What Is pld- Tutorial Overview PID stands for Proportional, Integral, Derivative Controllers are designed to eliminate the need for continuous operator attention. Cruise control in a car and a house thermostat are common examples of how controllers are used automatically adjust some variable to hold the measurement(or process variable)at the set-point. The set-point is where you would like the measurement to be. Error is defined as the difference between set-point and measurement (error)=(set-point)-(measurement) The variable being adjusted is called the manipulated variable which usually is equal to the output of the controller. The output of PID controllers will change in response to a change in measurement or set-point. Manufacturers of PId controllers use different names to identify the three odes. These equations show the relationships P Proportional Band=100/gain Integral=1/reset (units of time) Derivative =rate= pre-act (units of time) Depending on the manufacturer, integral or reset action is set in either time/repeat or repeat/time. One is just the reciprocal of the other. Note that manufacturers are not consistent and often use reset in units of time/repeat or integral in units of repeats/time. Derivative and rate are the same Proportional Band With proportional band, the controller output is proportional to the error or a change in measurement( depending on the controller) (controller output)=(error)*100/ (proportional band) With a proportional controller offset( deviation from set-point) is present Increasing the controller gain will make the loop go unstable Integral action was s Load Step Time Re Eile X-Axis Range Y-Axis Range AE=19232 ssE=790695 P only- notice the offset 6424462 Time(sec)
What Is PID - Tutorial Overview PID stands for Proportional, Integral, Derivative. Controllers are designed to eliminate the need for continuous operator attention. Cruise control in a car and a house thermostat are common examples of how controllers are used to automatically adjust some variable to hold the measurement (or process variable) at the set-point. The set-point is where you would like the measurement to be. Error is defined as the difference between set-point and measurement. (error) = (set-point) - (measurement) The variable being adjusted is called the manipulated variable which usually is equal to the output of the controller. The output of PID controllers will change in response to a change in measurement or set-point. Manufacturers of PID controllers use different names to identify the three modes. These equations show the relationships: P Proportional Band = 100/gain I Integral = 1/reset (units of time) D Derivative = rate = pre-act (units of time) Depending on the manufacturer, integral or reset action is set in either time/repeat or repeat/time. One is just the reciprocal of the other. Note that manufacturers are not consistent and often use reset in units of time/repeat or integral in units of repeats/time. Derivative and rate are the same. Proportional Band With proportional band, the controller output is proportional to the error or a change in measurement (depending on the controller). (controller output) = (error)*100/(proportional band) With a proportional controller offset (deviation from set-point) is present. Increasing the controller gain will make the loop go unstable. Integral action was
included in controllers to eliminate this offset Integral With integral action, the controller output is proportional to the amount of time the error is present. Integral action eliminates offset CONTROLLER OUTPUT=(1/INTEGRAL)(Integral ofe(t)d(t) Notice that the offset( deviation from set-point)in the time response plots is now gone. Integral action has eliminated the offset. The response is somewhat scillatory and can be stabilized some by adding derivative action. Graphic courtesy of Exper Tune Loop Simulator. Integral action gives the controller a large gain at low frequencies that results in eliminating offset and"beating down"load disturbances. The controller phase starts out at-90 degrees and increases to near 0 degrees at the break frequency. This additional phase lag is what you give up by adding integral action. Derivative action ldds phase lead and is used to compensate for the lag introduced by integral action Derivative With derivative action, the controller output is proportional to the rate of change of the measurement or error. The controller output is calculated by the rate of change of the measurement with time CONTROLLER OUTPUT= DERIVATIVE Where m is the measurement at time t Some manufacturers use the term rate or pre-act instead of derivative. Derivative rate and pre-act are the same thing DERIVATIVE= RATE= PRE ACT Derivative action can compensate for a changing measurement. Thus derivative takes action to inhibit more rapid changes of the measurement than proportional action. When a load or set-point change occurs, the derivative action causes the controller gain to move the"wrong"way when the measurement gets near the set-point. Derivative is often used to avoid overshoot Derivative action can stabilize loops since it adds phase lead. Generally, if you use derivative action, more controller gain and reset can be used
included in controllers to eliminate this offset. Integral With integral action, the controller output is proportional to the amount of time the error is present. Integral action eliminates offset. CONTROLLER OUTPUT = (1/INTEGRAL) (Integral of) e(t) d(t) Notice that the offset (deviation from set-point) in the time response plots is now gone. Integral action has eliminated the offset. The response is somewhat oscillatory and can be stabilized some by adding derivative action. (Graphic courtesy of ExperTune Loop Simulator.) Integral action gives the controller a large gain at low frequencies that results in eliminating offset and "beating down" load disturbances. The controller phase starts out at -90 degrees and increases to near 0 degrees at the break frequency. This additional phase lag is what you give up by adding integral action. Derivative action adds phase lead and is used to compensate for the lag introduced by integral action. Derivative With derivative action, the controller output is proportional to the rate of change of the measurement or error. The controller output is calculated by the rate of change of the measurement with time. dm CONTROLLER OUTPUT = DERIVATIVE ---- dt Where m is the measurement at time t. Some manufacturers use the term rate or pre-act instead of derivative. Derivative, rate and pre-act are the same thing. DERIVATIVE = RATE = PRE ACT Derivative action can compensate for a changing measurement. Thus derivative takes action to inhibit more rapid changes of the measurement than proportional action. When a load or set-point change occurs, the derivative action causes the controller gain to move the "wrong" way when the measurement gets near the set-point. Derivative is often used to avoid overshoot. Derivative action can stabilize loops since it adds phase lead. Generally, if you use derivative action, more controller gain and reset can be used
With a PId controller the amplitude ratio now has a dip near the center of the frequency response. Integral action gives the controller high gain at low frequencies, and derivative action causes the gain to start rising after the"dip".At highe frequencies the filter on derivative action limits the derivative action. At very high frequencies(above 314 radians/time; the Nyquist frequency)the controller phase and amplitude ratio increase and decrease quite a bit because of discrete sampling If the controller had no filter the controller amplitude ratio would steadily increase at high frequencies up to the Nyquist frequency (1/2 the sampling frequency ) The ontroller phase now has a hump due to the der Graphic courtesy of Ex The time response is less oscillatory than with the PI controller. Derivative action has helped stabilize the loop Control Loop Tuning It is important to keep in mind that understanding the process is fundamental to getting a well designed control loop. Sensors must be in appropriate locations and valves must be sized correctly with appropriate trim In general, for the tightest loop control, the dynamic controller gain should be as high as possible without causing the loop to be unstable PID Optimization Articles This picture(from the Loop Simulator )shows the effects of a PI controller with too much or too little P or I action. The process is typical with a dead time of 4 and lag time of 10. Optimal is red You can use the picture to recognize the shape of an optimally tuned loop. Also see the response shape of loops with I or P too high or low. To get your process response to compare, put the controller in manual change the output 5 or 10%, then put the controller back in auto P is in units of proportional band. I is in units of time/repeat. So increasing P or I decreases their action in the picture
With a PID controller the amplitude ratio now has a dip near the center of the frequency response. Integral action gives the controller high gain at low frequencies, and derivative action causes the gain to start rising after the "dip". At higher frequencies the filter on derivative action limits the derivative action. At very high frequencies (above 314 radians/time; the Nyquist frequency) the controller phase and amplitude ratio increase and decrease quite a bit because of discrete sampling. If the controller had no filter the controller amplitude ratio would steadily increase at high frequencies up to the Nyquist frequency (1/2 the sampling frequency). The controller phase now has a hump due to the derivative lead action and filtering. (Graphic courtesy of ExperTune Loop Simulator.) The time response is less oscillatory than with the PI controller. Derivative action has helped stabilize the loop. Control Loop Tuning It is important to keep in mind that understanding the process is fundamental to getting a well designed control loop. Sensors must be in appropriate locations and valves must be sized correctly with appropriate trim. In general, for the tightest loop control, the dynamic controller gain should be as high as possible without causing the loop to be unstable. PID Optimization Articles Fine Tuning "Rules" This picture (from the Loop Simulator) shows the effects of a PI controller with too much or too little P or I action. The process is typical with a dead time of 4 and lag time of 10. Optimal is red. You can use the picture to recognize the shape of an optimally tuned loop. Also see the response shape of loops with I or P too high or low. To get your process response to compare, put the controller in manual change the output 5 or 10%, then put the controller back in auto. P is in units of proportional band. I is in units of time/repeat. So increasing P or I, decreases their action in the picture
too higP too luw too haot-ltoul ler lype [D0 View this as a full page PID Optimization Articles Starting PID Settings For Common Control Loops Initial Settings For Common Control Loops For Some ldeal and Series Controllers oop Type Valve type min/re 50to500005to0520to200no Linear or Modified Percentage Liquid Pressure 50 to 500 005 to 05 20 to 200 none Linear or Modified Percentage 01 to 05 Linear or Modified Percentage emperature 2t0TUU 02 5 1 to 20 Equal Percentage These settings are rough, assume proper control loop design, ideal or senes algorithm and do not apply to all controllers Use Expertune PID Tuner to find the proper PID settings for your process and controller Comparison of PID Control Algorithms (All Controllers Are Not Created equa Modified from an article published in Control Engineering March, 1987. This article updated and re-written for the Web One fine day, a plant engineer, replaced his controllers. Even though he used the same settings on the new controllers, the retrofitted loops went out of control in automatic. He tried to tune these controllers the same way he had tuned the old ones. The loops seemed to get more unstable This mysterious and very real situation is the result of two manuyfacturer's using different PID algorithms. Read on to solve this and other common mysteries abor PId controllers
View this as a full page | PID Optimization Articles Starting PID Settings For Common Control Loops Comparison of PID Control Algorithms (All Controllers Are Not Created Equal) Modified from an article published in Control Engineering March, 1987. This article updated and re-written for the Web. One fine day, a plant engineer, replaced his controllers. Even though he used the same settings on the new controllers, the retrofitted loops went out of control in automatic. He tried to tune these controllers the same way he had tuned the old ones. The loops seemed to get more unstable. This mysterious and very real situation is the result of two manufacturer's using dif erent PID algorithms. Read on to solve this and other common mysteries about PID controllers
In practice, manufacturers of controllers don' t adhere to any industry wide standards for Pid algorithms. Different manufacturers and vendors use different Pld algorithms and sometimes have several algorithms available within their own duct lines The figures and graphs used in this article were produced using the Exper Tune Loop Simulator For PID loop tuning, analysis and simulation contact Exper Tune The name game Just as there are no adhered to industry standards for PId controllers, nomenclature and action for similar modes varies P Pre ntegral =1/reset Derivative =rate= pre-act Some manufacturers call Proportional Band the Proportional Gain. Manufacturers interchange names and units for integral or reset action. In this article integral action is defined in time/repeat and reset in repeat/time. One is the reciprocal of the other. The action of either reset or integral can be reversed depending on the manufacturers units The Algorithms There are three major classifications of PId algorithms that most manufacturer's algorithms fit under. These three are: series, ideal, and parallel. Again, manufacturers vary on the their names for these categories. The only way to really tell which one you have is to look at the equation for the controller. In simple form 1 d e(t Ideal algorithm OUTPUT Kc e(t)+ (t)dt>+ D Parallel OUTPUT =Kp Le<t)] (td(t)+ D OUTPUT= Kc e(t)+--le(t>d(t>1+D Kc, Kp are gain; I, Ip are integral and D, Dp are derivative settings. The series controller's strange looking form makes it act like an electronic controller. A three term controller can be made with only one pneumatic(or electronic)amplifier using the series form. Thus, pneumatic controllers and early electronic controllers often used the series form to save on amplifiers which were expensive at the time. Some
In practice, manufacturers of controllers don't adhere to any industry wide standards for PID algorithms. Different manufacturers and vendors use different PID algorithms and sometimes have several algorithms available within their own product lines. The figures and graphs used in this article were produced using the ExperTune Loop Simulator. For PID loop tuning, analysis and simulation contact ExperTune. The Name Game Just as there are no adhered to industry standards for PID controllers, nomenclature and action for similar modes varies. P Proportional Band = 100/gain I Integral = 1/reset D Derivative = rate = pre-act Some manufacturers call Proportional Band the Proportional Gain. Manufacturers interchange names and units for integral or reset action. In this article, integral action is defined in time/repeat and reset in repeat/time. One is the reciprocal of the other. The action of either reset or integral can be reversed depending on the manufacturers units. The Algorithms There are three major classifications of PID algorithms that most manufacturer's algorithms fit under. These three are: series, ideal, and parallel. Again, manufacturers vary on the their names for these categories. The only way to really tell which one you have is to look at the equation for the controller. In simple form these are: Kc, Kp are gain; I, Ip are integral and D, Dp are derivative settings. The series controller's strange looking form makes it act like an electronic controller. A three term controller can be made with only one pneumatic (or electronic) amplifier using the series form. Thus, pneumatic controllers and early electronic controllers often used the series form to save on amplifiers which were expensive at the time. Some