Industrial process control

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1. Industrial Process Control 1

2. Definitions 2

3. It Is defined as: Physical or chemical change of matter. Energy conversion e.g ., change in pressure, temperature, speed, electrical potential, etc. A process in a collection of vessels, pipes, fittings, gauges etc., is built for the purpose of producing a product or group of products. Process 3

4. The regulation or manipulation of variables influencing the conduct of a process in such a way as to obtain a product of desired quality and quantity in an efficient manner . Process Control 4

5. Input to Process: Mass or energy applied to the process. Output of Process: The product delivered by the process. This is a dynamic variable. Supply: Source of mass or energy input to process. Control Valve: Consists of the final actuator and final controlling elements. This is the forward controlling element which directly changes the value of the manipulated variable. Load: Anything that affects the value of the controlled variable under a constant supply input. 5

6. Open Loop: Control without feedback. Open loop can not cope with load upsets. Example of open loop: automatic dishwasher, automatic water sprinkling system, a control loop with the controller in manual. Primary Element: The measuring element that quantitatively converts the measured variable energy into a form suitable for measurement. Transmitter: A transducer which responds to a measured variable by means of a sensing element, and converts it to a standardized transmission signal which is a function only of the measured variable. 6

7. Controlled Variable: A variable the value of which is sensed to originate a feedback signal . (Also known as the process variable.) Controller: A device which operates automatically to regulate a controlled variable . Controller Algorithm (PID): A mathematical representation of the control action to be performed. Set Point: An input variable which sets the desired value of the controlled variable. 7

8. Error: In process instrumentation, the algebraic difference between the real value and ideal value of the measured signal. It is the quantity which when algebraically subtracted from the indicated signal gives the ideal value . Manipulated Variable: A quantity or condition which is varied as a function of the algebraic error signal so as to cause a change to the value of the directly controlled variable. 8

9. Feedback Control: Control action in which a measured variable is compared to its desired value to produce an actuating error signal which is acted upon in such a way as to reduce the magnitude of the error . Cascade Control: Control in which the output of one controller is introduced as the set point for another controller . Feedforward Control: Control action in which information concerning one or more conditions that can disturb the controlled variable is converted, outside of any feedback loop , into corrective action to minimize deviations of the controlled variable. 9

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13. The operator walked up and down a plant , looking at gauges and opening and closing valves is effective only at the time when the operator moves the valve. At that instant the loop is closed. Open loop control works only when the load(s) on the process are constant. Any load change or supply upset can affect the product quality . Open Loop Control 13

14. Increased productivity: Automatic closed loop control allows the amount of products made in a particular process to be maximized. On Spec Products: Industrial products are produced to meet certain purity levels . Energy and Material Conservation: A closed loop control application minimizes the amount of material and energy used in production. Safety: Closed loop control is the first line of defense before Emergency Shutdown Devices (ESD) override regulatory control devices. Advantages of Closed Loop Control 14

15. Continuous Control is used on continuous processes. A continuous process is one in which process material is continually flowing through the process equipment . Sequential is often referred to as on/off control. It is a series of discrete control actions performed in a specific order or sequence . Batch control is a combination of sequential and continuous control. A batch process is a process where the operation is time-dependent and repeatable. Types of Control 15

16. Positive Feedback It can be defined as the control action in which the error is reinforced until a limit is eventually reached. This obviously is not a desirable outcome of control action and should be avoided. Imagine a tank in which level is being controlled. When the level exceeds the set point , the control action will increase the level further until the tank overflows . 16

17. Negative Feedback It can be defined as the control action in which the error is minimized, made as small as possible, depending on the algorithm of the controller. This obviously is a desirable outcome of the control action and should be achieved in all feedback loops . 17

18. Direct Acting Element is one in which the value of the output signal increases as the value of the input signal increases . 18

19. Reverse Acting Element is one in which the value of the output signal decreases as the value of the input increases . 19

20. A control valve consists of a valve connected to an actuator mechanism. The actuator , in response to a signal from the controlling system, can change the position of a flow-controlling element in the control valve . The action of the final actuator is the first choice and is based on “Fail-Safe Control Valve Action”. (open , closed, and in place). Control Valves 20

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23. It can be set up (calibrated) as either direct acting or reverse acting . Transmitters 23

24. It can be either direct or reverse acting. Most processes are direct acting. Energy Flow Process Heat Exchanger Refrigeration Mass Flow Process Level Tank Pipe Flow Processes 24

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29. Rule for Achieving Negative Feedback To achieve negative feedback in a control loop you must have an odd number of reverse acting elements in the loop. 29

30. The odd number of reverse-acting elements for negative feedback can be determined through an open loop test, conducted in the following manner. Place the controller in manual (open loop), and step up the output of the controller (5-10%) and observe ( record) the output of the transmitter. 30

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32. Control Loop Elements And Their Contribution To Loop Performance 32

33. Transmitters 33

34. Accuracy (Error) = Precision Error + Bias Error 34

35. Range: The region between the limits within which a quantity is measured is the range of that measurement. Span: The measurement span is the algebraic difference between the upper and lower range values. Minimum Span : The minimum span of measurement that the primary element can be used to measure within its accuracy rating. Maximum Span: The maximum span of measurement that the primary element can be used to measure within its accuracy rating. Rangeability (Turndown): In flow applications, rangeability is the ratio of the maximum flow rate to the minimum flow rate within the stated accuracy rating. Zero Elevation and Suppression: The range at which the zero value of the measured variable is not at the lower range value. 35

36. Response Time: An output expressed as a function of time, resulting from the application of a specified input (step) under specific operating conditions. Time Constant: This is a specific measure of a response time. It is the time required for a first order system to reach 63.2% of the total change when forced by a step. 36

37. Characteristic Curve (Input-Output Relationship): A curve that shows the ideal value of an input-output relationship at steady state. Reproducibility: There should be a closeness of agreement among repeated measurements of the output for the same value of the input made under the same operating conditions over a period of time, approaching from both directions. Noise: In process instrumentation noise is an unwanted component of a signal or a process variable. 37

38. Control Valve 38

39. Flow Coefficient, CV - Is a capacity coefficient which is defined as the number of U.S gpm of 60°F water which will flow through a wide-open valve with a constant pressure drop of 1 psi across the valve. 39

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41. Current to Pressure Signal Converters, I/P 41

42. Analog to Digital, A/D, or Digital to Analog, D/A 42

43. Volume Booster 43

44. A valve positioner is a proportional-only controller whose main function is to eliminate or minimize valve hysteresis 44 Valve Positioner

45. The practical rangeability of a control valve is limited to approximately 100/1 with most valves falling below 50/1. These rangeability values are sufficient for most control applications. In some applications however, such as pH, the rangeability required may exceed 1000/1 and the control scheme must be designed to satisfy this requirement in order to achieve good control. In split ranged or sequenced strategies , the controller's output actuates more than one valve, typically two valves. 45 Valve Sequencing

46. Process Modeled Through Dead Time And Capacity 46

47. DEAD-TIME-ONLY PROCESSES 47

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49. The steady state gain of the dead-time element is the ratio of the output amplitude to the input amplitude when both are time invariant. 49 Steady State Gain (K) of Dead Time Process

50. Capacity Processes Level Tank - Stores Mass 50

51. Capacity Processes Heater - Stores Energy 51

52. A capacity is termed non-self-regulating when a change in the controlled variable has no affect on the process load. 52 Non-self-regulating or integrating capacity (NSR)

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54. Self-Regulating-Capacity or First-Order Lag In the self-regulating-capacity process, load is not independent of level. When level changes in this process the load also changes. Self regulation always tries to restore equilibrium and achieve steady state. 54

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56. This process operates as though it has a built-in automatic controller that achieves steady state by making fi = fo . In fact we would not need to control this process if the tank was very large (  ). Obviously, it is more practical to have a smaller tank and put a control loop on it. 56

57. Interacting capacities are identified as types of capacities in which the downstream capacities affect upstream capacities. C3 affects C2 and C2 affects C1. 57 Interacting Capacities

58. The non-interacting capacity can be identified as a capacity that has no effect upstream i.e. C3 does not affect C2 and C2 does not affect C1. 58 Non-Interacting Capacities

59. Input/Output Relationship of Non-Interacting Capacity Processes 59

60. Input/Output Relationship of Non-Interacting Capacity Processes 60

61. Input/Output Relationship of Interacting Capacity Processes 61

62. Basic Control Modes And Choice Of Controller Algorithm 62

63. The effective control of a process in a feedback loop depends on the correct choice of the controller mode or algorithm required for the given application. The controller algorithm is a mathematical expression described as the PID consisting of proportional, integral and derivative components. Each of these PID components affects the response of the loop and has certain advantages and limitations. INTRODUCTION 63

64. The simplest and most common type of control mode, considering home applications. Although there are multi-position discontinuous controllers available in industry, generally On-Off control refers to the two-position version. A consequence of this is that under On-Off control the loop never stabilizes. On-Off Algorithm 64

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68. 1) Processes where precise set point control, is not required e.g. some level tanks; and processes such as home heating, cooling or refrigeration. 2) Part of an emergency shutdown process (ESD). The objective here is not regulatory control but safe operation. 3) Large capacity processes having a low dynamic gain and a potentially small (acceptable) amplitude of oscillation. 68 Application of On-Off Control

69. Advantages and Limitations of On-Off Control Limitations Advantages Demand not balanced by supply Extremely simple Loop always cycles Inexpensive controller More energy used by the valve No tuning required for start up Less expensive valves 69

70. Proportional control is the minimum controller algorithm capable of balancing supply with the demand of the process and achieving steady state. A properly adjusted proportional controller can eliminate the oscillations that are inherently part of On-Off control. 70 Proportional Algorithm

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72. Assume initially that everything is balanced. The inflow to the tank equals the outflow of the tank at 50% and the process is in a steady state condition. Fin = Fout = 50% 72

73. Also assume that at the 50% load ( Fout ) for this particular tank: Measurement = Set Point = 50% c = r = 50% If this condition persists, that is Fin = Fout @ 50% load, and c=r, the operator does not need to take any control action since the supply is already balanced by the load. 73

74. Assume in this example that suddenly the load ( Fout ) changes from 50% to 60%. The first indication of the load increase will be a change in the level of the tank. Acting as a proportional controller, its task is to open the supply valve in order to stop the level from changing. When a balance is achieved between the supply and the demand such that Fin = Fout = 60%, the level stops changing. 74

75. Unfortunately, at this new steady state condition, the measurement is at a new value below the set point. The error (r-c) is called offset. It is a steady state error and is characteristic of all proportional controllers. The magnitude of the offset depends on the size of the load change and the capacity (size) of the tank. 75

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78. The output of the proportional controller is proportional to the input. m = Ge When the controller is switched to automatic its output goes to zero since the error is zero. m = G (r-c) = 0 As the output goes to zero the valve shuts, decreasing the Fin to 0% and causing the level to decrease. The level will stop decreasing only when the supply balances the load. This balance will occur only if Fin becomes 50% again. If the process dictates that the gain of the controller should be 20 when controlling at 50% load. The controller will operate with a 2.5% error. 50 = 20 (2.5) 78

79. Proportional controllers always operate with an error. The higher the controller gain , as dictated by the process gain, the smaller the error . (It should be pointed that the controller gain can not be set arbitrarily. It is dictated by the process gain and for a given loop gain has a reciprocal relationship to the controller gain). 79

80. To accommodate zero error situations m = Ge + Bias The Bias term has a fixed value and does not have the ability to change . The Bias is the output of the controller whenever the error is zero. m = Bias , if e = 0 Apply this algorithm to the previous example. Assume that we put the controller in manual and adjust all the signals to 50%: r = c = Fin = Fout = 50%. When we place the controller in automatic: m = Ge + Bias m = 0 + Bias = Bias A typical Bias setting being 50%, m = 50% 80

81. If the load changes an error will occur once again. m = Ge + Bias 60 = 20(e) + 50 20(e) = 10 e = 0.5% Some manufacturers write the expression m = (100/PB) e + Bias Proportional band is defined as the change in input required to produce a full range change in output due to proportional control action. It may also be seen as the change in measurement required to change the output 100% or to fully stroke the valve. 81

82. Different Proportional Bands and Gains 82

83. Proportional Offset m = (100/PB)e + Bias Offset = e = (m - Bias)(PB/100) There are two conditions which can make the offset equal to zero or a very small value. Small values of PB or high gains on the controller. Remember that the process dictates the controller gain or PB. It is not an arbitrarily assigned value. 2) If (m = bias): in this situation, when the load is equal to the Bias, there will be no offset. Since the Bias is fixed this implies that the load is also fixed. 83

84. Open Loop Response 84

85. Closed Loop Response 85

86. Proportional-only control is not a common control application. Processes where precise control at the set point is not required. Processes where offset can be tolerated. 2) Processes where the load changes are infrequent (seasonal). This allows matching load with Bias to eliminate or minimize the offset. 3) Low gain processes . Typically these are large capacity processes with low process gains. The low gain of the process allows a high gain on the controller minimizing the offset. 86 Application of Proportional-Only Control

87. Advantages and Limitations of Proportional-Only Control Limitations Advantages Offset Immediate response Easy to tune Good period of response Simple 87

88. Integral Algorithm The error in proportional algorithm could be eliminated if the two terms in the parenthesis were made to equal each other. Offset = e = (m - Bias) PB/100 Since the output of the controller m is directly related to the load our only choice is to vary the Bias term by making the Bias = m and thus eliminating the error. The integral mode fulfills this requirement by providing the variable Bias capability that automatically achieves this load balancing task while eliminating errors at steady state. 88

89. m I =(1/I)  edt + m o m I = T i  edt + m o where I = min./rep T i = rep./min. m I : is the output of the integral-only controller. I : is the gain adjustment for the integral-only controller known as the integral or reset time. m o : is the controller output at the time integration starts 89

90. Open Loop Response 90

91. Closed Loop Response 91

92. Whenever the integral mode is required in an application it is customary to have a small amount of proportional along with it. The integral mode eliminates the offset at a cost of slower loop response . Integral can be justified and should be the major contributor for the following applications. Slow loops designed to produce slow corrective action. The integral mode is the major contributor in fast flow control applications usually with a minor contribution from the proportional controller. 92 Application of Integral-Only Control

93. Saturation of the integral mode of a controller developing during times when control cannot be achieved, which causes the controlled variable to overshoot its setpoint when the obstacle to control is removed. 93 Windup

94. Advantages and Limitations of Integral-Only Control Limitations Advantages Slows the response Eliminates offset Potential windup or saturation Easy to tune Unstable with NSR capacity. (Always oscillates with NSR) Reduces integrated error Acts as a filter. Good on noisy processes. 94

95. Proportional Plus Integral Algorithm The need for precise control with zero error at steady state brought the integral mode in the picture. The integral mode eliminated the error at steady state but at an unacceptable cost of a slow loop response . Combining the two modes in a PI controller is a very effective compromise suitable for most process applications. 95

96. The following observations should be made: 1) Integral mode is a must for precise control. 2) The cost of integration is a slower response. 3) If unable to eliminate the error at steady state the potential exists for loss of control through what is known as windup or saturation. 96

97. The PI is by far the most common algorithm used in process control applications. In most plants the PI controller is used in excess of 80% of the time . The reason for its popularity is due to the fact that the algorithm benefits by getting an instantaneous response due to error from the proportional mode and the elimination of steady state error from the integral mode. 97

98. m = (100/PB) [e + (1/I)  edt ] 98

99. Open Loop Response of PI Controllers 99

100. Closed Loop Response of PI Controllers 100

101. Advantages and Limitations of PI Control Limitations Advantages More difficult to tune No offset Windup or saturation potential Can minimize integrated error Reasonably good period of response 101

102. Derivative Algorithm In some applications the increased period of response due to the integral mode is not acceptable Especially if we recognize that after an upset it takes about 3 cycles for a loop to settle down and reach steady state. Furthermore in approximately 10% of the processes the natural period of the loop is rather long and the penalty of even longer periods due to the need of having integral is not desirable. 102

103. The natural period of a distillation column is typically several hours. If a given column has a natural period of 4 hours and, assuming a penalty of a 50% longer period due to the integral mode. It would take approximately 18 hours (4 x 3 x 1.5 = 18) for this loop to reach steady state. The problem gets further aggravated if other upset(s) occurs before steady state is reached. 103

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105. Open Loop Response (D Setting Fixed) 105

106. Proportional plus Derivative Algorithm Remember that derivative-only controllers do not exist . The derivative mode must be combined with a proportional or a proportional plus integral controller and the phase will be limited to some value less than +90%. 106

107. The older version with the Derivative on error m = 100/PB ( e + Dde/dt ) + Bias 107

108. The newer version with the Derivative on measurement m = 100/PB ( e - Ddc / dt ) + Bias 108

109. The proportional plus derivative controller is not a frequent choice in process control applications. Its major limitation is its inability to eliminate offset or steady state error . To apply the derivative mode we have to make sure that the controlled variable is free of noise . 109 Application of Proportional plus Derivative Controllers

110. Regarding offset it has the same problem as the proportional-only controller. The addition of derivative however produces an improvement in the speed of response . PD controllers are recommended for large capacity processes where precise (set point) control is not required. The major application of this controller is in batch processes where because of the nature of the process (integrating process) it may not be desirable to use the integral mode. 110

111. Advantages and Limitations of PD Controllers Limitations Advantages Offset Good response period Can not handle noise Fastest to reach steady state Insufficient benefit on fast processes Easier to tune than PID 111

112. PID Algorithm This three-mode controller has the attributes of all the modes along with their limitations. In summary the PID uses the immediate response of the proportional mode followed by the integral mode's ability to eliminate the offset. The slowing down of the response due to integration is compensated for by the derivative mode. 112

113. To justify the application of the PID controller the process should satisfy the following conditions: The controlled variable should be free of noise. 2. The process should have a large capacity for optimum benefit. 3. The slower response due to the integral mode is not acceptable for good control. 113

114. Summary of Closed Loop Responses 114

115. Advantages and Limitations of PID Controllers Limitations Advantages Noisy measurement Good period of response Difficult to tune Compensates for the slow integral Windup concerns Minimizes integrated errors Optimizes control loops 115

116. 1. Let the system stabilize. 2. Open the loop by placing the controller in manual. 3. Make sure the system is at steady state, the output and the controlled variable maintaining their values. 4. Introduce a small disturbance by stepping up the output of the controller. 5. Record the reaction of the controlled variable. 6. Bring the output back to the normal operating point and switch to auto. 116 Procedure for Determining Process Characteristics

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119. Steady State Gains 119

120. Steady state gain is simply the slope of the input-output relationship of the element's response curve when both the input and output are time invariant (do not vary with time). 120 Steady State Gains of Elements

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122. Instead of tuning at the highest gain condition to be on the safe side, a better solution to the non-linearity problem is to use a complementary linearizing element in the loop through either the valve or other element. The objective of good control is to make the loop gain independent of the operating point as much as possible. 122 Linearization For Constant Loop Gain

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124. THE STEADY STATE GAIN OF MEASURING ELEMENTS/TRANSMITTERS 124

125. The most common industrial flow applications involve one of the following measuring Devices. NON LINEAR DEVICES LINEAR DEVICES Orifice Magnetic Flow Meters Venturi Positive Displacement Meters Flow Nozzle Vortex Meters Elbow Meters Turbine Meters Target Meters Ultrasonic Weirs Rotameter Flumes Coriolis 125 Flow Transmitters

126. Linearizing Differential Producers 126

127. It is possible to linearize the differential producer (orifice plate) with a complementary response curve. To find a curve (b) type function from one of the other elements in the loop, i.e. the valve. The advantage of this approach is the elimination of the need for a square root extractor. The disadvantage is that the loop will be operating with (Flow) 2 information. 127 Linearizing With A Compensating Response

128. Linearizing the Valve Characteristic 128

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130. As electronic controllers were introduced, it was possible to build non-linear PID controllers. In some applications it is not desirable to have a constant gain controller. Non-linear controllers were designed to handle processes with variable gain. They were set up to have low gain in the high-gain region of the process and high gain in the low-gain region of the process. 130 Non-Linear Controllers

131. Linearizing Process Characteristic with a Non-Linear Controller 131

132. Level Process 132

133. Linearizing a Non-Linear Process - Non-Uniform Tank 133

134. Heat Exchanger Process 134

135. Linearizing Processes Whose Gain Varies Inversely With Load 135

136. Tuning Feedback Control Loops 136

137. Acceptable Tuning Criteria Used in the Process Industry 137

138. If safety is the primary concern , speed and efficiency can be sacrificed and a critically damped response might be the best choice. If the objective is to eliminate the error and achieve steady state as quickly as possible after an upset, then some form of underdamped response will be the choice. Generally most of the better tuning techniques lead to an underdamped response, with some decay ratio and a specific speed of response (period.) 138

139. The objective of a well-tuned loop is to eliminate the error as quickly as possible by bringing the measurement equal to the set point. 139 Tuning Criteria Using Error Minimization Approaches

140. (QAD) is one of the most common under-damped response criteria. The controller gain is adjusted so that the amplitude of each successive cycle is one quarter of the previous amplitude . Unfortunately, this criteria does not completely define the response. Beyond an amplitude decay ratio, it gives no other information as to what the optimum period of the response should be. 140 Quarter Amplitude Decay Criteria

141. 141 There is no mathematical justification for the QAD response. Its popularity and acceptance are due to its open loop gain, which between 0.5 and 0.6 seems to be a reasonable compromise in damping and period.

142. The main criticism of QAD as a criterion is that it gives no information about speed of response , or period of a loop, and as such, it does not indicate an optimum response. In two or three mode controllers such as PI or PID there are an infinite number of settings that will give you a QAD response , only one of which will have the correct period for optimum response. 142

143. These techniques are especially useful if energy is used to make the product. Minimization of the area (error) under the curve leads to less energy consumption and higher efficiency. There are various error minimization criteria, each having certain advantages and limitations, and different PID settings. 143 Tuning Criteria Using Integral Error Minimization

144. 144 Integrated Error (IE) IE =  e dt Integral Absolute Error (IAE) IAE =  e dt Integrated Squared Error (ISE) ISE =  e2 dt Integrated Time Absolute Error (ITAE) ITAE =  e t dt

145. A loop tuned to particular criteria raises the question of loop stability when process conditions change. A robust control loop, has a safety factor built in to the controller tuning settings, allowing the loop to maintain stability even if the process undergoes moderate changes in gain or dead time. 145 Robustness

146. 146 A robustness plot allows an analysis of how safely a loop is tuned. The gain ratio is the ratio of the current process gain to the original process steady-state gain. The delay ratio is the ratio of the process dead time to the dead time existing when the process was tuned.

147. Making PID Adjustments and Observing their Effect on Loop Response 147

148. Proportional Band or Gain Adjustment 148

149. To change the response of the loop, adjust only with: PB or Gain. Decrease the loop gain to less than one in order to dampen the response. The obvious choices of response for this controller would range from an overdamped response to a Quarter Amplitude Decay response (QAD). To get a QAD response the Proportional Band would have to be doubled (2 x PBu ) to drive the loop gain to 0.5. 149

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151. The proportional band or gain adjustment can be summarized as follows: Changing gain or PB affects only the damping of the response. Increasing the PB setting decreases gain while the period stays roughly the same . 151

152. Any change of period length over  n is of minor consequence . The amount depending on the process characteristics. For dead-time only processes there would be no period change at all. For dead-time plus capacity processes the period might increase by 10 - 15% over the natural period  n . It is best to consider the proportional adjustment as a gain adjustment with no significant effect on the period of response. 152

153. PI Adjustment 153

154. PD Adjustment 154

155. PID Adjustment 155 Suppose we find our damping to be acceptable , but the period of response,  o is too long. We need to maintain our loop gain constant, but to either increase derivative action or decrease integral action. Changing either one alone will not only change  o , but will also change the gain vector which will in turn affect loop gain.

156. The correct procedure in this case would be to increase derivative gain G D , by increasing derivative time D, while at the same time to decrease integral gain G I by increasing integral time I. This will tend to increase derivative action while maintaining the length of the PID vector constant. As a result, damping will remain unchanged while response period  o is decreased. 156

157. There are at least two ways in which three-mode PID controllers can be built. The PID algorithm discussed so far is an ideal noninteracting controller algorithm. The noninteracting controller is designed such that its derivative and integral modes are in a parallel path and act independently of each other. The interacting PID controller is designed such that the integral and derivative modes interact. 157 Interacting And Noninteracting PID

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160. Effective PID values in terms of the actual settings 160

161. Over the years many tuning methods or approaches have been developed and used with varying degrees of success. There is no general agreement as to what method is the best to use , the preferred choice usually being the one , that the individual has the most experience with. 161 Reasons for Tuning Methods

162. Some of the methods are trial and error solutions to finding the desired response; others rely on mathematical relationships . The preferred tuning method might be, it is desirable to have the capability to apply more than one approach . In some cases, process or operational constraints dictate the method to use. With experience, you develop a feel of what approach works best for a given application, and tune accordingly. 162

163. Keep in mind that any tuning method, will give you only preliminary settings , which require fine tuning later for optimum response. The various tuning methods can be grouped into closed-loop and open-loop categories. 163

164. The main distinction between the two is as follows: In the closed-loop methods , adjustments are made and tested with the controller in automatic . In the open-loop methods , preliminary settings are calculated by an open loop test, with the controller in manual . These preliminary adjustments are introduced in the controller and tuning is continued with the controller in automatic. 164

165. Summary of making PID adjustments and observing their effect on loop response The table is designed to assist the user in deciding which direction the adjustments should be made. 165

166. Place controller in manual. Increase proportional band to a safe wide value . Place controller in automatic. Make a 5 - 10% set point change around the operating point. Reduce PB until constant amplitude cycling occurs. Double PB for QAD. Controller is tuned. Make a small upset and observe the response. Measurement will not be at set-point at steady state. 166 Procedure for Trial and Error Constant Cycling Method P-Only Controller

167. Increase I-time to maximum min/rep or minimum rep/min. (This eliminates the integral action.) Tune as a P-Only Controller. Increase Integral gain until constant amplitude cycling occurs. Double the I-time in min/rep for QAD. (Halve the I-time if in rep/min.) Make upset and observe the response. Measurement should reach set-point at steady state. 167 P + I Controller

168. 1. Adjust the integral time min/rep and proportional band to high values. 2. Adjust derivative time to a very low value. 3. Reduce PB until constant amplitude cycling just occurs. 4. Double PB for QAD. 5. Controller is now tuned as P-Only. 6. Increase derivative time until constant amplitude cycling occurs. 7. Cut derivative time by 1/2 for QAD. 8. Set integral time to a value of 2 to 4 times that of the derivative time. 9. Make upset and observe the response. Measurement should be at the set-point at steady state. 10. Readjust PB, I, and D small amounts to get desired response. 168 PID Controller (Interacting Types)

169. With the controller in manual, remove the Derivative and Integral modes. (Remove or turn off Derivative action. Set Integral to its lowest gain value, by setting to maximum min/rep or minimum rep/min.) Set the Proportional Band or gain to a safe value depending on the process. Examples of safe values of PB or Gain: · Flow PB 300-500 % or Gain 0.2 to 0.3 · Temperature PB 100 % or Gain 1.0 At this point, you have a low-gain, Proportional-only controller. 169 Procedure for Ziegler-Nichols and Cohen-Coon Constant Amplitude Cycling Method

170. 2. Switch the controller to automatic, put a small upset by introducing a 5-10% set-point change around the operating point and observing the response. You should get a safe sluggish response. 3. Increase the gain or decrease the Proportional Band and repeat step (2) until uniform or sustained oscillations occur as shown in curve (C). If the gain is too low such as curve (A) increase the gain or lower the PB. Avoid unstable responses such as curve (B). Record the following information at uniform oscillation. Make sure the oscillation is due to the loop gain and not due to a limit cycle. (e. g., Valve hitting the stops produces what looks like uniform oscillation but the gain > 1). 170

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173. Procedure for Obtaining a Process Reaction Curve and Optimum PID Settings from Ziegler-Nichols or Cohen-Coon Process Reaction Method 173

174. 1. Let the system stabilize at the normal operating point (set point and load at normal.) 2. Open the loop by placing the controller in manual. The output should hold at the same value as in step (1). 3. Make sure the system is at steady state with the output and the controlled variable maintaining their values. 4. Introduce a small disturbance by stepping up the output of the controller. The resulting output change should have enough resolution for analysis. 5. Record the reaction of the controlled variable. This is where a fast speed recorder at the output of the transmitter (in the order 1 in./min) comes in handy. 6. Bring the output back to the normal operating point and switch controller back to auto. 174

175. After obtaining the Process Reaction Curve, proceed to determine P, PI, or PID settings using either Ziegler-Nichols or Cohen and Coon equations as shown. 175

176. 176

177. Obtain a process reaction curve 177 Procedure and Summary of Integral Criteria-Driven Open-Loop Method

178. 178

179. Cascade Control 179

180. If the load ( F w ) suddenly increases, the temperature (T 2 ) decreases. The controller senses this and acts on this error through its algorithm. In two to three cycles, the loop stabilizes. 180

181. 181

182. Cascade Control may be defined as, "control in which the output of one controller is the set point for another controller." The set point to the flow controller defines the amount of flow required. On an upset in flow, the controller repositions the valve to bring the flow to the set point, r. 182

183. These cascade loops are known as the primary and secondary loops. The loop closest to the controlled variable is the primary loop and the loop manipulating the valve is the secondary loop. The primary loop is known also as the master loop, outer loop, or the slower loop. The secondary loop may be called the slave loop, the inner loop, or the faster loop. 183

184. The purpose of cascading is to have the secondary loop compensate for any supply upsets that may occur before they can influence the primary controlled variable . A supply upset to the primary loop is in effect a load upset to the secondary loop, and a fast-acting secondary can immediately correct for it . 184

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186. 186

187. 187

188. Results and Considerations In order for the cascaded control scheme to function without adversely affecting the gain of the primary loop, The  1 /  2 ratio must exceed 4 . The higher the ratio, the easier it is to cascade. 188

189. 1. Cascade control eliminates the effects of supply upsets. 2. Quicker return to set point in the primary loop and less integrated absolute error (IAE). 3. The secondary loop is more responsive to the demands of the primary. 4. The primary loop sets the amount of supply input rather than valve position. Thus, the effects of valve characteristics (including non- linearities ) are minimized, and effectively removed. 189 Advantages of Cascade

190. 1. More expensive because of additional hardware needs. 2. The primary loop must be substantially slower than the secondary loop. 3. In some applications it is difficult to break the process into a primary and secondary loop and identify the supply variable. 4. Compared to a feedback loop, it is more difficult to start up and tune a cascade loop. 190 Limitations of Cascade

191. Specific Cascade Applications Valve Positioner The primary reason for having a positioner is to remove hysteresis from the valve. 191

192. Limit Cycling Limit cycling can be another consequence of hysteresis, or dead band. The limit cycle is a clipped sine wave of the manipulated variable. Controller adjustments (tuning) cannot eliminate these oscillations. Widening PB will increase the amplitude and the period of oscillation, while decreasing integral action reduces amplitude and increases the period. Recognizing a limit cycle wave (clipped sine wave) can eliminate some frustrating and unsuccessful tuning effort. The only solutions to a limit cycle are as follows: • Use a valve positioner or other cascade application. • Remove integral action from the controller. 192

193. Temperature On Flow Cascade Control Temperature on flow is a good candidate for cascade control. The supply is well defined and the flow and temperature processes have significantly different natural periods allowing a good cascade within the natural period ratio criteria. 193

194. Temperature-On-Temperature Cascade Control Of An Exothermic Reactor The idea here is to keep the temperature inside the reactor (T1) at the desired value by controlling the temperature of the jacket (T2) by manipulating cooling water flow to the jacket. 194

195. Flow as the Inner Loop The secondary loop is frequently a flow loop as seen in the various temperature cascades. The benefits are that the flow loop protects the primary loop from supply upsets; overcomes non-linear valve characteristics; and, reduces the effect of valve friction on the primary controlled variable. 195

196. Level on Flow (Valve Positioner) Cascade A level application requiring precise control and unable to attain it due to valve hysteresis or frequent supply upsets. It is a good candidate for level valve position cascade. A cascade through either a valve positioner or a flow loop can be used since the level loop (primary) is most likely four times slower than the valve position loop, so that the criteria  1 /  2 > 4 is not violated. 196

197. Integral Windup Preventing Measures in Cascaded Loops If in attempting to eliminate a sustained error, the controller output goes beyond 0 to 100%, the controller is wound up. Windup occurs if the error persists, with the valve fully open and the controller output at 100%. The controller becomes saturated, with loss of control. 197

198. 198

199. Windup Prevention Measures Place controller in manual. The operator can intervene to get any controller (analog on digital) out of the windup state by putting it in manual. This is a simple solution, but not practical in most applications. Sooner or later this approach fails. 199

200. Tuning Cascade Loops Pre-Startup Check 200

201. Place the primary controller in manual and the secondary controller to the local set point. 2. Tune the secondary controller as if it were the only control loop present. 3. Return the secondary controller to remote set point and place the primary controller in auto. 4. Now tune the primary loop as if it were the only control loop present. Remember, when tuning the primary controller that there should be no interaction between the primary and secondary loops. 201

202. Feedforward Control 202

203. • Does not require extensive knowledge of the process. • Easy to implement (start up and tune). • Requires minimal amount of hardware (least expensive control strategy.) • Can be successfully implemented most of the time. (Feedback is sufficient 80 -90 % of the time.) • Reasonably good control. 203 Feedback Loop Advantages

204. • Process characteristics dictate the response. • Response is oscillatory. • Cannot handle frequent load upsets. • Trial and error solution to valve position consumes more energy. 204 Feedback Loop Disadvantages

205. If in addition to the load upsets the process was also subject to frequent supply upsets, cascade control was the solution . 205

206. Feedforward or calculation control is the alternative control strategy when we are unwilling or unable to accept an oscillatory type of response in a given application, or if the load upsets are very frequent (< 3  n ) the controlled variable does not have a chance to settle out. 206

207. 207

208. • Can handle processes with frequent load upsets (< 3tn). • Potentially perfect control without oscillations. • Response virtually independent of process characteristics. • Minimum integrated errors (IE, IAE) can approach zero. • Avoiding a trial error search of valve position conserves energy. 208 Feedforward Advantages

209. • Requires more knowledge of the process. • Requires additional engineering effort and time. • Requires additional hardware for implementation. • More expensive than feedback control. • Economic justification to implement feedforward is made conditionally. 209 Feedforward Disadvantages

210. The feedforward model attempts to predict the effect of steady state and dynamic loads on the product being made. It is not feasible to include all the loads that affect the product, in order to have a perfect feedforward model. It is impossible to come up with a perfect feedforward requiring the need to have a corrective feedback loop known as the feedback trim loop. 210 Feedback Trim Loops

211. 211

212. Mass Flow Processes @ S.S. LEVEL = CONSTANT as dh/ dt = 0 Thus the steady state calculation in this example will simply make the flow input equal to the flow output. @ S.S. Fin = Fout Therefore Fin = Fout 212

213. Level Tank Application 213

214. Applying Feedback Trim Loop to Tank Level Application 214

215. Single Element Drum Level Application 215

216. For negative feedback, an odd number of reverse-acting elements is needed. The final actuator, process and transmitter are all direct-acting elements. The controller is put in a reverse-acting mode for negative feedback. 216

217. In open-loop test to check, it is found that as the steam flow or load increases, the level in the drum initially increases (instead of decreasing as expected.) Typically, the level will go up initially and then come down as shown, temporarily creating a positive feedback situation and loss of control. This happens because as the load increases due to more steam flow, the pressure in the drum decreases, causing the liquid in the drum to temporarily increase or swell. 217

218. 218

219. During steady state operation the steam flow (load) information is used to control the feed water flow on a pound-to-pound basis responding immediately to any load changes. The drum-level feedback trim loop provides the necessary slow corrections to bring measurement back to the set point. This configuration assumes a linear and repeatable relationship between the load and the feed water valve. If this is true then two-element control is sufficient. 219 Two-Element Feedforward Drum Level Application

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221. Three-Element Feedforward Drum Level Application 221

222. Energy flow processes vary in their complexity. These processes must be sufficiently well defined before attempting feedforward control. For a given process there may be several loads that affect the product from the steady state point of view. 222 Energy Flow Feedforward Applications

223. Some of these load contributions are nonlinear and in some cases difficult to evaluate and implement in the model. These are the type of processes that consist of multiple lags and long dead-times which make them difficult to control with a feedback loop and thus good candidates for a feedforward strategy. 223

224. Simple Energy Flow Example To implement this in a feedforward loop, measure Q out and put an equal amount of Q in . If succeed, the temperature in the vessel will stay constant. 224

225. Heat Exchanger Energy Flow Example 225

226. Recognize that this equation is: Steady state without any dynamic considerations. 2. Only the major loads are represented in the model. 3. Minor loads are not accounted for. These include: • losses to ambient, • measuring element and transmitter accuracy, • change in efficiency due to fouling (scaling) or change in operating point, • heat lost in condensate. 4. Supply variations relating to the energy of the steam (enthalpy) are not accounted for. This might dictate cascade for supply upsets, not uncommon in this type of application. 226

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228. 228

229. Applying A Feedback Trim Loop To The Feedforward 229

230. Trim Loop Characteristics: • Use a P + I controller tuned for a slow response, no QAD. • Typical settings require wide proportional bands (low gain) and relatively long integral times in min/rep (i.e. 2-5 min/rep), no derivative action. • The idea is to take slow corrective action without affecting the major feedforward scheme. • Do not introduce non-linear elements that affect the gain versus operating point relationship of the loop. 230

231. • Remember, if unable to linearize for constant loop gain, tune at the highest gain, sluggish response is acceptable in this case. • If the feedforward model is reasonably accurate, the trim controllers output should be  50% during normal operation. • If this is not the case, i.e., output of trim either high or low, there is a good chance that the model does not accurately represent all major loads. 231

232. Ratio Control 232

233. Ratio is a rudimentary form of feedforward where one variable is controlled in ratio to another. It is used in processes where two components are mixed together in a certain proportion or ratio. The controlled variable in effect is the ratio. 233 Ratio Control Scheme

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235. Simple Ratio Example 235

236. Ratio Controller Application 236

237. Adding Feedback Trim 237

238. Selective Control 238

239. 239

240. Median Selectors 240

241. The typical applications of selector systems can be categorized as follows: • Protection against instrument failure • Control through most critical measurement • Protection of equipment (safety) 241

242. Protection Against Instrument Failures Furnace Pressure Measurement Protection 242

243. Exothermic Reactors 243

244. Control Through Most Critical Measurement 244

245. Parallel Metering Combustion Scheme In boiler applications the furnace control system must satisfy various needs: •Maintenance of safe furnace conditions •Maintenance of safe furnace pressure in balanced draft units •Satisfaction of the energy demand •Maintenance of correct air/fuel ratios 245 Protection of Equipment (Safety)

246. 246

247. Pumping Station On a Pipeline The system should provide protection against the following: • Cavitation . If the suction pressure drops below a predetermined low value, the valve starts closing to bring suction pressure up and avoid cavitation . • Motor Load. As the motor draws a current exceeding the motor specifications, the valve starts closing to protect the motor. • Downstream Pressure. If the discharge pressure attempts to exceed the maximum recommended downstream pressure, the valve closes to prevent overpressurizing process piping. 247

248. 248

249. Tune each loop and testing the system for functionality. When all loops are tuned, check scheme performance. Control should alternate smoothly, without a "bump," automatically transferring from one controller to another through the selective system. 249 Tuning Selective Loops

250. Adaptive Control 250

251. The word adapt means to change or fit by modification to new conditions. An adaptive control system may be defined as a system whose parameters automatically change in response to changing process characteristics . The automatic change of the control parameters allows compensation for the changes in the process characteristics and the maintenance of a constant loop gain. A simple linearization to achieve constant steady state is not considered adaptation since all the controller functions remain the same. 251

252. A nonlinear controller typically used in a pH application operates at different gains based on the loop operating point. This controller is not considered adaptive since its controller functions are fixed . 252

253. If the titration curve drifts (changes shape) the linearization loses its effectiveness and there is nothing the controller can do to take care of the problem. Therefore, this is strictly nonlinear control. Remember, to be adaptive, the controller must change its parameters in order to accommodate the changing process parameters. To accomplish this requires a more capable controller as well as additional communication between the process and the controller. 253

254. A few approaches have been used to implement adaptive control strategies: • Gain scheduling or programmed adaptation - based on a change in a process variable i.e. the set point. • Feedforward adaptation - based on a change in load. • Feedback adaptation - based on a change in the controlled variable (measurement.) 254 Approaches to Adaptation

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256. Example of Programmed Adaptation Using Process Variable Information 256

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259. Multivariable Control 259

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261. 261

262. Process Equations: C 1 = K 11 g 11 m 1 + K 12 g 12 m 2 C 2 = K 21 g 21 m 1 + K 22 g 22 m 2 Changing m 1 affects both C 1 and C 2 . Changing m 2 affects both C 2 and C 1 . 262

263. 263

264. Simultaneous Control of Pressure and Flow This involves the simultaneous control of pressure and flow with the fact that both valves affect both the flow and the pressure. The first consideration is to decide which valve should be assigned to control a particular variable. The second consideration is whether a control system can be designed to cancel the interaction between two loops. 264

265. Control Blocks 265

266. AI - Analog Input The Analog Input block takes the input data from the Transducer block, selected by channel number, and makes it available to other function blocks at its output. 266

267. DI - Discrete Input The DI block takes the manufacturer’s discrete input data, selected by channel number, and makes it available to other function blocks at its output. 267

268. PUL – Pulse Input The Pulse Input Block provides analog values based on a pulse (counter) transducer input. There are two primary outputs available. An accumulation output is intended to be connected to an integrator block for differencing, conversion, and integration. This is most useful when the count rate is low relative to the block execution rate. For high count rates, the accumulated count of pulses per block execution can be interpreted as an analog rate (vs. accumulation) value and can be alarmed. 268

269. PID - PID Control The PID block offers a lot of control algorithms that use the Proportional, integral and derivative terms. 269

270. EPID – Enhanced PID Control The EPID block has all parameters of the PID block. Additionally it provides 4 types for bumpless transference from Manual mode to Auto mode, and also a special treatment for tracking outputs. APID – Advanced PID Control The advanced PID function block provides the following additional features comparing to the standard PID algorithm and the enhanced PID: • Selection of the terms (proportional, integral, derivative) calculated on error or process variable • PI Sampling algorithm • Adaptive gain • Configurable Limits of anti reset wind-up • Special treatment for the error • Discrete output to indicate the actual mode 270

271. ARTH - Arithmetic The ARTH block can be used in calculating measurements from combinations of signals from sensors. It is not intended to be used in a control path, so it does not support cascades or back calculation. It does no conversions to percent, so scaling is not supported. It has no process alarms. 271

272. SPLT-Splitter The Splitter block provides the capability to drive multiple outputs from a single input, usually a PID. This block would normally be used in split ranging or sequencing of multiple valve applications. Included in the block features are the capability to open valves as part of a predetermined schedule and leave open or closed a given valve after the controller has transitioned off the valve. The splitter supports two outputs. Since this block will participate in the control path after a PID block, back calculation support is included. 272

273. CHAR - Signal Characterizer The block calculates OUT_1 from IN_1 and OUT_2 from IN_2, according to a curve given by the points: [x1 ;y1 ], [x2 ; y2 ]..............[x21 ; y21] Where x corresponds to the Input and y to the Output. OUT_1 is related to IN_1 and OUT_2 is related to IN_2 using the same curve, but there is no correlation between IN_1 and IN_2 or between OUT_1 and OUT_2. 273

274. INTG – Integrator The Integrator Function Block integrates a variable in function of the time or accumulates the counting of a Pulse Input block. The integrated value may go up, starting from zero, or down, starting from the trip value (parameter SP). The block has two inputs to calculate flow. This block is normally used to totalize flow, giving total mass or volume over a certain time, or totalize power, giving the total energy. 274

275. OSDL - Output Signal Selector and Dynamic Limiter The output signal selector and dynamic limiter block (OSDL) provides two different algorithms types. As Output Selector the cascade input may be routed for one of two outputs based on the value of the OP_SELECT input parameter. As Dynamic Limiter the cascade input is transferred to both output, but it is limited by the secondary inputs multiplied by a gain, plus a bias. The Dynamic LIMITER is extremely useful in one of its most important applications: combustion control with double cross limits. 275

276. 276 FMTH – Flexible Mathematical Block This block provides mathematical expression execution with inputs, outputs and auxiliary variables generated by the user, and also including conditional expressions. The FMTH block has the following characteristics: • It allows execute several mathematical expressions “customized” by user with input and output values, and also using auxiliary variables in these expressions. • Friendly edition of the mathematical expressions, similar to the Microsoft Excel.

277. 277 • It allows the usage of the following operations described in the table below:

278. AO - Analog Output The Analog Output Block is a function block used by devices that work as output elements in a control loop, like valves, actuators, positioners , etc. The AO block receives a signal from another function block and passes its results to an output transducer block through an internal channel reference. 278

279. DO - Discrete Output The DO block converts the value in SP_D to something useful for the hardware found at the CHANNEL selection. 279

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286. WorkShops 286