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 Led(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
manufacturers use the series form in their digital algorithms to keep tuning similar to electronic and pneumatic controllers Differences in Proportional Band Or Gain If you use only proportional action, the main difference between series and ideal algorithms is that some manufacturers use proportional band while others use gain On a controller using the gain setting, increasing this setting makes the loop more sensitive and less stable. While decreasing proportional band on controllers using it will have the same effect Some manufacturers allow more flexibility with P action by letting you choose whether gain(proportional)action works on set point changes. For example, Honeywell TDC has two types of algorithms that work differently on set point changes. With their type A algorithm, gain action acts on set point changes and with their type C it does not. For load upsets, type a and C act the same, but for set point changes the difference is dramatic Exper Tune Loop Simulator Windows compare responses of Honeywell TDC type A(proportional action on error)and C(proportional action on PV only) controllers on a simulated temperature loop. Bottom graph shows either type controller response to a step load change. Top plot red is response of Type A, top plot green of Type C. With the type C algorithm, damping and overshoot to step set point changes are similar to damping and overshoot on step load disturbances. Type C may be desirable over type A, since tuning for load or set point changes is similar with type C. Because of the sensitive set point response, you may want to use type A for the inner loop or slave in a cascade. Type C with smooth set point response may be better for the outer or master loop Bailey's"error input"and"PV and SP"algorithms are analogous to Honeywell's type A and C. Bailey's"error input"has sensitive set point response while Baileys "PV and SP" has smooth set point responses the load responses are the same for the different Bailey and Honeywell algorithm they have the same stability. For a fast analysis of the stabilities, Exper Tune allows a comparison of the robustness plots of the algorithms Differences In integral action Once you convert integral and reset values to the same units, PI controllers respond mostly the same for load disturbances. The proportional action may be different described above. Anti-reset windup is usually done differently, but the effect of
manufacturers use the series form in their digital algorithms to keep tuning similar to electronic and pneumatic controllers. Differences in Proportional Band Or Gain If you use only proportional action, the main difference between series and ideal algorithms is that some manufacturers use proportional band while others use gain. On a controller using the gain setting, increasing this setting makes the loop more sensitive and less stable. While decreasing proportional band on controllers using it will have the same effect. Some manufacturers allow more flexibility with P action by letting you choose whether gain (proportional) action works on set point changes. For example, Honeywell TDC has two types of algorithms that work differently on set point changes. With their type A algorithm, gain action acts on set point changes and with their type C it does not. For load upsets, type A and C act the same, but for set point changes, the difference is dramatic. ExperTune Loop Simulator Windows compare responses of Honeywell TDC type A (proportional action on error) and C (proportional action on PV only) controllers on a simulated temperature loop. Bottom graph shows either type controller response to a step load change. Top plot red is response of Type A, top plot green of Type C. With the type C algorithm, damping and overshoot to step set point changes are similar to damping and overshoot on step load disturbances. Type C may be desirable over type A, since tuning for load or set point changes is similar with type C. Because of the sensitive set point response, you may want to use type A for the inner loop or slave in a cascade. Type C with smooth set point response may be better for the outer or master loop. Bailey's "error input" and "PV and SP" algorithms are analogous to Honeywell's type A and C. Bailey's "error input" has sensitive set point response while Bailey's "PV and SP" has smooth set point responses. Like Honeywell's, the two Bailey algorithms give identical load responses. Because the load responses are the same for the different Bailey and Honeywell algorithms, they have the same stability. For a fast analysis of the stabilities, ExperTune allows a comparison of the robustness plots of the algorithms. Differences In Integral Action Once you convert integral and reset values to the same units, PI controllers respond mostly the same for load disturbances. The proportional action may be different as described above. Anti-reset windup is usually done differently, but the effect of
these differences is usually minor compared to other differences between Differences in derivative action The largest variation among controllers from different manufacturers is the way they handle derivative action. Virtually no two are the same. This is part of the reason why many people don' t use derivative action. The differences are caused from different methods of filtering or not filtering at all. whether the derivative works on set point changes or not, and how derivative interacts or does not interact with the integral action On controllers, when you set derivative to something besides zero, you get derivative action. In a series controller, when you use both integral and derivative actions the integral and derivative modes interact. Interaction causes the effective controller action to be different from what it would be in a ideal controller The effective proportional band is PB(effective)=PB/(1+D/) The effective integral time is (effective)=I+D The effective derivative time is D(effective)=1/(1/+1/D) Where PB, I and d are the proportional band, integral and derivative values you set or entered into the series controller. The effective values are equivalent ideal controller settings These equations show that for the series controller you cannot make the effective derivative time greater than 1/4 the effective integral time. The largest effective derivative occurs when D=l. When D is set larger than I. the effective integral time is adjusted more with D and the effective derivative is adjusted more with I Therefore it is usually good control practice to keep the values of d less than I for a series controller For example: Foxboro and Fisher use a series algorithm, AEG Modicon, Texas Instruments controllers use the ideal type. Honeywell has both series and ideal algorithms. Bailey, Allen Bradley, and ge have both ideal and parallel algorith
these differences is usually minor compared to other differences between algorithms. Differences In Derivative Action The largest variation among controllers from different manufacturers is the way they handle derivative action. Virtually no two are the same. This is part of the reason why many people don't use derivative action. The differences are caused from different methods of filtering or not filtering at all, whether the derivative works on set point changes or not, and how derivative interacts or does not interact with the integral action. On controllers, when you set derivative to something besides zero, you get derivative action. In a series controller, when you use both integral and derivative actions, the integral and derivative modes interact. Interaction causes the effective controller action to be different from what it would be in a ideal controller. The effective proportional band is: PB (effective) = PB/(1 + D/I) The effective integral time is: I (effective) = I + D The effective derivative time is: D (effective) = 1 / (1/I + 1/D) Where PB, I and D are the proportional band, integral and derivative values you set or entered into the series controller. The effective values are equivalent ideal controller settings. These equations show that for the series controller you cannot make the effective derivative time greater than 1/4 the effective integral time. The largest effective derivative occurs when D=I. When D is set larger than I, the effective integral time is adjusted more with D and the effective derivative is adjusted more with I! Therefore it is usually good control practice to keep the values of D less than I for a series controller. For example: Foxboro and Fisher use a series algorithm. AEG Modicon, Texas Instruments controllers use the ideal type. Honeywell has both series and ideal algorithms. Bailey, Allen Bradley, and GE have both ideal and parallel algorithms
Other Differences in Derivative Besides the interaction differences described above. derivative action among the series and ideal groups varies With most controllers, derivative works only on measurement On some controllers however, derivative action works on set point changes. Although response to a load disturbance will be the same, set point response on these controllers can get out of hand Since most controllers are used for regulating disturbances derivative action working on set point changes is usually not a problem except in cascade loops or ones where the set point is being manipulated Of more significance is whether and how filtering is done when you dial in derivative The unlimited derivative problem Some manufacturers do not filter or limit derivative action. Thus, at high frequencies, the amplitude ratio gets large. In the Figure the red line shows the amplitude ratio of unlimited derivative action The Figure shows the same Pv noise added to a PId controller with(green) and without(red)PV filtering. PV filtering limits the derivative gain nlimited derivative action does not help good loop control but does amplify measurement noise in the controller output. The result of unlimited derivative is a jumpy or nervous and noisy controller output. The lower graph in the Figure-red line is the time response of a controller to measurement noise. This can wear out alves, or drive a slave loops set point crazy. Worse yet, the noise can drive the controller into saturation which causes the anti-reset code to take over No wonder derivative is seldom used Filtering Limits derivative noise On the controllers that use filtering with derivative, usually the measurement signal gets the filtering. The time constant of filtering is usually calculated by these algorithms based on the derivative value dialed in. The amount of filtering changes with the amount of derivative. This has the effect of limiting derivative action at high frequencies In Figure the green line shows the amplitude ratio and controller output using limited derivative action Control loop performance is the same on both since unlimited derivative does not improve control loop performance. Parallel Controllers
Other Differences in Derivative Besides the interaction differences described above, derivative action among the series and ideal groups varies. With most controllers, derivative works only on measurement. On some controllers however, derivative action works on set point changes. Although response to a load disturbance will be the same, set point response on these controllers can get out of hand. Since most controllers are used for regulating disturbances, derivative action working on set point changes is usually not a problem except in cascade loops or ones where the set point is being manipulated. Of more significance is whether and how filtering is done when you dial in derivative. The Unlimited Derivative Problem Some manufacturers do not filter or limit derivative action. Thus, at high frequencies, the amplitude ratio gets large. In the Figure the red line shows the amplitude ratio of unlimited derivative action. The Figure shows the same PV noise added to a PID controller with (green) and without (red) PV filtering. PV filtering limits the derivative gain. Unlimited derivative action does not help good loop control but does amplify measurement noise in the controller output. The result of unlimited derivative is a "jumpy" or nervous and noisy controller output. The lower graph in the Figure - red line is the time response of a controller to measurement noise. This can wear out valves, or drive a slave loops set point crazy. Worse yet, the noise can drive the controller into saturation which causes the anti-reset code to take over. No wonder derivative is seldom used! Filtering Limits Derivative Noise On the controllers that use filtering with derivative, usually the measurement signal gets the filtering. The time constant of filtering is usually calculated by these algorithms based on the derivative value dialed in. The amount of filtering changes with the amount of derivative. This has the effect of limiting derivative action at high frequencies. In Figure the green line shows the amplitude ratio and controller output using limited derivative action. Control loop performance is the same on both since unlimited derivative does not improve control loop performance. Parallel Controllers
With parallel controllers, controller gain is not multiplied by the error signal only Integral and derivative actions are"independent"of the controller gain At first it might seem that the parallel controller is easier to work with because of this"independence". But, parallel algorithms require very different integral and derivative tuning parameters than other controllers. These equations show how to convert from parallel to ideal settings I= lp Kp(units of time/repeat) D= Dp/Kp(units of time There is more of a difference between parallel versus ideal controller tuning than series versus ideal tuning. The intuitive feel for tuning a parallel controller is very different from the others. The Figure below shows load response in a level loop The yellow curve is for a tuned (ideal or parallel) controller. Normally it would seem that lowering the controller gain will make the loop more stable as in fact it does with the ideal controller in the Figure. However, the parallel controller gets less stable with lower gain!. Like all controllers, it also gets less stable with more gain. So either increasing or decreasing the gain on a parallel controller can drive the loop unstable! The controllers in the Figure are PI controllers. The situation is more pronounced when you use derivative. With the parallel controller, the effective integral and derivative values change with the gain setting. So, lowering the controller gain also lowers the effective I increasing controller phase. Lowering gain also increases the effective D, moving the derivative phase to higher frequencies; eliminating its stabilizing effect controller integral action. The overall effect is unstabilizing as the Figure shows For example: Bailey and Allen Bradley both have a parallel algorithm available that hey describe as a"non-interacting"algorithm. They call the ideal algorithm an Interacting one Conclusions Choosing the best algorithm for your process is dependent on your process control needs and objectives. Different algorithms perform better in different situations. B using Exper Tune simulation software, these differences are easier to understand
With parallel controllers, controller gain is not multiplied by the error signal only. Integral and derivative actions are "independent" of the controller gain. At first it might seem that the parallel controller is easier to work with because of this "independence". But, parallel algorithms require very different integral and derivative tuning parameters than other controllers. These equations show how to convert from parallel to ideal settings: Kc = Kp I = Ip Kp (units of time/repeat) D = Dp/Kp (units of time) There is more of a difference between parallel versus ideal controller tuning than series versus ideal tuning. The intuitive feel for tuning a parallel controller is very different from the others. The Figure below shows load response in a level loop. The yellow curve is for a tuned (ideal or parallel) controller. Normally it would seem that lowering the controller gain will make the loop more stable as in fact it does with the ideal controller in the Figure. However, the parallel controller gets less stable with lower gain!. Like all controllers, it also gets less stable with more gain. So either increasing or decreasing the gain on a parallel controller can drive the loop unstable! The controllers in the Figure are PI controllers. The situation is more pronounced when you use derivative. With the parallel controller, the effective integral and derivative values change with the gain setting. So, lowering the controller gain also lowers the effective I; increasing controller phase. Lowering gain also increases the effective D, moving the derivative phase to higher frequencies; eliminating its stabilizing effect on controller integral action. The overall effect is unstabilizing as the Figure shows. For example: Bailey and Allen Bradley both have a parallel algorithm available that they describe as a "non-interacting" algorithm. They call the ideal algorithm an "interacting" one. Conclusions Choosing the best algorithm for your process is dependent on your process control needs and objectives. Different algorithms perform better in different situations. By using ExperTune simulation software, these differences are easier to understand
