Process control 2 chapter

Process control 2 chapter

• 1.
  Controller Principles 1 9AEI-406.9
• 2.
  2 9AEI-406.9 Control System parameters Controlsystem 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 em Block Diagram of Process Control Loop
• 4.
  4 9AEI-406.9 The deviation ofcontrolled 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 theerror 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 = Measuredvalue 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 erroras 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 • Thevariable 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 • Thecontrol 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.
• 11.
  11 9AEI-406.9 Example
• 12.
  12 9AEI-406.9 Control lag • “Controllag 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 • Timevariable 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 exampleof 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 • Thisis 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 thebehavior 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 interestedin 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.
• 18.
  Controller Modes 9AEI-406.10 18
• 19.
  9AEI-406.10 19 Controller Modes Two modesof 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 ofdiscontinuous modes •Two position mode •Multi position mode •Floating control mode
• 22.
  9AEI-406.10 22 Continuous mode • Incontinuous mode, smooth variation of the control parameters is possible
• 23.
  9AEI-406.10 23 Different types ofcontinuous modes • Proportional controller (P) • Integral controller (I) • Derivative controller (D) • Composite control modes
• 24.
  9AEI-406.10 24 Composite controller modes Compositecontroller modes combine the continuous control modes Proportional – Integral (PI) Proportional – Derivative (PD) Proportional – Integral – Derivative (PID)
• 25.
  9AEI-406.10 25 Control actions • Theerror 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 • Acontroller 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 • Acontrol 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 & 1231
• 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 Levelon / off controller
• 35.
  35 9AEI-406.11 & 12
• 36.
  36 9AEI-406.11 & 12
• 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 Neutralzone
• 40.
  40 9AEI-406.11 & 12 Neutralzone • 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 Twoposition 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 Neutralzone • 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 threeposition 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 longas 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 controlleraction Figure (1)
• 50.
  9AEI-406.13 50 Advantages • Reduce thecycling behavior • Reduce the overshoots • Reduce the undershoots
• 51.
  9AEI-406.13 51 Disadvantages • It requiresmore complicated final control element (It requires more than two settings).
• 52.
  52 9AEI-406.14 TO 16 Proportionalcontrol • 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 1653
• 54.
  54 9AEI-406.14 TO 16 Proportionalcontroller • 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 Proportionalcontroller 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 •Inthis 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 ProportionalBand (PB) •It is defined as the range of error to cover 0% to 100% controlled output.
• 60.
  60 9AEI-406.14 TO 1660 •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 1661 Fig.1
• 62.
  62 9AEI-406.14 TO 16 Aplot 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 1663 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 1664 Fig 2
• 65.
  65 9AEI-406.14 TO 1665 Fig.3
• 66.
  66 9AEI-406.14 TO 16 Advantagesof 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 Disadvantagesof 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
• 70.
  70 9AEI-406.14 TO 16 Fig.4
• 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 Examplefor 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.
• 78.
  78 9AEI-406.14 TO 16
• 79.
  79 9AEI-406.14 TO 16
• 80.
  9AEI-406.17 & 18 80 Integralcontroller • 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 Integralcontrol 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 8484 • 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 & 1886 The rate of output change for error change Fig.2
• 87.
  87 9AEI-406.17 & 1887 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 Characteristicsof 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 & 1890 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.
• 94.
  94 9AEI-406.17 & 18
• 95.
  9AEI-406.19 & 20 95 Derivativecontroller • 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 OtherTerms of Derivative controller • Rate response • Lead component • Anticipatory controller
• 97.
  9AEI-406.19 & 20 97 Derivativecontrol 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
• 98.
  9AEI-406.19 & 20 98
• 99.
  9AEI-406.19 & 20 99
• 100.
  9AEI-406.19 & 20 100 Derivativemode output for error Fig. 5