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1、 PID controllerFrom Wikipedia the free encyclopediaA proportionalintegralderivative controller PID controller is a generic control loop feedback mechanism widely used in industrial control systems A PID controller attempts to correct the error between a measured process variable and a desired setpoi

2、nt by calculating and then outputting a corrective action that can adjust the process accordinglyThe PID controller calculation algorithm involves three separate parameters the Proportional the Integral and Derivative values The Proportional value determines the reaction to the current error the Int

3、egral determines the reaction based on the sum of recent errors and the Derivative determines the reaction to the rate at which the error has been changing The weightedsum of these three actions is used to adjust the process via a control element such as the position of a control valve or the power

4、supply of a heating elementBy tuning the three constants in the PID controller algorithm the PID can provide control action designed for specific process requirements The response of the controller can be described in terms of the responsiveness of the controller to an error the degree to which the

5、controller overshoots the setpoint and the degree of system oscillation Note that the use of the PID algorithm for control does not guarantee optimal control of the system or system stabilitySome applications may require using only one or two modes to provide the appropriate system control This is a

6、chieved by setting the gain of undesired control outputs to zero A PID controller will be called a PI PD P or I controller in the absence of the respective control actions PI controllers are particularly common since derivative action is very sensitive to measurement noise and the absence of an inte

7、gral value may prevent the system from reaching its target value due to the control actionA block diagram of a PID controllerNote Due to the diversity of the field of control theory and application many naming conventions for the relevant variables are in common use1Control loop basicsA familiar exa

8、mple of a control loop is the action taken to keep ones shower water at the ideal temperature which typically involves the mixing of two process streams cold and hot water The person feels the water to estimate its temperature Based on this measurement they perform a control action use the cold wate

9、r tap to adjust the process The person would repeat this input-output control loop adjusting the hot water flow until the process temperature stabilized at the desired valueFeeling the water temperature is taking a measurement of the process value or process variable PV The desired temperature is ca

10、lled the setpoint SP The output from the controller and input to the process the tap position is called the manipulated variable MV The difference between the measurement and the setpoint is the error e too hot or too cold and by how muchAs a controller one decides roughly how much to change the tap

11、 position MV after one determines the temperature PV and therefore the error This first estimate is the equivalent of the proportional action of a PID controller The integral action of a PID controller can be thought of as gradually adjusting the temperature when it is almost right Derivative action

12、 can be thought of as noticing the water temperature is getting hotter or colder and how fast and taking that into account when deciding how to adjust the tapMaking a change that is too large when the error is small is equivalent to a high gain controller and will lead to overshoot If the controller

13、 were to repeatedly make changes that were too large and repeatedly overshoot the target this control loop would be termed unstable and the output would oscillate around the setpoint in either a constant growing or decaying sinusoid A human would not do this because we are adaptive controllers learn

14、ing from the process history but PID controllers do not have the ability to learn and must be set up correctly Selecting the correct gains for effective control is known as tuning the controllerIf a controller starts from a stable state at zero error PV SP then further changes by the controller will

15、 be in response to changes in other measured or unmeasured inputs to the process that impact on the process and hence on the PV Variables that impact on the process other than the MV are known as disturbances and generally controllers are used to reject disturbances andor implement setpoint changes

16、Changes in feed water temperature constitute a disturbance to the shower processIn theory a controller can be used to control any process which has a measurable output PV a known ideal value for that output SP and an input to the process MV that will affect the relevant PV Controllers are used in in

17、dustry to regulate temperature pressure flow rate chemical composition speed and practically every other variable for which a measurement exists Automobile cruise control is an example of a process which utilizes automated controlDue to their long history simplicity well grounded theory and simple s

18、etup and maintenance requirements PID controllers are the controllers of choice for many of these applications2PID controller theoryNote This section describes the ideal parallel or non-interacting form of the PID controller For other forms please see the Section Alternative notation and PID formsTh

19、e PID control scheme is named after its three correcting terms whose sum constitutes the manipulated variable MV Hencewhere Pout Iout and Dout are the contributions to the output from the PID controller from each of the three terms as defined below21 Proportional termThe proportional term makes a ch

20、ange to the output that is proportional to the current error value The proportional response can be adjusted by multiplying the error by a constant Kp called the proportional gainThe proportional term is given byWherePout Proportional output Kp Proportional Gain a tuning parameter e Error SP PV t Ti

21、me or instantaneous time the present Change of response for varying KpA high proportional gain results in a large change in the output for a given change in the error If the proportional gain is too high the system can become unstable See the section on Loop Tuning In contrast a small gain results i

22、n a small output response to a large input error and a less responsive or sensitive controller If the proportional gain is too low the control action may be too small when responding to system disturbancesIn the absence of disturbances pure proportional control will not settle at its target value bu

23、t will retain a steady state error that is a function of the proportional gain and the process gain Despite the steady-state offset both tuning theory and industrial practice indicate that it is the proportional term that should contribute the bulk of the output changecomgral termThe contribution fr

24、om the integral term is proportional to both the magnitude of the error and the duration of the error Summing the instantaneous error over time integrating the error gives the accumulated offset that should have been corrected previously The accumulated error is then multiplied by the integral gain

25、and added to the controller output The magnitude of the contribution of the integral term to the overall control action is determined by the integral gain KiThe integral term is given byChange of response for varying KiWhere Iout Integral output Ki Integral Gain a tuning parameter e Error SP PV Time

26、 in the past contributing to the integral response The integral term when added to the proportional term accelerates the movement of the process towards setpoint and eliminates the residual steady-state error that occurs with a proportional only controller However since the integral term is respondi

27、ng to accumulated errors from the past it can cause the present value to overshoot the setpoint value cross over the setpoint and then create a deviation in the other direction For further notes regarding integral gain tuning and controller stability see the section on loop tuning23 Derivative termT

28、he rate of change of the process error is calculated by determining the slope of the error over time ie its first derivative with respect to time and multiplying this rate of change by the derivative gain Kd The magnitude of the contribution of the derivative term to the overall control action is te

29、rmed the derivative gain KdThe derivative term is given by Change of response for varying KdWhere Dout Derivative output Kd Derivative Gain a tuning parameter e Error SP PV t Time or instantaneous time the present The derivative term slows the rate of change of the controller output and this effect

30、is most noticeable close to the controller setpoint Hence derivative control is used to reduce the magnitude of the overshoot produced by the integral component and improve the combined controller-process stability However differentiation of a signal amplifies noise and thus this term in the control

31、ler is highly sensitive to noise in the error term and can cause a process to become unstable if the noise and the derivative gain are sufficiently large24 SummaryThe output from the three terms the proportional the integral and the derivative terms are summed to calculate the output of the PID cont

32、roller Defining u t as the controller output the final form of the PID algorithm isand the tuning parameters areKp Proportional Gain - Larger Kp typically means faster response since the larger the error the larger the Proportional term compensation An excessively large proportional gain will lead t

33、o process instability and oscillation Ki Integral Gain - Larger Ki implies steady state errors are eliminated quicker The trade-off is larger overshoot any negative error integrated during transient response must be integrated away by positive error before we reach steady state Kd Derivative Gain -

34、Larger Kd decreases overshoot but slows down transient response and may lead to instability due to signal noise amplification in the differentiation of the error 3 Loop tuningIf the PID controller parameters the gains of the proportional integral and derivative terms are chosen incorrectly the contr

35、olled process input can be unstable ie its output diverges with or without oscillation and is limited only by saturation or mechanical breakage Tuning a control loop is the adjustment of its control parameters gainproportional band integral gainreset derivative gainrate to the optimum values for the

36、 desired control responseThe optimum behavior on a process change or setpoint change varies depending on the application Some processes must not allow an overshoot of the process variable beyond the setpoint if for example this would be unsafe Other processes must minimize the energy expended in rea

37、ching a new setpoint Generally stability of response the reverse of instability is required and the process must not oscillate for any combination of process conditions and setpoints Some processes have a degree of non-linearity and so parameters that work well at full-load conditions dont work when

38、 the process is starting up from no-load This section describes some traditional manual methods for loop tuningThere are several methods for tuning a PID loop The most effective methods generally involve the development of some form of process model then choosing P I and D based on the dynamic model

39、 parameters Manual tuning methods can be relatively inefficientThe choice of method will depend largely on whether or not the loop can be taken offline for tuning and the response time of the system If the system can be taken offline the best tuning method often involves subjecting the system to a s

40、tep change in input measuring the output as a function of time and using this response to determine the control parameters Choosing a Tuning Method MethodAdvantagesDisadvantages Manual TuningNo math required Online methodRequires experienced personnel ZieglerNicholsProven Method Online methodProcess

41、 upset some trial-and-error very aggressive tuning Software ToolsConsistent tuning Online or offline method May include valve and sensor analysis Allow simulation before downloadingSome cost and training involved Cohen-CoonGood process modelsSome math Offline method Only good for first-order process

42、es31 Manual tuningIf the system must remain online one tuning method is to first set the I and D values to zero Increase the P until the output of the loop oscillates then the P should be left set to be approximately half of that value for a quarter amplitude decay type response Then increase D unti

43、l any offset is correct in sufficient time for the process However too much D will cause instability Finally increase I if required until the loop is acceptably quick to reach its reference after a load disturbance However too much I will cause excessive response and overshoot A fast PID loop tuning

44、 usually overshoots slightly to reach the setpoint more quickly however some systems cannot accept overshoot in which case an over-damped closed-loop system is required which will require a P setting significantly less than half that of the P setting causing oscillationEffects of increasing paramete

45、rsParameterRise TimeshootSettlingTimeSS ErrorKpDecreaseIncreaseSmall ChangeDecreaseKiDecreaseIncreaseIncreaseEliminateKdSmall DecreaseDecreaseDecreaseNone32ZieglerNichols methodAnother tuning method is formally known as the ZieglerNichols method introduced by John G Ziegler and Nathaniel B Nichols A

46、s in the method above the I and D gains are first set to zero The P gain is increased until it reaches the critical gain Kc at which the output of the loop starts to oscillate Kc and the oscillation period Pc are used to set the gains as shownZieglerNichols methodControl TypeKpKiKdP05 Kc-PI045Kc12 K

47、p Pc-PID06 Kc2Kp PcKpPc 833 PID tuning softwareMost modern industrial facilities no longer tune loops using the manual calculation methods shown above Instead PID tuning and loop optimization software are used to ensure consistent results These software packages will gather the data develop process

48、models and suggest optimal tuning Some software packages can even develop tuning by gathering data from reference changesMathematical PID loop tuning induces an impulse in the system and then uses the controlled systems frequency response to design the PID loop values In loops with response times of several minutes mathematical loop tuning is recommended because trial and error can literally take days just to find a stable set of loop values Optimal values are harder to find Some digital loop con