process identificationprocess identification pid control and tuningpid control and tuning cascade...

Process IdentificationProcess Identification PID Control and TuningPID Control and Tuning Cascade ControlCascade Control Feed Forward Control Feed Forward Control Non-linear Level Control Non-linear Level Control Ratio Control Ratio Control Override Control Override Control Dead Time Compensation Dead Time Compensation Pass Balancing Pass Balancing Constraint Control Constraint Control Relative Gains Relative Gains Background of MPC Background of MPC Implementation of MPC Implementation of MPC Fractionator ControlFractionator Control Fractionator Conceptual Model Fractionator Conceptual Model Inferred Properties Model Inferred Properties Model Inferred Properties Control Inferred Properties Control Benefit Calculations Benefit Calculations BASIC AND ADVANCED CONTROLS

Process Identification,

The variables (Flow, Temperature, Pressure, Composition) associated with chemical process are divided into 2 groups INPUT VARIABLE: INPUT VARIABLE:: Which denote the effect of surroundings on the process. OUTPUT VARIABLES: OUTPUT VARIABLES: Which denote the effect of process on surroundings The input variables can be further classified into: MANIPULATED (or adjustable): MANIPULATED (or adjustable): V ariables which can be adjusted freely. DISTURBANCE VARIABLES: DISTURBANCE VARIABLES: All input variables other than manipulated variable. Disturbance Variables can be Measured Unmeasured Unmeasured To AIRFO F,T BASIC DEFINITIONS

Process Identification Why is it required? TO INVESTIGATE, How the behavior of a process (outputs) changes with time under influence of changes in external disturbance and Manipulated Variable. To design an appropriate controller: kBetter insight into process behavior leads to better control. kFor a given change in input to a process, we need to know how much the output will ultimately change. kIn which direction will the change take place?. How long it will take for output to change? kWhat trajectory the output will follow.

SELF REGULATORY PROCESS For a step change in input, output attains a new steady state. Even when no control (feedback)action exists. NON-SELF REGULATORY PROCESS For a step change in input, the output does not attain a new Steady State, if no control (feedback) action exists. e. g increase water to tank and level will continue to increase unless control is exercised e. g increase feed to column; temperature will attain a new equilibrium level without any contrast FC Level will keep building Time

LINEARITY THE RESPONSE IS PROPORTIONAL TO THE MAGNITUDE OF INPUT. OUTPUT INPUT TIME NON LINEARITY OUTPUT INPUT

INVERSE RESPONSE INPUT OUTPUT TIME INVERSE RESPONSE

PROCESS DYNAMICS Process control is concerned with the operation of process under steady state and unsteady state (dynamic)conditions. STEADY STATE Defined by steady state material and energy balance equations(as got from steady state simulator for e.g.) Process variables do not change with time. UNSTEADY STATE (DYNAMIC) Defined by unsteady state equations. Process variables change with time before attaining a new steady state. The way a process behaves between 2 steady states is known as its transient response. Process design affects transient response

Change in output Change in input Where, change is the change from one steady state to another. PROCESS GAIN is a measure of the sensitivity of the Process. A Process having a very small gain would be rather insensitive to input. This can be compensated by controlling the Process with a controller having a high gain. PROCESS GAIN (Kp) or STEADY STATE GAIN: Kp=

TIME CONSTANT ( ) TIME CONSTANT is a measure of the capacitance of the Process. Capacitance slows down Process dynamics. TIME CONSTANT can be defined as: Hold-up of the Process Flow through the Process TIME CONSTANT ( )=

CAPACITANCE SLOWS PROCESS DYNAMICS CASE 1 VERY LOW CAPACITANCE ( ALSO CALLED INSTANTANEOUS PROCESS ) HENCE MINIMAL DYNAMICS CASE 2 ---------- IN THIS CASE DYNAMICS ARE SLOWER BECAUSE OF LARGE CAPACITANCE IN TANK T1T1 T1T1

DELAY OR DEAD TIME ( ) A process transportation delay can also adversely affect dynamics. A typical example is plug flow through a pipeline. Any disturbance at the inlet of the pipeline is sensed at the outlet only after a delay, which can be expressed as: Length of the pipeline Velocity of the fluid DELAY ( ) =

Capacitance enable the process to remain at or near Steady State even when distributed.Capacitance enable the process to remain at or near Steady State even when distributed. Capacitance helps controlCapacitance helps control while process delay (dead time) makes control difficult.while process delay (dead time) makes control difficult. DEAD TIME WHENEVER AN INPUT VARIABLE CHANGES, THERE IS A TIME INTERVAL (SHORT OR LONG) DURING WHICH NO EFFECT IS OBSERVED ON THE OUPUTS OF THE SYSTEM. THIS TIME INTERVAL IS CALLED DEAD TIME, OR TRANSPORTATION LAG, OR PURE LAG, OR DISTANCE VELOCITY LAG. PIPELINE CONVEYOR OUTPUT THE OUTPUT DOES NOT SENSE THE DISTURBANCE WHICH HAS ENTERED THE SYSTEM FOR SOME FINITE TIME ( DEAD TIME ) AFTER WHICH IT REACTS ABRUPTLY. OUTPUT DELAY = DEAD TIME =LENGTH VELOCITY DELAY

Process Identification A TYPICAL SELF REGULATORY PROCESS CAN BE APPROXIMATED BY A TRANSFER FUNCITON MODEL OF 3 PARAMETERS : TIME CONSTANT = , DEAD TIME = , PROCESS GAIN = Kp WE CAN USE THESE PARAMETERS TO MODEL A PROCESS AS FIRST-ORDER, FIRST ORDER WITH DEAD TIME OR A HIGHER ORDER PROCESS ( RARE ) : TYPICALLY A PROCESS IS MODELLED AS A FIRST ORDER PROCESS WITH DEAD TIME : OUTPUT CHANGE INPUT CHANGE Y(s) X(s) Kp. e (- S ) 1 + s TRANSFER FUNCTION = = =

In this time domain this equation becomes: OUTPUT INPUT Where, t = elapsed time = time constant of the process Kp = steady state gain of the process It is evident that when the elapsed time equals 1 time constant then OUTPUT INPUT = Kp * ( 1 - e -t/ ) = Kp * ( 1 - e -1 ) = 0.632 * Kp

Method: BROIDA Model: Y(s) = K p e - s X(s) s + 1 = 5.5 (t 2 -t 1 ) = 2.8 t 1 1.8 t 2 Where K p = Process Gain = Dead Time = Time Constant

AA BB ABAB

0 0.2 0.4 0.6 0.8 1.0 1 / A = 0.57 2 / A = 0.20 Get 1, 2 B / A =0.76 METHOD: OLDNBOURG AND SARTORIUS Y(S) Kp X(S) ( 1 S +1)( 2 s+1) =

Non-self regulatory Process

PID Control &Tuning

Introduction to Basic Controls

HOT WATER SIGNAL TO CTL ROOM STEAM COLD WATER T COND Controlled Variablee.gWater outlet Temperature Manipulated Variablee.g Steam Pressure Load Variablee.g Water Flow Basics Concepts and Terminology for Process Control

The Control Problem : Relationship among controlled, manipulated and load variable qualifies the need for process control. kThe Control system is required to keep the controlled variables at its desired value. kThe Control problem can be solved in only two ways, each of which corresponds to basic control system. FEEDBACK SYSTEM : FEED FORWARD SYSTEM : Feed Back System : YSolves the control problem through trial and error procedure. YStarts working when there is imbalance between the controlled variable and set point. MV Load CV PROCESS

WHAT A FEED BACK CAN AND CAN NOT DO uVery rugged works irrespective of source and type of disturbances. uIs very simple to implement and tune without much knowledge about the process. Tuning can be done online. B u t uStarts working only after some damage is already done. uAn error must exist for the controller to start. Thus incapable of perfect control. uMay perform poorly if lags & delays are large.

NEGATIVE FEEDBACK For a feedback loop to be successful, it must have negative feedback.The controller must change its output in the direction that opposes the change in measurement variable While negative feedback is necessary, combination of negative feedback and lags in the process means that oscillation is the natural response of a feedback control loop to an upset. The characteristics of this oscillation are the primary means for evaluating the performance of the control loop. Engineers are interested in period and the dampening ratio of the cycle. For good control,the cycle in pv and mv should steadily decay and end with the pv returned to sp and mv at the new value. Oscillation represents the trial and error search for the new solution to the control problem as the controller is not aware of load variables.

Feedback Control Modes (PID) PROPORTIONAL CONTROLS : The controller response should be proportional to the size of the error. OP ERROR Where, ERROR = (SP - PV) OP = Kc * (SP - PV) + BIAS BIAS = 50 OP = Kc * E DYNAMIC PROPERTIES OF PROPORTIONAL ACTION ]The output change occurs simultaneously with error change. No delay occurs in the proportional response. Each value of the error for given proportional gain generates a unique value of the output. This is limitation of proportional only controller. ]The proportional only controller always has offset which varies with the load.

LOAD LTLCSP MANIPULATED VARIABLE PV CONTROLLED VARIABLE 75 50 25 0 75 50 25 0 75 50 25 0 LEVEL OUTFLOW CONTROLLER OP

O = Kc. E. dt + Bias A B C D E F TIME INTEGRAL ACTION RESPONDS TO SIGN SIZE AND DURATION OF ERROR SET POINT OUTPUT Measurement Integral Controls Ti

Integral Time min / repeat 1 repeat Where as proportional action has unique output at one error, the integral action can achieve any output value and stopping when error is zero. This property of integral action eliminates the offset. For constant error, up to time Ti; O = Kc. E. dt = Kc. Ti / Ti = Kc Ti

Proportional plus integral Control. O = Kc * E + Kc edt + Constant,Where E = SP - PV here bais = Kc / Ti Edt 1 repeat Proportional Response Ti OUTPUT 2525 50 75 100 LOAD +20 -20 The Integral changes the bias term as a function of the error. Integral action introduce the lag in the controller which increases the period. Like proportional action integral action increases the gain of the controller. Too much of either can cause the loop to cycle. Ti

Proportional and Integral Control O = Kc * Error + Kc Error dt qWhen compared with Proportional Controller the only difference is bias term. qIn proportional controller the Bias is fixed where as integral action in above equation uses the integral of error to adjust the bias - stopping when bias is zero. qThe proportional mode will be more effective than integral mode in responding quickly to process upsets EFFECT OF INTEGRAL TIME q Larger the integral time, longer it will take to reach set point qAs the integral time is decreased, process becomes more oscillatory Ti

PI - CONTROL (CONTD.) rThe lowest value that does not make process significantly oscillatory. rThe shape of the response is basically determined by proportional setting and integral times is adjusted so as to remove the offset as quickly as possible without making process oscillatory. r Another performance criterion is quarter decay ratio. rFor any process,there will be a gain for which proportional only controller will give 1/4 decay ratio. For this or any smaller gain, the integral time can be adjusted to give 1/4 decay ratio If primary purpose of Integral Action Is To Eliminate Offset And If Any Integral Time Setting Could Eliminate Offset, Then What Determines Proper Integral Time ?

PI - CONTROL (CONTD.) However,when speed of response is an important consideration,then the largest gain consistent with the response objectives should be used For any response criterion(minimum overshoot,1/4th decay ratio or other),the following tuning procedure will give faster response from a PI controller Remove integral action; Adjust Kc to give desired response ignoring offset; Adjust the Ti to eliminate offset

DERIVATIVE CONTROL DERIVATIVE CONTROL OUTPUT OF CONTROLLER IS PROPORTIONAL TO RATE OF CHANGE OF ERROR OP = Kc. Td.de/dt + BIAS Derivative action works on change in the measurement. whenever measurement stops changing the derivative contribution returns to zero. Derivative action generates an immediate response proportional to its rate of change. This is also called leading action. The proportional response has been advanced in time. the size of this advance is the derivative time Td. The leading characteristics shortens the periods.

ABCD 0 MEASUREMENT DERIVATIVECONTRIBUTION

Td P+D PROPORTIONAL ONLY DERIVATIVE TIME MEASUREMENT

CONTINUOUS MODE (ANALOGUE CONTROLLER): MV(t) = Kc [E(T) + 1 E(t)dt + Td d (E(t)) ] + CONSTANT DIGITAL MODE (FULL POSITION OR POSITION ALGORITHM): n MVn = Kc (En + t.E + Td (En - En -1 ) ) + CONSTANT i=1 Ti t DIGITAL MODE (INCREMENTAL OR VELOCITY): MVn = Kc (En En-1 + En ( t) + Td (En- 2En-1 + En-2)) Ti t t = CONTROLLER EXECUTION PERIOD Ti dt

The velocity mode is popular because of: Bumpless transfer No immediate change in the MV when the controller is put on AUTO or MANUAL mode. The derivative mode for the velocity case is usually on the PROCESS variable rather than the error to prevent large change from occurring when there is a SET POINT CHANGE. The final equation for the VELOCITY ALGORITHM is: MVn = Kc (En En-1 + En ( t) + Td (-PVn + 2PVn-1 - PVn-2) Ti t Apart from the current value, the two previous values of the PROCESS VARIABLE (PV) have got to be stored.

Tuning parameters are selected based on process dynamics The ratio /( + ) is a measure of control difficulty: 0:control is easy 1:control is very difficult A reasonable basis for parameter selection is: Kc * Kp = LOOP GAIN:3 + ---- large (very fast response) :0.7 ---- small (sluggish response) Ti / + ----for RESET action : around 0.5 Td / + ----for DERIVATIVE action: around 0.1

ZIEGLER-NICHOLS recommended settings be: MODEPPIPID Kcd/R0.9d/R1.2d/R Ti-3.3 2.0 Td--0.5 The goal behind these settings is to obtain a 4:1 DECAY RATIO of adjacent peaks in CLOSED LOOP dynamic response. Comments on the method: Closed loop response tends to be oscillatory. The derivative time is too large.

The suggested settings are: MODEP PI PID Kc0.5 Ku0.45Ku0.6Ku Ti-Pu/1.2Pu/2 Td--Pu/8 Comments on the method: -The procedure causes prolonged process upsets.

PID TUNING GUIDELINES MODEPID FLOWS0.30.6250.0 LEVELS (FAST)1.08.00.0 LEVELS (SLOW)0.2516.00.0 PRESS (FAST)2.00.50.0 PRESS (SLOW)1.02.00.125 TEMP. (FAST)1.02.00.0 TEMP. (SLOW)1.016.00.250 COMPRESSOR1.02.00.0

Cascade Control

CASCADE CONTROL Cascade control is a multi-loop control in which there is a secondary inner loop with a second controller. The set point of this secondary controller is given by the primary controller. Cascade control therefore relies on a secondary controller measured variable

For cascade control to be effective the dynamics of the inner loop should be much faster than that of the outer loop. The response of the inner loop should be at least 3 and preferably 5 to 10 times faster than the response of the outer loop: 3 * ( + ) Secondary ( + ) Primary PCV SCV LV OPEN LOOP CLOSED LOOP WITHOUT CASCADE CLOSED LOOP WITH CASCADE

Tuning of Cascade Control Loops The stepwise procedure is as follows: The secondary loop is to be first tuned using the methods described earlier (Open loop response and tuning graphs). Obtain the open loop response between the secondary set point and primary controlled variable. Calculate the primary tuning constants from tuning graphs. Fine tune the primary controller.

Feed Forward Control

FEED FORWARD CONTROL WE WOULD LIKE TO: Control all inputs to the unit (and hold its state variables) at Set Points. A static unit-- ideal. If a disturbance does enter, (uncontrollable), use some other variable to compensate for it before it affects the output. If the unit has got affected,(output is disturbed), bring it back to steady state as soon as possible.

WHEN TO USE FF CONTROL UPSETS ARE MEASURABLE FEEDBACK IS SLOW IN ACTION SIMPLE MODEL CAN BE DEVELOPED DISADVANTAGE OF FF DISTURBANCES MUST BE MEASURED ONLINE A REASONABLY GOOD MODEL IS REQUIRED. MAY BE DETRIMENTAL OTHERWISE IDEAL FF MAY BE PHYSICALLY UNREALISABLE BUT APPROXIMATIONS ARE USUALLY GOOD ENOUGH

Gp Gc FEED BACK U Gu Gp FF CONTROL MV BASIC FB STRUCTURE BASIC FF STRUCTURE SINCE DISTURBANCE IS MEASURED BEFORE PERFECT CONTROL IS POSSIBLE PERFECT CONTROL IS POSSIBLE ENHANCES FB ACTION ENHANCES FB ACTION DOES NOT CAUSE INSTABILITY..ALGEBRAIC EQUATION CONFIRMS IT. DOES NOT CAUSE INSTABILITY..ALGEBRAIC EQUATION CONFIRMS IT. Y sp + MV PV U

FC FF FF COMPENSATES FOR MEASURED UPSETS

K u (1+ p s ) e -( u- p)s K p (1+ u s) -

In the Laplace domain the feed forward controller can be represented as: - F.F.Controller= Kff* ( 1 + LD S ) *e - ff S (1 + LG S) GAIN = - Ku / Kp LEAD = LD = p LAG = LG = u ff = u - p ff should be 0.0 The LEAD/LAG algorithm of feed forward controller DYNAMICALLY COMPENSATES for upset and control dynamics.

LEAD LAG 63.2 % Recovery

STEP-2: FINE TUNE THE DYNAMIC COMPENSATION

P > U EFFECT OF DEADTIME ACTION CANNOT BE PREPONED !!! PP CV SET POINT CV MV DV

DYNAMIC FEEDFORWARD TO FULLY COMPENSATE FOR A DISTURBANCE, MVS EFFECT ON PV SHOULD BE FELT AS FAST AS THE EFFECT OF DISTURBANCE. ACTION CANNOT BE TAKEN BEFORE DISTURBANCE IS MEASURED.

Non-linear Level Control

Objective : To utilise hold up to reduce variation in outflow to reduce disturbances in downstream processes. Method: Reduce controller gain as the level approaches set point. Increase controller gain as the level approaches high or low limit.

Algorithm: When PV is outside High-Low limits set gain high (say Kh) When PV is between set point and high limit set gain = Kh*(SP-PV)/(HL-SP) When PV is between set point and low limit set gain= Kh*(PV-SP))/(SP-LL)

Ratio Control

RATIO CONTROL Ratio control is a special type of feed forward control where 2 disturbance (load) are measured and held in a constant ratio to each other. It is mostly used to control the ratio of flow rates of two streams. Both flow rates are measured but only one can be controlled. The stream where flow rate is not under control is usually referred to as wild stream.

FT Divider FT RC X - + Wild Stream Controlled Stream FT FC X Wild Stream Controlled Stream FT X - + Desired Ratio Alternate Configurations of Ratio Control

Applications of Ratio Control Ratio control is used extensively in the industry with the following as most commonly encountered examples: Keep constant ratio between feed flow rate and the steam (heating media) in reboiler in distillation column. Hold constant the reflux ratio in a distillation column. Control the ratio of 2 reactants entering a reactor at a desired value.

Applications of Ratio Control Hold the ratio of 2 blended streams constant in order to maintain the composition of the blend at the desire ratio. Keep the ratio of fuel/air in a burner at its optimum value. Maintain the ratio of the liquid flow rate to vapour flow rate in an absorber constant, in order to achieve the desired composition in the exit vapour stream. Maintain the ratio of steam flow rate to strippers to bottom product flow rate from stripper in order to achieve optimum use of steam.

Example of Ratio Control This controller adjust steam flow in ratio of bottom product of stripper Striping Steam Flow = Ratio * RCO Flow Steam RCO Ratio Control Ratio FC

Example of Ratio Control

Override Control

During the normal operation of a plant or during its start-up or shutdown, it is possible that dangerous situation may arise which may lead to destruction of equipment and operating personnel. In such cases it is necessary to change from the normal control action and attempt to prevent a process variable from exceeding an allowable upper or lower limit.

Override Control This can be achieved through the use of special types of switches. The high selector switch (HSS) is used whenever a variable should not exceed an upper limit. The low selector switch (LSS) is employed to prevent a process variable from exceeding lower limit.

DEAD TIME COMPENSATION

Feedback control using a conventional PID controller is seriously limited when it comes to handling processes with substantial time delays. These time delays are commonly called deadtimes. Deadtime is described mathematically by: Laplace domain : Y(s) X(s) Time domain: Y (t) = X (t - ) Where = dead time DEAD TIME COMPENSATION = e - s

BLOCK DIAGRAM REPRESENTATIVE OF SMITH PREDICTOR DEAD TIME COMPENSATION E* = R-Y* E = E*-E = E* - Y - Y = R - Y* - Y + Y = R - (Y* - Y + Y)

- + + Controller PROCESS K p s + 1 K p. e - s s + 1 - - + - + - - + Load Variable E Y Y* Y Y* - Y + E* = R-Y* E = E*-E = E* - Y - Y = R - Y* - Y + Y = R - (Y* - Y + Y) DEAD TIME COMPENSATION (Alternate Configuration)

Pass Balancing

Typical Constraints Max Allowable Flow Change Max % Flow Imbalance Max Pass Flow Set Point Min Absolute Flow Through Each Pass X FC Crude Flow Ratios Heater Pass Balancing XXX Pass Flows Pass COT

Pass Balancing 50 m3/h 305 C 50 m3/h 310 C 50 m3/h 290 C 50 m3/h 295 C

Objective of scheme: It should distribute the change in flow to all the passes It should manipulate individual pass flow to get all passes Coil Outlet within 1 C. Manipulated Variables: Passes Flows Control Variable: Pass Coil Outlet Temp Constraints: Furnace tube skin Temp Fire box temperatures Pass flow valves Openings Minimum number of passes available for control.

Pass Balancing Pass Balancing: Step1: Check if Minimum passes are in Cascade Step2: Check if C/V OP are within limit. If not drop that MV. Step3: Check if Skin temperatures are within limit Feed Controller: 1.0 Calculate the Total Feed flow as a PV TOTFEED.PV = F1+F2+F3+F4 2.0 Set Point of Total Feed Controller TOTFEED.SP : Operator Entered Value 3.0 Change in feed flow control F1_New = F1*TOTFEED.SP/TOTFEED.PV 4.0 Check for delta change in feed Feed = F1_new - F1 5.0 if abs ( Feed) > Max Change Then Clamp Value to Max Change

Pass Balancing: 1.0 Calculate weighted average temp TAVG = (F1*T1+F2*T2+F3*T3+F4*T4)/(F1+F2+F3+F4) 2.0 Calculate Pass Balancing Factor X1 = T1/TAVG X2 = T2/TAVG .. 3.0 Calculate Change in Flow required for PBAL F1 = F1*(T1/TAVG-1) 4.0 Check for delta change in feed if abs ( Feed) > Max Change Then Clamp Value to Max Change 5.0 Set new value of pass flow.

Exercise on passbalancing F1 = 50*(295/300-1) = F2 = 50*(290/300-1) = F3 = 50*(310/300-1) = F4 = 50*(305/300-1) = -0.833333 -1.666667 1.66667 0.83333 Total Feed = 50+50+50+50 =200 Tavg = (295*50 + 290*50 + 310*50 +305*50)/200 = 300 50 m3/h 305 C 50 m3/h 310 C 50 m3/h 290 C 50 m3/h 295 C

Multi-constraint Control

Multi-Constraint Controller IR V Objective: Maximisation of Re-boiler Duty Constraints: Internal Reflux Vapour Velocity Pressure Controller CV Opening

Multi Constraint Controller Define: Objective Function of Manipulated Variable MIN / MAX Identify the Constraints C1, C2, C3 are three constraints Limits of Constraints Decide constraints and delta constraints limits Initial proportional and integral gains Calculate ERR = CV(current value) - CL(constraint limit) Proportional output PO = Kp*[CV - OV (old value)] Integral Output IO = Kp*ERR*CT/Ti

Multi Constraint Controller Select most limiting constraint The limiting Constraint will have Minimum margin from limit If objective is MIN, select maximum IO else select minimum IO. If controller is wound up If wound up HI or HILO & IO>0 set selected IO=0 If wound up LO or HILO & IO

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