5. Oct 2017•0 gefällt mir•4,510 views

Downloaden Sie, um offline zu lesen

Melden

Ingenieurwesen

Process load,process lag,self regulation,error,control lag,dead time,cycling,discontinious control modes,two position control modes,flaoting control modes,propotional band,offset,propotional control, integral control,derivative control,pid control,pi control,pd control,tuning of pid control

Srinivasa RaoFolgen

- 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)
- 31. 31 9AEI-406.11 & 12 31
- 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
- 39. 39 9AEI-406.11 & 12 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)
- 49. 9AEI-406.13 49 Three position controller action 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.
- 53. 53 9AEI-406.14 TO 16 53
- 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
- 61. 61 9AEI-406.14 TO 16 61 Fig.1
- 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
- 64. 64 9AEI-406.14 TO 16 64 Fig 2
- 65. 65 9AEI-406.14 TO 16 65 Fig.3
- 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))
- 109. 109 9AEI-406.21
- 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
- 118. 118 9AEI-406.22
- 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.