# Process control 2 chapter

Head of Dept,Govt Polytechnic Kothagudem um Government
5. Oct 2017
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### Process control 2 chapter

• 2. 2 9AEI-406.9 Control System parameters Control system parameters are • Error • Controller output • Control lag • Dead time • Cycling
• 3. 3 9AEI-406.9 C F.C.E P F.B + - S.P C.V e m Block Diagram of Process Control Loop
• 4. 4 9AEI-406.9 The deviation of controlled variable from set point is called error It is given by e = r – b Where b = measured value r = set point e = error Error + -r b e = r-b Error detector
• 5. 5 9AEI-406.9 • Express the error as percent of measured variable range (i.e. span). • The measured value of a variable can be expressed as percent of span over a range of measurement by equation. Cp ={(C - Cmin) / (Cmax - Cmin)} * 100
• 6. 6 9AEI-406.9 Where Cp = Measured value as percent of measurement range C = Actual measured value Cmax = Maximum of measured value Cmin = Minimum of measured value
• 7. 7 9AEI-406.9 Error To express error as a percent of span, the measured indication of minimum and maximum can be used as below. ep ={ (r - b) / bmax – bmin} * 100 where ep = error expressed as percent of span.
• 8. 8 9AEI-406.9 Variable range • The variable under control has a range of values within which control is maintained. • This range can be expressed as the minimum and maximum value of the variable or the nominal value plus and minus the spread about this nominal. • If a standard 4-20mA signal transmission is employed, then 4mA represents the minimum value of the variable and 20mA the maximum. 8
• 9. 9 9AEI-406.9 Control parameter range • The controller output range is the translation of output to the range of possible values of the final control element. • This range also is expressed as the 4-20mA standard signal again with the minimum and maximum effects in terms of the minimum and maximum current. 9
• 10. 10 9AEI-406.9 Control lag • The control system also has a lag associated with its operation that must be compared to the process lag. • When a controlled variable experiences a sudden change, the process-control loop reacts by outputting a command to the final control element to adopt a new value to compensate for the detected change.
• 12. 12 9AEI-406.9 Control lag • “Control lag refers to the time for the process-control loop to make necessary adjustments to the final control element”. • If a sudden change in liquid temperature occurs, it requires some finite time for the control system to physically actuate the steam control value. 12
• 13. 13 9AEI-406.9 Dead time • Time variable associated with process control is both a function of the process-control system and the process. • “This is the elapsed time between the instant deviation (error) occurs and the correction action first occurs”.
• 14. 14 9AEI-406.9 • An example of dead time occurs in the control of a chemical reaction by varying reactant flow rate through a long pipe. • When a deviation is detected, a control system quickly changes a value setting to adjust flow rate. but if pipe is quite long, there is a period of time during which no effect is felt in the reaction vessel.
• 15. 15 9AEI-406.9 Dead Time • This is the time required for the new flow rate to move down the length of the pipe. • Such dead times can have a very profound effect on the performance of control operations on a process. 15
• 16. 16 9AEI-406.9 Cycling • Cycling the behavior of the dynamic variable error under various modes of control. • One of the most important modes is an oscillation of the error about zero. • This means the variable is cycling above and below the set point value. • Such cycling may continue indefinitely, in which case we have ‘steady-state cycling’. 16
• 17. 17 9AEI-406.9 Cycling • Here interested in both the peak amplitude of the ‘error ‘and the ‘period of the oscillation’. • If the cycling amplitude decays to zero, however, we have a cyclic transient error. • Here we are interested in the ‘initial error’, the period of the cyclic oscillation, and ‘decay time’ for the error to reach zero.
• 19. 9AEI-406.10 19 Controller Modes Two modes of control action • Discontinuous control mode • Continuous controller
• 20. 9AEI-406.10 20 Discontinuous control mode • In Discontinuous mode the controller command intimates a discontinuous change in in the controller parameters.
• 21. 9AEI-406.10 21 Different types of discontinuous modes •Two position mode •Multi position mode •Floating control mode
• 22. 9AEI-406.10 22 Continuous mode • In continuous mode, smooth variation of the control parameters is possible
• 23. 9AEI-406.10 23 Different types of continuous modes • Proportional controller (P) • Integral controller (I) • Derivative controller (D) • Composite control modes
• 24. 9AEI-406.10 24 Composite controller modes Composite controller modes combine the continuous control modes Proportional – Integral (PI) Proportional – Derivative (PD) Proportional – Integral – Derivative (PID)
• 25. 9AEI-406.10 25 Control actions • The error that result from the measurement of the controlled variable may be positive or negative. Types of control action • Direct action • Reverse action
• 26. 9AEI-406.10 26 Direct action • A controller is said to be operated with direct action when an increasing value of the controller output. • Example level control system. • If the level rises (controlled variable increases) the control output should increase to open the valve more to keep the level under control.
• 27. 9AEI-406.10 27 Reverse action • A control is said to be operating with reverse action when an increasing value of the controlled variable causes a decreasing value of the controller output. • Example a simple temperature control of furnace with fuel as heat energy. • If the temperature increases, the control output should decrease to close the valve for decreasing the fuel input to bring the temperature under control
• 28. 28 9AEI-406.11 & 12 ON - OFF Controller • Two position control is a position type of a controller action in which manipulated variable is quickly changed to either maximum (or) minimum value depending upon whether the controlled variable is greater or less than the set point • Two position control mode is also called ON – OFF control mode 28
• 29. 29 9AEI-406.11 & 12 P = 0% Cp > Sp = 100% Cp < Sp P = controller output Cp = controlling parameter Sp = set point The controller output in two position Mode can be expressed as Two position mode
• 30. 30 9AEI-406.11 & 12 ON - OFF Controller • The minimum value of manipulated variable is zero (off) • The maximum value is the full amount possible (on)
• 32. 32 9AEI-406.11 & 12 ON - OFF Controller The relation ship shows that • When the measured value is less than set point, full control output result. • When is more than set point, the controller output is zero.
• 33. 33 9AEI-406.11 & 12 • Liquid bath temperature control • Level control • Room heating System • Air conditioners Applications
• 34. 34 9AEI-406.11 & 12 Level on / off controller
• 37. 37 9AEI-406.11 & 12 Advantages • Simplest and cheapest. • Two position controller is suitable for system with slow process rates.
• 38. 38 9AEI-406.11 & 12 Disadvantages • Over shoot and Under shoot resultant continuous oscillation • Neutral zone
• 40. 40 9AEI-406.11 & 12 Neutral zone • In practical implementation of the two position controller • There is an overlap as ep increases through zero or decreases through zero • In this span, no change in controller output occurs fig.1
• 41. 41 9AEI-406.11 & 12 Two position mode controller Fig.1
• 42. 42 9AEI-406.11 & 12 • The controller output changes to 100% when the error changes above Δ ep • The controller output changes to 0% when the error changes below Δ ep Neutral zone
• 43. 43 9AEI-406.11 & 12 Neutral zone • The range 2 Δ ep is called as the neutral zone • This is also called as differential gap • This is purposefully designed above a certain level • This prevents excessive cycling • This is a desirable Hysteresis in a system
• 44. 9AEI-406.13 44 Multi position mode • A logical extension of two position control is to provide several inter mediate rather than only two settings of the controller output. • Multi position mode is used to reduce the cycling behavior and over shoot & undershoot inherent in two position mode.
• 45. 9AEI-406.13 45 • A three position mode is one in which the manipulated variable takes one of three value. • High • Medium • Low
• 46. 9AEI-406.13 46 Multi position mode p = pi , e p > ei i = 1,2,3,4---------n • As Error exceeds ± e i, Controller output is adjusted to preset values of pi . • This mode is represented by following equation
• 47. 9AEI-406.13 47 • Three - position controller is best example for multi position controller • The controller output in 3- position controller is P = 100 % e p > e2 = 50 % - e1< e p < e2 = 0 % ep < - e1 Example for multi position controller
• 48. 9AEI-406.13 48 • As long as the error is between e2 and e1 of the set point the controller stays at some nominal setting indicated by a controller output as 50%. • If the error exceeds the set point by e2 or more then the output is increased to 100%. • If the error is less than set point by -e1or more , the controller output is zero. • Three position controller action can be shown in figure (1)
• 50. 9AEI-406.13 50 Advantages • Reduce the cycling behavior • Reduce the overshoots • Reduce the undershoots
• 51. 9AEI-406.13 51 Disadvantages • It requires more complicated final control element (It requires more than two settings).
• 52. 52 9AEI-406.14 TO 16 Proportional control • A proportional control system is a type of linear feedback control system. • Two classic mechanical examples are the toilet bowl float proportioning valve and the fly-ball governor.
• 54. 54 9AEI-406.14 TO 16 Proportional controller • Proportional action is a mode of controller action in which there is a continuous linear relation exist between the controller and error. 54
• 55. 55 9AEI-406.14 TO 16 • Proportion action is mode of control action In which there is a continuous linear relation between value of the deviation and manipulated variable. • The action of control variable is repeated and amplified in the action of the control element. 55
• 56. 56 9AEI-406.14 TO 16 Proportional controller Proportional controller also called • Correspondence controller • Droop control • Modulating controller
• 57. 57 9AEI-406.14 TO 16 • In the proportional control algorithm, the controller output is proportional to the error signal, which is the difference between the set point and the process variable. • In other words, the output of a proportional controller is the multiplication product of the error signal and the proportional gain.
• 58. 58 9AEI-406.14 TO 16 •In this control mode a linear relationship exists between the controller output and error. P = k p e p + p0 •K p = proportional gain between error and controller output •P0 = controller output with no error •e p = error Proportional control mode
• 59. 59 9AEI-406.14 TO 16 Proportional Band (PB) •It is defined as the range of error to cover 0% to 100% controlled output.
• 60. 60 9AEI-406.14 TO 16 60 •PB can be expressed by the equation PB = K p = proportional gain PB = proportional band • PB is dependent on gain. High gain means large response to an error 100 Kp
• 62. 62 9AEI-406.14 TO 16 A plot of the proportional mode output verses error shown in fig. • Po has been set to 50% and two different gains have been used. • Proportional band is depend on the gain. • A High gain means large response to an error but also a narrow error band with in which output is not saturated. • A High percentage of PB (Wide band ) correspond to less sensitive controller settings.
• 63. 63 9AEI-406.14 TO 16 63 a) If the error is zero, the output is constant equal to Po. b) If there is error, for every 1 % of error a correction of Kp percent is added to or subtracted from Po. depending on the reverse or direct action of the controller. The characteristics of proportional mode
• 66. 66 9AEI-406.14 TO 16 Advantages of Proportional Control • Does not require precise analytical model of the system being controlled. • Simple implementation. • Proper for Applications with simple requirement (Overshoot, settling time, oscillation and so on).
• 67. 67 9AEI-406.14 TO 16 Disadvantages of Proportional Control • Inaccurate model may cause steady-state error nonzero • Disturbance input is non zero • Reference input is non zero • Noise input • Inaccurate model may cause oscillations. 67
• 68. 68 9AEI-406.14 TO 16 Applications • Proportional control generally used in processes where large load changes are unlikely or with moderate to small process lag.
• 69. 69 9AEI-406.14 TO 16 • Offset is a permanent ‘residual error’ in the operating point of the controlled variable when load change occurs • Offset can be minimized by a larger value of Kp (proportional gain). OFFSET
• 71. 71 9AEI-406.14 TO 16 OFFSET • consider a system under nominal load with the controller at 50%and the error zero as shown in Fig 2. • If the transient error occurs the system respond by changing controller out put in correspondence with the transient to effect return to zero error
• 72. 72 9AEI-406.14 TO 16 • If the transient error occurs the system respond by changing controller out put in correspondence with the transient to effect return to zero error. • A load change error that requires a permanent change in controller output to produce the zero error state. • One to one correspondence exist between controller out put and error , it is clear that a new zero controller out put never be achieved. • The system produces a small permanent offset in reaching a compromise position of controller output under new load
• 73. 73 9AEI-406.14 TO 16 Example for offset error Fig 5. Control valve A Control valve B
• 74. 74 9AEI-406.14 TO 16 • Consider the proportional mode level control system as shown in fig 1. • For understanding the offset error some of the numerical values regarding proportional controller output and gain values are assumed.
• 75. 75 9AEI-406.14 TO 16 LET • Valve A is linear with a flow scale factor = 10 m3 /hour/% • Controller output P = 50% • Proportional gain Kp=10% • When load change occurs through B valve ,output changes from 500m3 /hr to 600m3 /hr • Then A valve moves to new position 600m3 /hr • There fore P= 60 %
• 76. 76 9AEI-406.14 TO 16 • In proportional controller we have • P = kpe p + p0 • ep = =1% So,1% OFF set error occurs when load changed 0 P P-P 60 - 50 = % K 10
• 77. 77 9AEI-406.14 TO 16 • Offset is eliminated by increase in the proportional gain which result produces oscillations. • Fig shows the effect of Kp on the offset.
• 80. 9AEI-406.17 & 18 80 Integral controller • Integral action is a mode of action in which the value of the manipulated variable is changed at rate proporonal to the derivation. • Integral controller can also be called as Reset Controller.
• 81. 9AEI-406.17 & 18 81 • If the deviation is double over a previous value , the final control element is moved twice as faster. • When the controlled variable is at the set point (zero deviation), the final control element is stationary.
• 82. 9AEI-406.17 & 18 82 Integral control mode •Analytically reset action can be expressed as = KI ep ……( 1 ) = rate of controller output change (%/s) KI = constant relating the rate of the ep = error(%/s/%) Because of process lags it is used for small process capacities dt dp dt dp
• 83. 9AEI-406.17 & 18 83 • The inverse of K I, called the integral time Ti =1/Ki, Expressed in seconds or minutes, is used to describe the integral mode. • Ti is defined as the time of change of controlled variable caused by unit change of deviation.
• 84. 9AEI-406.17 & 18 84 84 • For actual controller output equation 1 can be integrated and is given by Where p (0) = the controller output at t = 0. • This equation shows that present controller output p(t) depends upon the history of error from when obserervation started at t=0 t t p 0 p(t) = k e ( t)dt + p(0)∫
• 85. 9AEI-406.17 & 18 85 • If the error doubles ,the rate of controller output change also doubles. • The constant ki expressed the scaling between error and controller output. • A larger value of ki means that small error produces large rate of change of p and vice versa.
• 86. 86 9AEI-406.17 & 18 86 The rate of output change for error change Fig.2
• 87. 87 9AEI-406.17 & 18 87 Integral controller output for error input Fig.3
• 88. 88 9AEI-406.17 & 18 • We see that the faster rate provided by Ki cause s much greater control output at a particular time after the error is generated.
• 89. 89 9AEI-406.17 & 18 Characteristics of integral controller • If the error is zero, the output stay fixed at a value to what it was when error went to zero. • If the error is not zero, the output will begin to increase or decrease at a rate of ki percent per second for every one percentage of error.
• 90. 90 9AEI-406.17 & 18 90 Integral mode output for error with effect of process and control lag Fig. 4
• 91. 91 9AEI-406.17 & 18 Advantages • Eliminate the offset. • Produces sluggish and log oscillation responses. • If increase gain Kp to produce faster response the system become more oscillatory and may be led to instability. 91
• 92. 92 9AEI-406.17 & 18 Disadvantages • Slow response • Process lag is to large cyclic response
• 93. 93 9AEI-406.17 & 18 Applications • The integral control mode is not used alone but can be for systems with small process lags and correspondingly small capacities.
• 95. 9AEI-406.19 & 20 95 Derivative controller • The derivative mode of controller operation provides that the controller output depends on the rate of change of error.
• 96. 9AEI-406.19 & 20 96 Other Terms of Derivative controller • Rate response • Lead component • Anticipatory controller
• 97. 9AEI-406.19 & 20 97 Derivative control mode • Derivative control mode is also known as rate or Anticipatory mode. • Controller output depends on the rate of change of error KD = derivative gain constant (%-s/%) = rate of change of error(%/s) P = controller output p D de P=K dt p de dt
• 100. 9AEI-406.19 & 20 100 Derivative mode output for error Fig. 5
• 101. 9AEI-406.19 & 20 101 101 • The characteristics of the derivative control mode are: a) If the error is zero, the mode provides no output. b) If the error is constant in time, the mode provides no output.
• 102. 9AEI-406.19 & 20 102 102 c) If the error is changing in time, the mode contributes an output of KD percent for every 1% per second rate of change of error. d) For direct action, a positive rate of change of error produces a positive derivative mode output.
• 103. 9AEI-406.19 & 20 103 Advantages • The derivative term the controller anticipate what the error will be in the immediate future and applies control action which is proportional to the current rate of change of error. • Fast response (Derivative mode predict process error before they have evolved and take corrective action in advance of that occurrence).
• 104. 9AEI-406.19 & 20 104 Disadvantages • Noisy response with almost zero error it can compute large derivatives and thus yield large control action, although it is not needed.
• 105. 9AEI-406.19 & 20 105 Flow controlling • Chemical reactors • Petroleum industries • Power production Applications
• 106. 106 9AEI-406.21 • This mode is also called as proportional plus reset action controller. • Combination of proportional controller and integral controller is called PI controller. Proportional + integral control
• 107. 107 9AEI-406.21 • Proportional control mode provides a stabilizing influence. • Integral control mode provide corrective action when deviation in controlled variable from set point. • Integral control mode has a phase lag of 90º over proportional control. • Small process lag permits the use of a large amount of integral action.
• 108. 108 9AEI-406.21 Analytical expression for controller output in PI controller P = Kp ep +Kp KI ∫ep dt +pI(0) PI(0) = integral term value at t = 0(initial value))
• 110. 110 9AEI-406.21 Advantages • Smooth controlling by one to one correspondence of proportional controller. • Eliminates the offset by integral action. • It shows a maximum overshoot and settling time similar to the P controller but no steady-state error. • PI mode can be used in a system with frequent or large load change.
• 111. 111 9AEI-406.21 Disadvantages • Integration time ,the process must have relatively slow changes in load to prevent oscillations induced by the integral overshoot. • During the start up of a batch process the integral action causes considerable overshoot error.
• 112. 112 9AEI-406.21 Application • PI controller can be used in systems with frequent (or) large load charges. • Overshoot and cycling often result when PI mode Control is used in startup of batch process. 112
• 113. 113 9AEI-406.21 Characteristics of PI controller • When the error is zero the controller out put is fixed at the value that the integral term had when the error went to zero. • If the error is not zero, the proportional term contribute a correction and the integral term begin to increase or decrease the accumulation value depends on the sign of error and direct or reverse action
• 114. 114 9AEI-406.21 PI control action error input for reverse action Fig.2
• 115. 115 9AEI-406.22 115 • This mode is also called as proportional plus reset action controller. • Combination of proportional controller and Derivative controller is called PD controller. Proportional + integral control
• 116. 116 9AEI-406.22 • Derivative action provides the boost necessary to counter act the time delay associated with such control systems. • Derivative control leads proportional control by 90º Proportional + derivative control
• 117. 117 9AEI-406.22 Analytical expression for PD controller is: P = Kp ep +Kp KD dep +p0 dt
• 119. 119 9AEI-406.22 Advantages • Handled fast process load changes as long as the load change offset error is acceptable. • Reduce the magnitude of offset because of narrow proportional band. • Properly fits and adjusts to a process and prevent controlled variable deviation. • Reduces the time required to stabilize.
• 120. 120 9AEI-406.22 • Used in multi capacity process applications. • Flow process • Batching operations like periodic shutdown, emptying and refilling. Applications
• 121. 121 9AEI-406.22 Disadvantages • Does not eliminate offset after a load disturbance. • It cannot be used where the system lags are less.
• 122. 122 9AEI-406.22 122 PD control action for error input Fig.7
• 123. 123 9AEI-406.22 • The effect of derivative action in moving the controller output in relations to the error rate change.