Presentation on theme: "ERT 210 Process Control & dynamics"— Presentation transcript:
1 ERT 210 Process Control & dynamics CHAPTER 8Feedback ControllersAnis Atikah binti Ahmad
2 Chapter 8 Feedback Controller Chapter 8 Example 1 Corrective action occurs when the controlled variable deviates from the set pointExample 1Control objective: to keep the tank exit composition, x, at the desired value (set point) by adjusting the flow rate, w2, via the control valveChapter 8Chapter 8VariablesControlled variable: exit composition, xManipulated variable: flow rate of A,w2Figure 8.1: Schematic diagram for a stirred-tank blending system
3 Example 2The flow rate of a process stream is measured and transmitted electronically to a flow controller (FC)The controller compares the measured value to the set point value and takes appropriate corrective action by sending an output signal to the current-to-pressure (I/P) transducer.I/P transducer sends a corresponding pneumatic signal to the control valve.Chapter 8Figure 8.2: Flow control system
4 In feedback control, the objective is to reduce the error signal to zero where andChapter 8Chapter 8
5 Basic Control Modes Chapter 8 Chapter 8 Three basic control modes: highly endothermic reactionProportional controlChapter 8Chapter 8costlyIntegral controlrequires very intensive energyDerivative control
6 Proportional Control Chapter 8 Chapter 8 For proportional control, the controller output is proportional to the error signal,Chapter 8Chapter 8where:At time t = 25 min, e(25) = 60–56 = 4At time t = 40 min, e(40) = 60–62 = –2
8 The key concepts behind proportional control are the following: the controller gain (Kc) can be adjusted to make the controller output changes as sensitive as desired to deviations between set point and controlled variable;the sign of Kc can be chosen to make the controller output increase (or decrease) as the error signal increases.Chapter 8Some controllers have a proportional band setting instead of a controller gain. The proportional band PB (in %) is defined as≜Large PB correspond to a small value of Kc and vice versa
9 In order to derive the transfer function for an ideal proportional controller (without saturation limits), define a deviation variable as≜Then Eq. 8-2 can be written asChapter 8Chapter 8The transfer function for proportional-only control:An inherent disadvantage of proportional-only control is that a steady-state error (or offset) occurs after a set-point change or a sustained disturbance.
10 Integral Control Chapter 8 For integral control action, the controller output depends on the integral of the error signal over time,where ,= integral time/reset timeChapter 8Integral action eliminates steady-state error(i.e., offset) Why??? e 0 p is changing withtime until e = 0, where p reaches steady state.
11 Proportional-Integral (PI) Control Integral control action is normally used in conjunction with proportional control as the proportional-integral (PI) controller:The corresponding transfer function for the PI controller in Eq. 8-8 is given by
12 Chapter 8 Disadvantage of Integral Action: Reset Windup The integral mode causes the controller output to change as long as e(t*) ≠ 0 in Eq. 8-8Can grow very largeIf an error is large enough and/or persists long enoughCan produce p(t) that causes the final control element (FCE) to saturate.That is, the controller drives the FCE (e.g. valve, pump, compressor) to its physical limit of fully open/on/maximum or fully closed/off/minimum.Chapter 8If this extreme value is still not sufficient to eliminate the errorthe integral term continue growing,the controller command the FCE to move to 110%, then 120% and morethis command has no physical meaning (no impact on the process)*Antireset windup reduce the windup by temporarily halting the integral control action whenever the controller output saturates and resumes when the output is no longer saturates.
13 Chapter 8 Chapter 8 Integral action eliminates steady-state error (i.e., offset) Why??? e 0 p is changing withtime until e = 0, where p reaches steady state.Transfer function for PI controlChapter 8Chapter 8
14 Derivative Control Chapter 8 Chapter 8 The function of derivative control action is to anticipate the future behavior of the error signal by considering its rate of change.Controller output is proportional to the rate of change of the error signal or the controlled variable.Thus, for ideal derivative action,Chapter 8Chapter 8where , the derivative time, has units of time.
15 Advantages of derivative action By providing anticipatory control action, the derivative mode tends to stabilize the controlled process.Derivative control action tends to improve dynamic response of the controlled variableChapter 8Chapter 8
16 Physically unrealizable Derivative action always used in conjunction with proportional or proportional-integral control.Unfortunately, the ideal proportional-derivative control algorithm in Eq is physically unrealizable because it cannot be implemented exactly.For example, an “ideal” PD controller has the transfer function:Physically unrealizableChapter 8Chapter 8
17 For “real” PD controller, the transfer function in (8-11) can be approximated by Chapter 8Chapter 8where the constant α typically has a value between 0.05 and 0.2, with 0.1 being a common choice.In Eq the derivative term includes a derivative mode filter (also called a derivative filter) that reduces the sensitivity of the control calculations to high-frequency noise in the measurement.
18 Chapter 8 Proportional-Integral-Derivative (PID) Control Chapter 8 3 common PID control forms are:highly endothermic reactionParallel formcostlyChapter 8Chapter 8Series formrequires very intensive energyExpanded form
19 Chapter 8 Parallel Form of PID Control The parallel form of the PID control algorithm (without a derivative “Ideal” PID control is given byChapter 8The corresponding transfer function for “Ideal” PID control is:
20 The corresponding transfer function for “Real” PID control (parallel), with derivative filter is: Chapter 8Chapter 8Figure 8.8 Block diagram of the parallel form of PID control (without a derivative filter)
21 Chapter 8 Chapter 8 Series Form of PID Control Constructed by having PI element and a PD element operated in series.Commercial versions of the series-form controller have a derivative filter as indicated in Eq 8-15.PIPDChapter 8Chapter 8Figure 8.9 Block diagram of the series form of PID control (without a derivative filter)
22 Chapter 8 Chapter 8 Expanded Form of PID Control Used in MATLABExpanded Form of PID ControlIn addition to the well-known series and parallel forms, the expanded form of PID control in Eq is sometimes used:Chapter 8Chapter 8
23 Chapter 8 Controller Comparison Chapter 8 P - Simplest controller to tune (Kc).- Offset with sustained disturbance or setpointchange.PI - More complicated to tune (Kc, I) .- Better performance than P- No offset- Most popular FB controllerChapter 8Chapter 8PID - Most complicated to tune (Kc, I, D) .- Better performance than PI- No offset- Derivative action may be affected by noise
24 From a parallel form of PID control in Eq. 8-13 Features of PID ControllersDerivative and Proportional KickOne disadvantage of the previous PID controllers :derivative kick : when there is a sudden change in set point (and hence the error, e) that will cause the derivative term to become very large.Chapter 8Chapter 8This sudden change is undesirable and can be avoided by basing the derivative action on the measurement, ym, rather than on the error signal, e.Replacing de/dt by –dym/dt givesFrom a parallel form of PID control in Eq. 8-13
25 Chapter 8 Reverse or Direct Action Chapter 8 The controller gain can be made either negative or positive.Chapter 8Chapter 8Direct (Kc < 0)Reverse (Kc > 0)Controller output p(t) increases as the input signal ym(t) increasesController output p(t) increases as its input signal ym(t) decreases
27 On-Off Controllers Chapter 8 Chapter 8 Synonyms: “two-position” or “bang-bang” controllers.ym(t)↓ym(t)↑Chapter 8Chapter 8eg: thermostat in home heating system.-if the temperature is too high, the thermostat turns the heater OFF. -If the temperature is too low, the thermostat turns the heater ON.Controller output has two possible values.
28 On-Off Controllers (continued) Common use:residential heatingdomestic refrigeratorsAdvantagesSimpleCheapDisadvantagescontinual cycling of controlled variableproduce excessive wear on control valve.Chapter 8Chapter 8
29 Chapter 8 Chapter 8 Typical Response of Feedback Control Systems Consider response of a controlled system after asustained disturbance occurs (e.g., step change inthe disturbance variable)No control: the process slowly reaches a new steady stateP – speed up the process response & reduces the offsetPI – eliminate offset & the response more oscillatoryPID – reduces degree of oscillation and the response timeChapter 8Chapter 8Figure Typical process responses with feedback control.
30 Chapter 8Chapter 8Figure Proportional control: effect of controller gain.Increasing Kc tends to make the process response less sluggish (faster)Too large of Kc, results in undesirable degree of oscillation or even become unstableIntermediate value of Kc usually results in the best control.
31 Chapter 8Chapter 8Figure PI control: (a) effect of reset time (b) effect of controller gain.Increasing τI tends to make the process response more sluggish (slower)Too large of τI, the controlled variable will return to the set point very slowly after a disturbance set-point change occurs.
32 Chapter 8Chapter 8Figure PID control: effect of derivative time.Increasing τD tends to improve the process response by reducing the maximum deviation, response time and degree of oscillation.Too large of τD: measurement noise is amplified and process response more oscillatory.The intermediate value of τD is desirable.