![COMPOSITE CONTROL MODES – P+I
• Proportional-Integral Control (PI)
• The main advantage of this composite control mode is that the one-to-one
correspondence of the proportional mode is available and the integral mode eliminates
the inherent offset.
Characteristics of the PI mode
• When the error is zero, the controller output 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 contributes a correction, and the integral
term begins to increase or decrease the accumulated value [initially, PI(0)], depending on
the sign of the error and the direct or reverse action.](https://image.slidesharecdn.com/3-230817180119-5a80fff8/85/3-CONTROL-ACTIONS-pptx-33-320.jpg)
3.CONTROL ACTIONS.pptx
- 1. CONTROL ACTIONS Unit -3 Process Control
- 2. INTRODUCTION • The nature of controller action for systems with operations and variables that range over continuous values. • The controller inputs the result of a measurement of the controlled variable and determines an appropriate output to the final control element. • The controller is some form of computer—either analog or digital, pneumatic or electronic—that, using input measurements, solves certain equations to calculate the proper output.
- 3. PROCESS CHARACTERISTICS • Process Equation – The equation which describes the process is called process equation • Process Load - From the process equation, it is possible to identify a set of values for the process parameters that results in the controlled variable having the set point value. This set of parameters is called the nominal set. The term process load refers to this set of all parameters, excluding the controlled variable. • Process Lag - At some point in time, a process-load change or transient causes a change in the controlled variable. The process-control loop responds to ensure that, some finite time later, the variable returns to the set point value. Part of this time is consumed by the process itself and is called the process lag. • Self-Regulation - Some processes has the tendency to adopt a specific value of • the controlled variable for nominal load with no control operations. That is called Self-Regulation
- 4. CONTROL OF TEMPERATURE BY PROCESS CONTROL This process could be described by a process equation where liquid temperature is a function as
- 5. CONTROL SYSTEM PARAMETERS Error Error in %
- 6. CONTROLER OUTPUT IN %
- 7. EXAMPLE PROBLEM -1 The temperature in a certain process has a range of 300 to 440 K and a set point of 384 K. Find the percent of span error when the temperature is 379 K.
- 8. CONTROL SYSTEM PARAMETERS • Control lag refers to the time for the process-control loop to make necessary adjustments to the final control element. • Dead time - This is the elapsed time between the instant a deviation (error) occurs and when the corrective action first occurs. • Cycling – This means the variable is cycling above and below the setpoint value. • Controller (Direct action) – A controller operates with direct action when an increasing value of the controlled variable causes an increasing value of the controller output. Ex: A level-control system that outputs a signal to an output valve. Clearly, if the level rises (increases), the valve should be opened. • Reverse action is the opposite case, where an increase in a controlled variable causes a decrease in controller output. An example of this would be a simple temperature control from a heater. If the temperature increases, the drive to the heater should be decreased.
- 9. CONTROLLER MODES • DISCONTINUOUS CONTROLLER MODES These controller modes shows discontinuous changes in controller output as controlled variable error occurs. • CONTINUOUS CONTROLLER MODES The most common controller action used in process control is one or a combination of continuous controller modes. In these modes, the output of the controller changes smoothly in response to the error or rate of change of error.
- 10. DISCONTINUOUS CONTROLLER MODES Classified into: • Two-Position Mode • Multi-position Mode • Floating-Control Mode (Single speed and Multi speed)
- 11. TWO-POSITION MODE The range 2 ∆ep which is referred to as the neutral zone or differential gap, where there will be NO CONTROL ACTION.
- 12. EXAMPLE PROBLEM - 2 A liquid-level control system linearly converts a displacement of 2 to 3 m into a 4- to 20-mA control signal. A relay serves as the two-position controller to open or close an inlet valve. The relay closes at 12 mA and opens at 10 mA. Find: (a) the relation between displacement level and current, and (b) the neutral zone or displacement gap in meters.
- 13. TWO-POSITION MODE - APPLICATIONS • The two-position control mode is best adapted to large-scale systems with relatively slow process rates. • In the example of either a room heating or air- conditioning system, the capacity of the system is very large in terms of air volume, and the overall effect of the heater or cooler is relatively slow. Sudden, large-scale changes are not common to such systems. • Other examples of two position control applications are liquid bath-temperature control and level control in large-volume tanks.
- 14. MULTIPOSITION MODE Three-position controller action.
- 15. RELATIONSHIP BETWEEN ERROR AND THREE-POSITION CONTROLLER ACTION, INCLUDING THE EFFECTS OF LAG.
- 16. FLOATING-CONTROL MODE • Single Speed In the single-speed floating-control mode, the output of the control element changes at a fixed rate when the error exceeds the neutral zone. An equation for this action is If the above equation is integrated for the actual controller output, we get
- 17. SINGLE SPEED FLOATING CONTROL single-speed controller action as the output rate of change to input error, An example of error and controller response.
- 18. SINGLE SPEED FLOATING CONTROL - APPLICATIONS • Primary applications of the floating-control mode are for the single- speed controllers with a neutral zone. This mode has an inherent cycle nature much like the two-position, although this cycling can be minimized, depending on the application. • Generally, the method is well suited to self-regulation processes with very small lag or dead time, which implies small-capacity processes. Single-speed floating-control action applied to a flow-control system. The rate of controller output change has a strong effect on error recovery in a floating controller.
- 19. EXAMPLE PROBLEM - 3 A process error lies within the neutral zone with P=25%. At t=0, the error falls below the neutral zone. If K=+2% per second, find the time when the output saturates.
- 20. CONTINUOUS CONTROLLER MODES In these modes, the output of the controller changes smoothly in response to the error or rate of change of error. • Proportional Control Mode (P) • Integral-Control Mode (I) • Derivative-Control Mode (D) COMPOSITE CONTROL MODES • Proportional-Integral Control (PI) • Proportional-Derivative Control Mode (PD) • Three-Mode Controller (PID)
- 21. PROPORTIONAL CONTROL MODE • Proportional mode is the extension of the discontinuous types, where a smooth, linear relationship exists between the controller output and the error. • Thus, over some range of errors about the setpoint, each value of error has a unique value of controller output in one-to-one correspondence. • The range of error to cover the 0% to 100% controller output is called the proportional band, because the one-to-one correspondence exists only for errors in this range. P = KPep + P0 Where, KP = proportional gain between error and controller output (% per %) P0 = controller output with no error (%)
- 22. • The proportional band is defined by the equation • Direct/reverse action This specifies whether the controller output should increase (direct) or decrease (reverse) for an increasing controlled variable. The action is specified by the sign of the proportional gain; KP<0 is direct, and KP > 0 is reverse. The characteristics of the Proportional mode: • If the error is zero, the output is a constant equal to PO • If there is error, for every 1% of error, a correction of KP percent is added to or subtracted from PO, depending on the sign of the error. • There is a band of error about zero of magnitude PB within which the output is not saturated at 0% or 100%.
- 23. P-MODE - OFFSET ERROR Offset: An important characteristic of the proportional control mode is that it produces a permanent residual error in the operating point of the controlled variable when a change in load occurs. This error is referred to as offset. It can be minimized by a larger constant, which also reduces the proportional band.
- 24. EXAMPLE PROBLEM - 4 Consider the proportional-mode level-control system shown in fig. Value A is linear, with a flow scale factor of 10 m3 / h per percent controller output. The controller output is nominally 50% with a constant of KP = 10% per %. A load change occurs when flow through valve B changes from 500 m3 / h to 600 m3 / h Calculate the new controller output and offset error.
- 25. APPLICATIONS OF P-MODE • The offset limits use of the proportional mode to only a few cases. • Used in processes where large load changes are unlikely or with moderate to small process lag times.
- 26. INTEGRAL-CONTROL MODE • The offset error of the proportional mode occurs because the controller cannot adapt to changing external conditions—that is, changing loads. • The integral mode eliminates this problem by allowing the controller to adapt to changing external conditions by changing the zero-error output. • Integral action is provided by summing the error over time, multiplying that sum by a gain, and adding the result to the present controller output. OR where p(0) is the controller output when the integral action starts. The gain expresses how much controller output in percent is needed for every percent-time accumulation of error.
- 27. INTEGRAL MODE CONTROLLER ACTION The rate of output change depends on error. Illustration of integral mode output and error. • The controller output begins to ramp up at a rate determined by the gain. • At gain K1, the output finally saturates at 100% and no further action can occur.
- 28. CHARACTERISTICS OF THE INTEGRAL MODE • If the error is zero, the output stays fixed at a value equal to what it was when the error went to zero. • If the error is not zero, the output will begin to increase or decrease at a rate of KI percent/second for every 1% of error. • The integral gain, KI is often represented by the inverse, which is called the integral time, or the reset action, TI = 1/KI
- 29. EXAMPLE PROBLEM - 5 An integral controller is used for speed control with a setpoint of 12 rpm within a range of 10 to 15 rpm. The controller output is 22% initially. The constant KI = -0.15% controller output per second per percentage error. If the speed jumps to 13.5 rpm, calculate the controller output after 2 s for a constant ep.
- 30. INTEGRAL WINDUP / RESET WINDUP • Often, when the error cannot be eliminated quickly, and give enough time this mode produces larger and larger values for integral term, which turn keeps increasing the control action until it is saturated. • This condition called integral windup. • This occurs during changeover operations and shutdowns etc.
- 31. DERIVATIVE-CONTROL MODE • Derivation controller action responds to the rate at which the error is changing— that is, the derivative of the error. • The equation for this mode is given by the expression • Derivative action is not used alone because it provides no output when the error is constant. • Derivative controller action is also called rate action and anticipatory control.
- 32. DERIVATIVE MODE CONTROLLER ACTION Derivative mode controller action changes depending on the rate of error. Characteristics of the derivative mode • If the error is zero, the mode provides no output. • If the error is constant in time, the mode provides no output. • 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.
- 33. COMPOSITE CONTROL MODES – P+I • Proportional-Integral Control (PI) • The main advantage of this composite control mode is that the one-to-one correspondence of the proportional mode is available and the integral mode eliminates the inherent offset. Characteristics of the PI mode • When the error is zero, the controller output 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 contributes a correction, and the integral term begins to increase or decrease the accumulated value [initially, PI(0)], depending on the sign of the error and the direct or reverse action.
- 34. PROPORTIONAL-INTEGRAL (PI) ACTION Application It can be used in systems with frequent or large load changes.
- 35. APPLICATION, MERITS & DEMERITS OF PI APPLICATION • PI mode can be used in systems with frequent or large load changes. • The process must have relatively slow changes in load to prevent oscillations induced by the integral overshoot. Advantage: • One-one correspondence of the proportional mode is available and the integral mode eliminates the offset. Disadvantage: • During startup of a batch process, the integral action causes a considerable overshoot of the error and output before settling to a operation point.
- 36. COMPOSITE CONTROL MODES – P+D • A second combination of control modes has many industrial applications. It involves the serial (cascaded) use of the proportional and derivative modes. • Proportional-Derivative Control Mode (PD) • It cannot eliminate the offset of proportional controllers. • It handles fast process load changes.
- 37. PROPORTIONAL-DERIVATIVE (PD) ACTION Proportional-derivative (PD) action showing the offset error from the proportional mode. This is for reverse action.
- 38. THREE-MODE CONTROLLER (PID) • One of the most powerful but complex controller mode operations combines the proportional, integral, and derivative modes. • This mode eliminates the offset of the proportional mode and still provides fast response.
- 39. EXAMPLE PROBLEM 6 For the given the error of figure, plot a graph of a proportional-integral controller output as a function of time. KP = 5, KI = 1.0S-1, and PI(0) = 20%.
- 40. EXAMPLE PROBLEM 7 Suppose the error, in the figure is applied to a proportional- derivative controller with KP=5, KD = 0.5 s, and P0 = 20%. Draw a graph of the resulting controller output.
- 41. EXAMPLE PROBLEM 8 (assignment)
- 42. PRACTICAL FORMS OF PID Direct implementation of a three-mode (PID) controller with op amps.
- 43. PRACTICAL FORMS OF PID - contd Pneumatic three-mode (PID) controller
- 44. PID IMPLEMENTATION ISSUES • Bumpless Transfer • Auto/Manual mode transfer • Anti-reset wind up
- 45. Bumpless Transfer - Auto/Manual mode transfer • Bumpless transfer is either a manual or automatic transfer procedure used when switching a PID controller from auto to manual or vice versa. • Its aim is to keep the controllers output the same when switching auto/manual, that is if the controller is at 50% output in auto it should retain that 50% output as you switch it to manual. • If you switch from manual to auto the same should apply. • Most modern PID controllers have bumpless transfer built in, including PLC ,DCS and PID controllers.
- 46. INTEGRAL (RESET) WINDUP • A valve cannot open more than all the way. A pump cannot go slower than stopped. Yet an improperly programmed control algorithm can issue such commands. The integral sum starts accumulating when the controller is first put in automatic and continues to change as long as controller error exists. This large integral, when combined with the other terms in the equation, can produce a CO value that causes the final control element (FCE) to saturate. That is, the CO drives the FCE (e.g. valve, pump, compressor) to its physical limit of fully open/on/maximum or fully closed/off/minimum.
- 47. DUE TO INTEGRAL WINDUP – CONTROL LOST • If the integral term grows unchecked, the equation above can command the valve, pump or compressor to move to 110%, then 120% and more. Clearly, however, when an FCE reaches its full 100% value, these last commands have no physical meaning and consequently, no impact on the process. • Once we cross over to a “no physical meaning” computation, the controller has lost the ability to regulate the process. • When the computed CO exceeds the physical capabilities of the FCE because the integral term has reached a large positive or negative value, the controller is suffering from windup. Because windup is associated with the integral term, it is often referred to as integral windup or reset windup.
- 48. VISUALIZING WINDUP The sustained error permits the controller to windup (saturate). While it is not obvious from the plot, the PI algorithm is computing values for CO that ask the valve to be open –5%, –8% and more. The control algorithm is just simple math with no ability to recognize that a valve cannot be open to a negative value.
- 49. ANTI RESET WIND-UP Several anti-windup techniques exist two common ones are 1)back-calculation and 2) clamping.
- 51. Thank You