial differential equations Classification of Fundamental Models

34 Tier 1Module 15PIECE Process Control and Process Integration 33 Dynamic state vs. Steady-State. Steady State Dynamic State Model Basic Equations No Accumulation Term Accumulation Term Algebraic Equations Differential Equations

35 Tier 1Module 15PIECE Process Control and Process Integration 34 Mass in Mass consumed Mass produced Mass out =-+ - Steady State Conservation Law Rate of change Rate of mass in Rate of mass consumed Rate of mass produced Rate of mass out =-+ - Dynamic State Conservation Law

36 Tier 1Module 15PIECE Process Control and Process Integration 35 The dynamic model gives a relation for determining the output variable as function of time for arbitrary variations in the input. Accumulation Term Variation with time !! T L CACA (Energy) (Inventory) (Species)

37 Tier 1Module 15PIECE Process Control and Process Integration 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. Differential equations Model Solution Laplace Inverse Laplace Time Domain Laplace Domain BUT Just for linear equations !!

38 Tier 1Module 15PIECE Process Control and Process Integration 37 Linearization Very 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.

39 Tier 1Module 15PIECE Process Control and Process Integration 38 The linear approximation about (x s,y s ) can be obtained by applying a Taylor series expansion to this function truncating the second order and higher order terms. For this non linear function These terms are known because they are evaluated at x s and y s

40 Tier 1Module 15PIECE Process Control and Process Integration 39 Transfer Functions

41 Tier 1Module 15PIECE Process Control and Process Integration 40 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. Changes in variable from initial values or conditions. How? Deviation variables Initial conditions New conditions

42 Tier 1Module 15PIECE Process Control and Process Integration 41 Model Deviation variables Laplace Transform Transfer Function G (s) Y (s) X (s)

43 Tier 1Module 15PIECE Process Control and Process Integration 42 Input Output Dynamic relation Input-Output (Laplace Domain) Physical Realizability Condition Transfer 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.

44 Tier 1Module 15PIECE Process Control and Process Integration 43 Steps to obtain a transfer function Model Linear Non Linear Linearization Transfer Function Laplace TransforLaplace Transfor m Deviation variables

45 Tier 1Module 15PIECE Process Control and Process Integration 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 units Large Value Small Value Slow process response Fast process response

46 Tier 1Module 15PIECE Process Control and Process Integration 45 Steady-State Transfer function of different systems. Differential Equation Transfer Function 63%

47 Tier 1Module 15PIECE Process Control and Process Integration 46 Steady-State Testing another transfer function Time

48 Tier 1Module 15PIECE Process Control and Process Integration 47 Degree of oscillation in a process response after a perturbation. Differential Equation Transfer Function Overdamped Underdamped Critically Damped

49 Tier 1Module 15PIECE Process Control and Process Integration 48 Every process can be characterized in term for its values of time constant and gain.

50 Tier 1Module 15PIECE Process Control and Process Integration 49 Key characteristics of an underdamped second order response. a)Rise Time (t rise ) Time required to first cross the new steady state value and is given by b) Percentage overshoot (B/D*100)

51 Tier 1Module 15PIECE Process Control and Process Integration 50 e) Response time Time required for the response to remain within a ± 5% band, based upon the steady state change in y. c) Decay Ratio (C/B) d) Period of oscillation (T )

52 Tier 1Module 15PIECE Process Control and Process Integration 51 Period of oscillation D B t rise C Time

53 Tier 1Module 15PIECE Process Control and Process Integration 52 Time Delay Change Impulse Response θ Time

54 Tier 1Module 15PIECE Process Control and Process Integration 53 And what is stability……? How is it possible to know if a system is stable? It is necessary to analyze the poles in the general form of a transfer function When is a system stable?

55 Tier 1Module 15PIECE Process Control and Process Integration 54 General Form Numerator Polynomial in s of order m Denominator polynomial of s of order n Poles are the roots of P(s), it means the values that render P(s) zero. Poles of transfer function

56 Tier 1Module 15PIECE Process Control and Process Integration 55 a) Assume that P(s) can be factorized into a series of real poles P i Inverse Laplace transform Re Im x x p>0 p=0 p<0 Time It grows to infinity.

57 Tier 1Module 15PIECE Process Control and Process Integration 56 b) Assume that one of the factors o P(s) is The roots are Inverse transform Laplace Sinusoidal behavior with amplitude of c/p Re Im x x Time

58 Tier 1Module 15PIECE Process Control and Process Integration 57 c) Assume that one of the factors of P(s) is (s 2 +as+b) Inverse transform Laplace Factoring If a 2 - 4b>0 apply a) If a 2 - 4b=0 Critically damped behavior. If a 2 - 4b<0 apply the next result:

59 Tier 1Module 15PIECE Process Control and Process Integration 58 P<0 P>0 Time Inverse transform Laplace It grows periodically. Re ● ● ● ● Im

60 Tier 1Module 15PIECE Process Control and Process Integration 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.

61 Tier 1Module 15PIECE Process Control and Process Integration 60 Re Im Unstable Region Plane Imaginary - Real If there are positive real roots, even if it is a complex number, it will be unstable Negative real roots is stable

62 Tier 1Module 15PIECE Process Control and Process Integration 61 A system is stable when bounded input changes result in bounded output, otherwise it is unstable. Stability 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. A variable is bounded when it does not increase in magnitude to infinity as time increases.

63 Tier 1Module 15PIECE Process Control and Process Integration 62 Block Diagrams. Disturbance Individual elements Physical Model Sensor Process Final Control Element Representation This is the block diagram for the system Every element has a transfer function !! GvGv GSGS GPGP GDGD

64 Tier 1Module 15PIECE Process Control and Process Integration 63 Block Diagram Algebra It provides the method for combining individual transfer functions into an overall transfer function behavior. G 1 (s) Y (s) X (s) CauseEffect G n (s)G 3 (s)G 2 (s) G 1 (s) X0X0 X0X0 X2X2 X3X3 XnXn

65 Tier 1Module 15PIECE Process Control and Process Integration 64 G 2 (s) G 1 (s) G 2 (s) G 1 (s) X0X0 G 2 (s) G 1 (s) X0X0 + X2X2 X3X3 Parallel Structures Recycling Structures

66 Tier 1Module 15PIECE Process Control and Process Integration 65 Feedback Control

67 Tier 1Module 15PIECE Process Control and Process Integration 66 Open Loop. G (s) u (s)Y (s) Stimulus Response G (s) u (s)Y (s) Stimulus Response Closed Loop. Control action depends the output Action Comparison open-loop and closed-loop

68 Tier 1Module 15PIECE Process Control and Process Integration 67 Feedback makes use of a output of a system to influence an input to the same system Negative Positive Action tends to reduce the error from desired Action tends to increase the error from desired Sensor Input Output Disturbances Final Control Element Process Desired Temperature Controller

69 Tier 1Module 15PIECE Process Control and Process Integration 68 a) Maintain safe operation. b) Maintain quality product. Objectives of a feedback control

70 Tier 1Module 15PIECE Process Control and Process Integration 69 Structure Measurement Element Error Detection Element Control Element Measurement Comparison and Calculation Correction Basic ElementsBasic Actions

71 Tier 1Module 15PIECE Process Control and Process Integration 70 InputOutput Gv Gp Gs Gc E(s) U(s) C(s) Gd Y sp (s) Y(s) D(s) Measurement Comparison Correction Y sp (s) ≠ Y(s) + - Process Final element Controller Disturbances Sensor Desired Output

72 Tier 1Module 15PIECE Process Control and Process Integration 71 Performance Measurement Element (Sensor)  Span  Zero  Accuracy  Repeatability  Process measurement dynamics  Calibration

73 Tier 1Module 15PIECE Process Control and Process Integration 72 Closed Loop Transfer Function

74 Tier 1Module 15PIECE Process Control and Process Integration 73 Process Defining Gp U(s) Gd D(s) Y(s)

75 Tier 1Module 15PIECE Process Control and Process Integration 74 Actuator Controller Gv U(s) C(s) Gc E(s) C(s)

76 Tier 1Module 15PIECE Process Control and Process Integration 75 Sensor Error E(s)Y sp (s) Ys(s) Gs Ys(s) Y(s)

77 Tier 1Module 15PIECE Process Control and Process Integration 76 Closed Loop Transfer Function Characteristic Equation Servo Control

78 Tier 1Module 15PIECE Process Control and Process Integration 77 Analyzing the roots of the characteristic equation is possible to know the dynamic behavior, therefore, to know if the system is stable or unstable. Regulatory control

79 Tier 1Module 15PIECE Process Control and Process Integration 78 PID Controller Tuning

80 Tier 1Module 15PIECE Process Control and Process Integration 79 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. The controller does this task Set Point

81 Tier 1Module 15PIECE Process Control and Process Integration 80 Standard form for the PID (Proportional-Integral-Derivative) algorithm Tuning parameters of controller

82 Tier 1Module 15PIECE Process Control and Process Integration 81 a) Proportional Control action is proportional to error.

83 Tier 1Module 15PIECE Process Control and Process Integration 82 a) Proportional action does not change the order of the process. b) Closed Loop time constant is smaller then the open loop time constant. Proportional action makes faster the response of the process. c) There is an offset. (The manipulated variable will change until the error is constant) Characteristics of Proportional Action.

84 Tier 1Module 15PIECE Process Control and Process Integration 83 b) Integral Integral Control action is proportional to the integral of the error. It allows to reduce the error to zero

85 Tier 1Module 15PIECE Process Control and Process Integration 84 Characteristics of Integral Action. a) All steady state corrections for disturbances or set point changes must come from integral actions. b) There is no offset at steady state. (The manipulated variable will change until error equal to zero) c) Integral action increase the order of the process dynamics by 1. d) Increasing the amount of integral action ( decreasing ) results in a faster responding feedback process, but increases the degree of oscillatory behavior.

86 Tier 1Module 15PIECE Process Control and Process Integration 85 c) Derivative Derivative Control action that is proportional to the derivative of rate of change or error

87 Tier 1Module 15PIECE Process Control and Process Integration 86 Characteristics of Derivative Action. a) It does not change the order of the process b) It does not eliminate offset c) Derivative action tends to reduce the oscillatory nature of feedback, however it amplifies process noise.

88 Tier 1Module 15PIECE Process Control and Process Integration 87 Comparison between P, PI and PID action PID P PI Offset

89 Tier 1Module 15PIECE Process Control and Process Integration 88 Tuning Criteria a) Eliminate deviations from set point. b) Good set point tracking should be minimized. c) Excessive variations of the manipulated variable should be avoided d) The controlled process should remain stable for major disturbances upsets.

90 Tier 1Module 15PIECE Process Control and Process Integration 89 PID controller Performance Reliability Deviations from set point Controller’s ability to remain in service while handling major disturbances Tuning consists to find the best parameters for the controller to achieve the control objective.

91 Tier 1Module 15PIECE Process Control and Process Integration 90 Performance Assessment IAE (Integral Absolute Error) ITAE (Integral Time Absolute Error) ISE (Integral Square Error) ITSE (Integral Time Square Error)

92 Tier 1Module 15PIECE Process Control and Process Integration 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 Tier 1Module 15PIECE Process Control and Process Integration 92 Classical Tuning Methods

94 Tier 1Module 15PIECE Process Control and Process Integration 93 Cohen and Coon It assumes that a FOPDT model of the process is available. FOPDT (First Order plus Delay Time)

95 Tier 1Module 15PIECE Process Control and Process Integration 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. PPIPID KcKc 0.5K cu 0.45K cu 0.6 K cu II -P u /1.2P u /2 DD --P u /8 KuPu Ultimate GainUltimate Period

96 Tier 1Module 15PIECE Process Control and Process Integration 95 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. Direct Method Synthesis This block diagram InputOutput Gv Gp Gc Y sp (s) Y(s) has the next closed loop equation for changes in set point: - +

97 Tier 1Module 15PIECE Process Control and Process Integration 96 If the system’s response for the relation Y/Y sp, is specified. Then the controller that will give this closed loop response characteristic is that which satisfies the following equation: This is called Synthesis Equation Thus, the required controller can be designed if we have a model of the process, it may have a PID form.

98 Tier 1Module 15PIECE Process Control and Process Integration 97 If the desired response form is Then The process model is required

99 Tier 1Module 15PIECE Process Control and Process Integration 98 If the process model is a first order process The controller strategy is: This is simply a PI controller with settings Depending the process model, is possible to have a PID controller.

100 Tier 1Module 15PIECE Process Control and Process Integration 99 Achieves zero steady state offset for all step-like input. Uses only one measurement Algorithm and tunes rules available ADVANTAGES FEEDBACK

101 Tier 1Module 15PIECE Process Control and Process Integration 100 Process output must be upset before feedback action begin Feedback control performance can be poor for some combinations of disturbance frequencies and feedback dynamics Poor feedback can cause instability, PID does not provide the best possible control for all process. DISADVANTAGES

102 Tier 1Module 15PIECE Process Control and Process Integration 101 MIMO SYSTEMS

103 Tier 1Module 15PIECE Process Control and Process Integration 102 There are many industrial systems which have multiple inputs and multiples outputs …..

104 Tier 1Module 15PIECE Process Control and Process Integration 103 Distillation Columns  Steam and reflux affect both top and bottom product compositions Gas-liquid separator  Gas and liquid product flows affect both tank level and pressure.

105 Tier 1Module 15PIECE Process Control and Process Integration 104 Multi-input Multi-output (MIMO) processes  Several CV’s and several MV’s  The numbers of CV’s and MV’s are not necessary same.  One MV affects all or some of CV’s. ( Process interaction )  Which 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. Characteristics

106 Tier 1Module 15PIECE Process Control and Process Integration 105 Single-input single-output (SISO) processes  One CV and one MV: No need of pairing In contrast

107 Tier 1Module 15PIECE Process Control and Process Integration 106 In a general form

108 Tier 1Module 15PIECE Process Control and Process Integration 107 Affects U(s) Y(s) SISO One Output One Input

109 Tier 1Module 15PIECE Process Control and Process Integration 108 A multivariable process is said to have interaction when process input (manipulated) variables affect more than one process output (controlled) variable. Affects U 1 (s) U 2 (s) Y 1 (s) MIMO Two* Outputs One Input Y 2 (s) It means that there is interaction !!

110 Tier 1Module 15PIECE Process Control and Process Integration 109 Controllability Resiliency Measures the degree to which a processing system can meet its design despite external disturbances and uncertainties in its design parameters. The ease with a continuous plant can be held at a specific steady state.

111 Tier 1Module 15PIECE Process Control and Process Integration 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.

112 Tier 1Module 15PIECE Process Control and Process Integration 111 RGA (Relative Gain Array) (Bristol, 1966) Niderlinski Index Condition Number Commonly used controllability measures Resiliency measures Relative Disturbance Gain Disturbance Cost (Lewin, 1996) Disturbance Condition Number (Skogestad & Morari, 1987) Model of the process necessary Model of the process and disturbances necessary

113 Tier 1Module 15PIECE Process Control and Process Integration 112 G 11 G 21 G 12 G 22 + + Controller K 11 + Δy i Effect Interaction Closed Loop Gain Open Loop Gain Closed Loop 11 : measure of the interaction using u 1 to control y 1 Steady state u 1 (s) u 2 (s) y 2 (s) y 1 (s) u 1 – y 1 K 11 OL Open Loop K 11 CL = Relative Array Gain

114 Tier 1Module 15PIECE Process Control and Process Integration 113 Pair Do not pair Avoid Do not pair Avoid Recommendation to pairing With the other loops open

115 Tier 1Module 15PIECE Process Control and Process Integration 114 NI<0 Sufficient condition for instability if independently tuned controllers with integral action are used. NI>0 Necessary condition for stability of the closed loop system in the case of independent controller tuning. Niderlinski Index Tool for input-output pairing multi-loop SISO controllers with integral action.

116 Tier 1Module 15PIECE Process Control and Process Integration 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

117 Tier 1Module 15PIECE Process Control and Process Integration 116 Matrix V First Column Last Column Represents the input direction with the largest amplification. Represents the input direction with the smallest amplification. Matrix U First Column Last Column Output direction where inputs are more effective Output direction where inputs are least effective

118 Tier 1Module 15PIECE Process Control and Process Integration 117 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. Σ is a diagonal matrix containing the singular values of G

119 Tier 1Module 15PIECE Process Control and Process Integration 118 Condition Number Gain Matrix It 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. If CN is large (CN >10), K is ill-conditioned. If CN is one, K is perfectly conditioned.

120 Tier 1Module 15PIECE Process Control and Process Integration 119 u1u1 u2u2 The graphical representation of the condition number is showed next:

121 Tier 1Module 15PIECE Process Control and Process Integration 120 Dynamic Simulations

122 Tier 1Module 15PIECE Process Control and Process Integration 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.

123 Tier 1Module 15PIECE Process Control and Process Integration 122 SimulationWhat if ….. However to develop the model is essential part of the simulation. Dynamic simulation predicts how process variables change with time when moving from one steady-state to another or during a transient upset.

124 Tier 1Module 15PIECE Process Control and Process Integration 123 Process Design Analysis Off line systems On line systems Quasi on line systems Education, Training/Control System Development Advancement of plant operations /Optimization Optimization of plant operations Application Areas of Dynamic Simulation The 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 plants Results obtained from the dynamic simulator in the system are not immediately applied to actual plant operations.

125 Tier 1Module 15PIECE Process Control and Process Integration 124 Process Design The 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 Contributions of Dynamic Simulation

126 Tier 1Module 15PIECE Process Control and Process Integration 125 What if analysis Evaluate 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

127 Tier 1Module 15PIECE Process Control and Process Integration 126 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. Process control design

128 Tier 1Module 15PIECE Process Control and Process Integration 127 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. Process Control Development Strategy

129 Tier 1Module 15PIECE Process Control and Process Integration 128 Compare the dynamic performance of alternatives control strategies. Perform control-loop tuning. Investigate star-up, shut-down, low, mid, max throughput operations.

130 Tier 1Module 15PIECE Process Control and Process Integration 129 Training The 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.

131 Tier 1Module 15PIECE Process Control and Process Integration 130 What if… changes to the process equipment, feed materials and operating conditions ?? Real Plant Simulation Two options Faster Dynamic simulation technology plays a very important role in achieving safer and optimal plant operations.

132 Tier 1Module 15PIECE Process Control and Process Integration 131 Glossary

133 Tier 1Module 15PIECE Process Control and Process Integration 132 Control System A 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. Input Control system input is the stimulus applied to a control system from an external source to produce a specified response from the control system. Output Control system output is the response to the input applied.

134 Tier 1Module 15PIECE Process Control and Process Integration 133 Open-Loop system An open-loop control system is a control system in which the control action is independent of the output. Open Closed-Loop A closed-loop control system is one in which control action is dependent on the output Time Delay It represents the time to have a response of the system.

135 Tier 1Module 15PIECE Process Control and Process Integration 134 Offset Error between the new set point and the new steady state controlled variable value. Ultimate period Period of oscillation of the system at the margin of stability Ultimate Gain Controller gain that brings the system to the margin of stability at the critical frequency

136 Tier 1Module 15PIECE Process Control and Process Integration 135 Spam Is the difference between the largest measurement value made by the sensor/transmitter and de lowest value Zero Is the lowest reading available from the sensor/ transmitter. Accuracy Is the difference between the value of the measured variable indicate by the sensor and its true value.

137 Tier 1Module 15PIECE Process Control and Process Integration 136 Process measurement dynamic It indicates how quickly the sensor responds to changes in the value of the measured variable. Calibration Involves the adjustment between the sensor output and the predicted measurement Repeatability Is related to the difference between the sensor readings while the process conditions remains constant

138 Tier 1Module 15PIECE Process Control and Process Integration 137 Noise Is 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 Point It is the desirable value of the controllable variable

139 Tier 1Module 15PIECE Process Control and Process Integration 138 QUIZ

140 Tier 1Module 15PIECE Process Control and Process Integration 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.

141 Tier 1Module 15PIECE Process Control and Process Integration 140 2.- A dynamic state differs from steady state: b) Accumulation term is included in variation equations a) Accumulation term is not included in variation equations to built a model. c) There is no difference between them

142 Tier 1Module 15PIECE Process Control and Process Integration 141 3.- To control process is important because: b) To decrease the variability of key variables of the process without forget the objectives of the control system. a) To transform raw materials in manufactured products.

143 Tier 1Module 15PIECE Process Control and Process Integration 142 4.- A characteristic of feedback : b) It uses an output to influence the input to the system. c) It is just a process control concept a) It uses an input to influence the output to the system.

144 Tier 1Module 15PIECE Process Control and Process Integration 143 Correct Answer To continue, click on the figure

145 Tier 1Module 15PIECE Process Control and Process Integration 144  Try another Answer To continue, click on the figure

146 Tier 1Module 15PIECE Process Control and Process Integration 145 Correct Answer To continue, click on the figure

147 Tier 1Module 15PIECE Process Control and Process Integration 146  Try another Answer To continue, click on the figure

148 Tier 1Module 15PIECE Process Control and Process Integration 147 Correct Answer To continue, click on the figure

149 Tier 1Module 15PIECE Process Control and Process Integration 148  Try another Answer To continue, click on the figure

150 Tier 1Module 15PIECE Process Control and Process Integration 149 Correct Answer To continue, click on the figure

151 Tier 1Module 15PIECE Process Control and Process Integration 150  Try another Answer To continue, click on the figure

152 Tier 1Module 15PIECE Process Control and Process Integration 151 Now you know different basics concepts about process control


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