14 Industrial Applications of PID Control
`Gregory K. McMillan
`
`Abstract
`
`The industrial PID has many options, tools, and parameters for dealing with the
`wide spectrum of difficulties and opportunities in manufacturing plants. Some of
`the options such as “dynamic reset limit” have existed for decades but the full
`value and applicability has not been realized. Also, the possibilities extend consid-
`erably beyond the original intent into improving process efficiency, operability,
`and compliance for sustainable manufacturing. An enhanced PID developed for
`wireless measurements has been found to inherently eliminate oscillations from a
`wide variety of sources including discontinuous and delayed responses in the
`automation system and interactions between loops when used with a threshold
`sensitivity setting and the dynamic reset limit. The advancements in new tech-
`niques and a greater understanding of existing capabilities enable the PID to not
`only improve loop performance but to individually optimize unit operations.
`
`Introduction
`
`The PID controller is an essential part of every control loop in the process in-
`dustry [1]. Studies have shown that the PID provides an optimal solution of the
`regulator problem (rejection of disturbances) and with simple enhancements, pro-
`vides an optimum servo response (setpoint response) [3]. Tests show that the PID
`performs better than Model Predictive Control (MPC) for unmeasured distur-
`bances in terms of peak error, integrated error, or robustness [7]. The PID control-
`ler in the modern Distributed Control System (DCS) has an extensive set of fea-
`tures. However, primarily due to the lack of understanding of the functionality and
`applicability of the PID, the full power of the PID is rarely utilized [23]. This sec-
`tion explores key PID features and provides examples of their importance for ad-
`dressing challenging applications and control objectives for common unit opera-
`tion applications in the process industry.
`
`Industrial processes are characterized by unmeasured disturbances, nonlinear
`process dynamics, noise, measurement delays and lags, resolution and sensitivity
`limits, and valve nonlinearities and non-idealities. It will be shown that the total
`PID loop deadtime in industrial processes determines the ultimate limit to loop
`performance. The total loop deadtime has many sources most of which are vari-
`able. The process deadtimes and time constants are rarely constant. In a first order
`plus deadtime approximation, all of the time constants smaller than the largest
`open loop time constant ((cid:87)o) become an equivalent deadtime ((cid:84)o). The fraction of
`the small time constant converted to deadtime approaches 1 as the ratio of small to
`largest time constant approaches 0 [5]. Examples of small time constants are
`valve actuator lags, process heat transfer and mixing lags, thermowell and sensor
`lags, transmitter damping settings, and signal filters. The deadtime from these lags
`are summed with the pure delays from valve pre-stroke delay, valve backlash and
`
`PID Control in the third Millennium: Lessons Learned and New Approaches
`Editors Ramon Vilanova and Antonio Visioli, Springer 2011
`
`
`
`BTL EX2016
`Allergan v. BTL
`PGR2021-00024
`
`

`

`2
`
`
`
`Gregory K. McMillan
`
`
`
`stiction, process and sample transportation delays, analyzer and wireless meas-
`urement update times, and PID execution time [2,4,5,23,25]. Except for damping
`settings, signal filters, analyzer and wireless update times, and PID execution
`times, these lags and delays are generally unknown and variable. The key features
`in a PID offer the flexibility and capability to achieve the ultimate limit to loop
`performance despite the challenging characteristics of industrial processes [22,24].
`
`14.1 Challenges and Solutions
`
` A
`
` myriad of options and techniques have been used to address industrial auto-
`mation system limitations and process objectives. Before we look at specific solu-
`tions used in industry we need to understand the practical and ultimate limits to
`PID performance for unmeasured load disturbances in industrial processes. The
`first subsection provides practical equations developed over the years to detail the
`important relationships between load performance and dynamics and tuning. This
`subsection also offers a new equation to show how an important metric for set-
`point performance also depends upon dynamics and tuning. Since setpoint
`changes unlike unmeasured disturbances are exactly known many methods exist to
`circumvent the limitations imposed by tuning. Subsequent subsections discuss
`methods such as setpoint feedforward and smart bang-bang logic.
`
`14.1.1 Practical and Ultimate Limits to PID Performance
`
`In the process industry, automation system and process dynamics, and in par-
`ticular the loop deadtime, set the ultimate limit to loop performance but controller
`tuning sets the practical limit for unmeasured disturbances. For example, a loop
`with a small deadtime will perform as badly as a loop with a large deadtime if the
`PID has sluggish tuning. On the other hand, a PID with fast tuning may have an
`excessive oscillatory response for increases in the loop deadtime or process gain.
`Equation 14-1 shows the peak error (Ex) (maximum error for a disturbance) is in-
`versely proportional to 1 plus the product of the PID gain (Kc) and the process
`gain (Kp) [2,4,5,23,25]. Equation 14-2 indicates the integrated error (Ei) (integral
`of error for a disturbance) is proportional to the ratio of the PID integral time to
`gain (Ti/Kc) [2,4,5,23,25,29,30,31,33]. For small filters ((cid:87)f ) and PID execution
`time ((cid:39)Tx), the controller gain is decreased and the integral time is increased based
`on the increase in loop deadtime. Also, the filter and execution time should be
`added to the integral time for the integrated error (2) [9]. For a PID tuned for
`maximum disturbance rejection, Equation 14-3 reveals that the ultimate limit to
`the peak error depends upon the ratio of the total loop deadtime ((cid:84)o) to process
`time constant ((cid:87)P) [2,4,5,23,25]. Equation 14-4 indicates that the integrated error
`depends upon the ratio of the loop deadtime squared to process time constant. A
`PID controller tuned for maximum disturbance rejection has a controller gain pro-
`portional to the ratio of the largest open loop time constant to loop deadtime
`and
`an
`integral
`time proportional
`to
`the
`loop deadtime
`((cid:87)o/(cid:84)o),
`
`

`

`14 Industrial Applications of PID Control
`
`3
`
`[2,4,5,23,25,29,30,31,33]. Note that the controller tuning depends upon the largest
`open loop time constant and not the process time constant. If the largest time con-
`stant is in the measurement path, the observed peak error in the measurement pre-
`dicted by Equation 14-1 will be smaller than the actual peak error in the process
`because of the signal filtering effect of the large measurement time constant.
`
`The peak error is important for preventing: shutdowns from reaching trip set-
`tings of safety instrumentation systems (SIS), environmental emissions and proc-
`ess losses from reaching the relief settings of rupture discs and relief valves, off-
`spec paper sheet and plastic web from exceeding permissible variation in thick-
`ness and clarity, compressor shutdowns from crossing surge curve, and recordable
`incidents by exceeding environmental limits [23].
`
`The integrated error is a good indicator of the quantity of liquid product off-
`spec in equipment with back mixing. In these volumes positive and negative fluc-
`tuations in concentration are averaged out unless irreversible reactions are occur-
`ring [23].
`
`E
`
`(cid:32)
`
`x
`
`1(
`
`(cid:14)
`
`1
`KK
`p
`
`)
`
`c
`
`E
`
`o
`
`
`
`
`
`
`
`
`
`
`
`(14-1)
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`(14-2)
`
`(14-3)
`
`(14-4)
`
`
`
`
`
`
`
`
`E
`
`i
`
`T
`i
`
`(cid:32)
`
`T
`(cid:14)
`(cid:39)
`x
`KK
`p
`
`(cid:87)(cid:14)
`f
`
`c
`
`E
`
`o
`
`
`
`
`
`
`
`E
`
`o
`
`
`
`)
`
`(cid:84) (cid:14)
`
`o
`(
`(cid:87)(cid:84)
`o
`p
`
`(cid:32)
`
`x
`
`E
`
`o
`
`
`
`)
`
`2
`o
`(
`(cid:87)(cid:84)
`o
`p
`
`(cid:84) (cid:14)
`
`(cid:32)
`
`i
`
`
`E
`
`
`E
`
`
`Common metrics for a setpoint response are rise time (time to reach setpoint),
`overshoot (maximum error after crossing setpoint), and settling time (time settle
`out within a specified band around the setpoint). The ultimate limit for rise time is
`proportional to the loop deadtime. The ultimate limit for overshoot and settling
`time is theoretically zero. The practical limit to rise time is similar to the practical
`limit for peak error for fast tuning settings but degrades to the relationship for the
`integrated error for sluggish tuning settings. Fortunately there are many features
`that can be used to readily help achieve the ultimate limit to the rise time. The
`practical limits for overshoot and settling time depend upon a balance between the
`contributions from the integral and proportional modes. In general, the controller
`
`

`

`4
`
`
`
`Gregory K. McMillan
`
`
`
`gain for maximum disturbance rejection can be used to minimize rise time and the
`integral time can be increased to minimize overshoot and settling time [23,25].
`
`The minimum rise time (Tr) can be approximated as the change in setpoint
`((cid:39)SP) divided by the maximum rate of change of the process variable. For an in-
`tegrating or “near integrating” process, the maximum PV ramp rate is the integrat-
`ing process (Ki) gain multiplied by the change in controller output as detailed in
`the denominator of Equation 14-5a. If the step change in controller output from
`the proportional mode for a structure of proportional action on error (structure 3),
`is less than the maximum available output change (difference between current
`output and output limit), Equation 14-5a simplifies to Equation 14-5b for feedback
`control. The output change must be corrected for methods used to make the set-
`point response faster. For setpoint feedforward, the step change in output is a
`combination of the feedforward and feedback action. For smart bang-bang logic,
`the step output change is the maximum available output change.
`
`T
`r
`
`(cid:32)
`
`(
`
`K
`
`i
`
`min(|
`
`(cid:39)
`
`SP
`(cid:39)
`CO
`
`max
`
`|,
`
`K
`
`c
`
`(cid:84)(cid:14)
`o
`
`
`
`
`
`(cid:39)
`
`SP
`
`)
`
`
`
`(14-5a)
`
`
`For a maximum available output change larger than the step from the propor-
`CO
`SP
`K
`|
`(cid:33)|
`(cid:39)
`c(cid:39)
`tional mode (
`) the change in setpoint in the numerator and
`max
`denominator cancel out yielding a simpler equation:
`
`
`
`
`T
`r
`
`1
`KK
`i
`
`c
`
`(cid:32)
`
`(
`
`(cid:84)(cid:14)
`o
`
`
`
`
`
`)
`
`
`
`
`
`
`
`
`
`(14-5b)
`
`
`For the “near integrating” process response seen in vessel and column tempera-
`ture loops where the process time constant is significantly larger than the total
`loop deadtime, the integrating gain is the open loop gain (Ko) divided by the open
`loop time constant ((cid:87)o) and Equation 14-5b becomes Equation 14-5c [5,10,25].
`
`T
`r
`
`(cid:32)
`
`K
`o
`K
`(
`(cid:87)
`o
`
`c
`
`(cid:14)
`
`(cid:84)
`o
`
`
`
`
`
`)
`
`
`
`
`
`
`
`
`
`(14-5c)
`
`
`The practical and ultimate limit to loop performance can be reconciled by real-
`izing that there is an implied deadtime ((cid:84)i) from the tuning. Equation 14-6 shows
`the implied deadtime that can be approximated as the original deadtime ((cid:84)o) mul-
`tiplied by a factor that is 0.5 plus Lambda ((cid:79)) [14,16,22,24]. Lambda is the closed
`loop time constant for a setpoint change. For a PID tuned for maximum distur-
`bance rejection, Lambda is set equal to the original deadtime. The implied dead-
`time is then equal to the original deadtime [14,16,23,25].
`
`

`

`14 Industrial Applications of PID Control
`
`5
`
`
`(cid:84)
`i
`
`(cid:32)
`
`(5.0
`
`o
`
`(cid:84)(cid:79)(cid:14)
`
`)
`
`
`
`
`
`
`
`
`
`
`
`
`
`(14-6)
`
`(cid:32)
`
`1(
`
`L
`
`e
`/(cid:87)(cid:84)(cid:16)(cid:16)
`
`o
`
`L
`
`)
`
`E
`
`
`
`o
`
`
`
`
`
`
`
`
`
`(14-7)
`
`The peak and integrated errors for unmeasured step disturbances represents the
`worst case. Step disturbances originate from manual actions, safety, switches, and
`sequential operations. If discrete actions (e.g. the opening and closing of on-off
`valves and the starting and stopping of pumps) are replaced by control loops with
`modulated final control elements (throttling valves and variable speed drives) or
`are attenuated by intervening volumes, the step disturbances are smoothed. The at-
`tenuated load disturbance has a time constant ((cid:87)L) that is the residence time of the
`volume or closed loop time constant of the upstream control loop. To include the
`effect of a load time constant, the process excursion in the first deadtime, which is
`the key time for determining minimum peak error, can be computed by Equation
`14-7. The open loop error (Eo) in the equations for peak and integrated error can
`be replaced with the load disturbance (EL) that is the open loop error multiplied by
`the exponential response of the disturbance in one deadtime The effect is miti-
`gated by a reset time that is slow relative to the disturbance time constant [23,25].
`
`E
`
`PID controllers tuned too fast can introduce process variability from an oscilla-
`tory response, PID controllers tuned too slow can make a loop with good dynam-
`ics perform as badly as a loop with poor dynamics. In other words, money in-
`vested to reduce process deadtime or to get faster measurements and valves is
`wasted unless the PID controller tuning is commensurate with the speed of the
`process so that the practical limit approaches the ultimate limit to loop perform-
`ance.
`
`In some cases, slower tuning, longer wireless update times, and a PID enhanced
`for wireless will reduce the oscillations from feedforward timing errors and inter-
`action between loops. Also, in cases of blend control, all of the flow loops may be
`forced through tuning to be as slow as the flow loop with the largest deadtime to
`provide a coordination of flows that leads to greater product consistency.
`
`Since industrial processes have valve, process, and measurement dynamics that
`vary with time, operating point, and step size, it is important to have automated
`methods of tuning.
`
`14.1.2 On-Demand and Adaptive Tuning
`
`On-Demand and Adaptive Tuning integrated into the PID function block in a
`DCS enables the use of PID tuning that achieves the ultimate performance limit.
`The relay method by Karl Astrom provides a straightforward On-Demand Tuner
`
`

`

`6
`
`
`
`Gregory K. McMillan
`
`
`
`[1,2,4,5,10]. A user-selected step change is injected into the PID output initially
`and any time the process variable reverses direction and crosses the setpoint and
`the corresponding noise band. The controller action is used to determine if the re-
`versal in the process variable is in the correct direction to drive the process vari-
`able back to setpoint. The ultimate period (Tu) is the oscillation period. Equation
`14-8 is used to compute the ultimate gain (Ku) from the PID output step size (d)
`and the process variable amplitude (a) corrected for the noise band (n). Figure 14-
`1 shows the relay oscillation method with a large change in the process variable
`(PV) for illustrative purposes. For processes with large time constants, the PV am-
`plitude (a) is so small, the oscillation is barely perceptible and the oscillation pe-
`riod is about 4 deadtimes. Since the more important PID loops, such as tempera-
`ture have a large process time constant, the auto tuner provides a test that is less
`disruptive and faster than an open loop test that is waiting to reach a new steady
`state to identify the process time constant. The time constant identified in relay os-
`cillation method is not very accurate. Thus, when the relay oscillation method,
`tuning settings based on the ultimate period and ultimate gain are more accurate
`than those that require knowledge of the process time constant.
`
`
`
`Fig. 14-1 Relay Oscillation Method Offers Fast Tuning Test [24]
`
`Ku
`
`(cid:32)
`
`(cid:83)
`
`(cid:14)
`
`d
`4
`a
`2
`
`(cid:16)
`
`2
`
`n
`
`
`
`
`
`
`
`(14-8)
`
`
`
`
`
`
`
`
`The PID gain is the ultimate gain multiplied by a 0.25 factor [23,25]. The PID
`integral time is the ultimate period multiplied by 1.0 factor for self-regulating and
`10.0 for non-self-regulating processes [10,23,25]. The PID rate time is the ulti-
`mate period multiplied by 0.1 when derivative action is beneficial [10,23,25]. If
`
`

`

`14 Industrial Applications of PID Control
`
`7
`
`the ultimate period is less than 3 times the dead time, the rate time should be 0
`since the loop is deadtime dominant (deadtime is significantly greater than the
`largest time constant in the loop) [10]. If the ultimate period is greater than 4 times
`the deadtime, rate time should be used to prevent a runaway since the process may
`have positive feedback and an unstable open loop response. These factors are gen-
`erally in the direction to provide a non oscillatory PID response that is more robust
`(more resistance to excessive oscillations from changes in process dynamics). The
`Ziegler-Nichols factors were designed to provide a quarter amplitude response
`(amplitude of each succeeding oscillation is ¼ the amplitude of last oscillation).
`Most publications on tuning based on the ultimate period and ultimate gain use the
`Ziegler-Nichols factors leading to improper conclusions on smoothness and ro-
`bustness of the tuning method [10].
`
`Adaptive tuners use a more advanced method to identify process dynamics
`without relay oscillations. Significant manual and remote output changes and set-
`point changes trigger the search for the dynamic parameters for a first order plus
`deadtime approximation (process gain, deadtime, and time constant) that provides
`a model’s response that matches the process response. A particular adaptive tuner
`computes the integrated squared error (ISE) between the model and the process
`output for changes in each of three model parameters from the last best value.
`Exploring all combinations of three values (low, middle, and high) for three pa-
`rameters, results in 27 models. The correction in each model parameter is interpo-
`lated by the application of weighting factors that are based on the ISE for each
`model normalized to a total ISE for all the models over the period of interest. Af-
`ter the best values are computed for each parameter, they are assigned as the mid-
`dle values for the next iteration. This model switching with interpolation and re-
`centering has been proven mathematically by the University of California, Santa
`Barbara to be equivalent to a least square identification that provides an optimum
`approach to the correct model [9,35].
`
`Adaptive tuners schedule tuning settings identified for regions defined by a
`user-selected variable. For valves with nonlinear characteristics such as equal per-
`centage, the variable for scheduling is the PID’s output. For nonlinear processes,
`such as pH, the variable for scheduling is the PID’s process variable. The schedul-
`ing provides preemptive correction of the tuning settings eliminating the delay in
`performance associated with the re-identification of settings as the PID moves into
`another region [9,19,25,35]. For a gravity discharge conical tank, adaptive tuning
`made the level setpoint response fast with a consistent settling time over the entire
`range of operation by increasing the process time constant as the cross section area
`decreased from bottom to top [19]. In this example, the gravity discharge flow
`makes the process self-regulating rather than integrating. Consequently, the
`nonlinearity of the change in cross sectional area predominantly affects the proc-
`ess time constant rather than the process gain. Figure 14-2 shows the models
`
`

`

`8
`
`
`
`Gregory K. McMillan
`
`
`
`automatically identified in five regions for scheduling tuning settings to account
`for the changes in cross section with level.
`
`Since an adaptive tuner uses current tuning settings to compute process dynam-
`ics as the starting point for its search, the number of tests required to get an adap-
`tive model with a high fidelity rating can be minimized by first running the On-
`Demand tuner with a requirement of just 2 or 3 cycles. Since the cycle period is on
`the average the ultimate period, the test is usually faster than an Adaptive Tuning
`test, especially for the overly conservative (sluggish) tuning commonly found in
`industrial PID controllers that have not been tuned by an automated method.
`
`The step size in the output for On-Demand and Adaptive Tuning should be at
`least: 5 times the noise band, the trigger level of a wireless device, and the dead
`band and resolution-sensitivity of the control valve [2]. Note that these step
`changes will not show the deadtime from wireless update times and valve back-
`lash and stick-slip. For wireless devices, about half of the default update rate
`should be added to the identified deadtime [14,23,25,29,30,31,35].
`
`
`
`Fig. 14-2 Models Enable Adaptive Level Control of Conical Tank [18]
`
`14.1.3 Positive Feedback Implementation of Integral Mode
`
`
`
`Instead of integrating the error, the feeding back of the controller output or ex-
`ternal reset signal through a filter block and adding it to the contribution of the
`proportional and derivative modes creates an integral mode action where the filter
`time constant is the integral time setting [4,25]. When the error is zero, the output
`
`

`

`14 Industrial Applications of PID Control
`
`9
`
`of the filter block is simply the controller output or external reset signal and inte-
`gral action stops. The positive feedback implementation illustrated in Figure 14-3
`enables several important PID options, such as dynamic reset limit, enhancement
`for wireless, and deadtime compensation.
`
`The 8 PID structures commonly used in industrial processes are:
`
`
`1. PID action on error (cid:11)(cid:69)(cid:3)(cid:32)(cid:3)(cid:20)(cid:15)(cid:3)(cid:74)(cid:3)(cid:32)(cid:3)(cid:20)(cid:12)
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`2. PI action on error, D action on PV(cid:3)(cid:11)(cid:69)(cid:3)(cid:32)(cid:3)(cid:20)(cid:15)(cid:3)(cid:74)(cid:3)(cid:32)(cid:3)(cid:19)(cid:12)(cid:3)
`
`3.
`
`I action on error, PD action on PV (cid:11)(cid:69)(cid:3)(cid:32)(cid:3)(cid:19)(cid:15)(cid:3)(cid:74)(cid:3)(cid:32)(cid:3)(cid:19)(cid:12)
`
`4. PD action on error (cid:11)(cid:69)(cid:3)(cid:32)(cid:3)(cid:20)(cid:15)(cid:3)(cid:74)(cid:3)(cid:32)(cid:3)(cid:20)(cid:12) (no I action)
`
`5. P action on error, D action on PV (cid:11)(cid:69)(cid:3)(cid:32)(cid:3)(cid:20)(cid:15)(cid:3)(cid:74)(cid:3)(cid:32)(cid:3)(cid:19)(cid:12) (no I action)
`
`6.
`
`7.
`
`ID action on error (cid:1182)((cid:74)(cid:3)(cid:32)(cid:3)(cid:20)(cid:12)(cid:1175) (no P action)
`
`I action on error, D action on PV (cid:1182)((cid:74)(cid:3)(cid:32)(cid:3)(cid:19)(cid:12)(cid:3)(no P action)
`
`8. Two degrees of freedom controller ((cid:69)(cid:3)and(cid:3)(cid:74) adjustable 0 to 1)
`
`
`Fig. 14-3 Positive Feedback Integral Mode Enables Key PID Features (External
`Reset, Wireless Enhancement, and Deadtime Compensation) [4,24]
`
`
`
`

`

`10
`
`
`
`Gregory K. McMillan
`
`
`
`(cid:69)(cid:3)and (cid:74) are setpoint multiplication factors for the proportional and derivative
`modes, respectively to determine how much proportional and derivative action oc-
`curs on setpoint changes. These factors do not affect the ability of the PID to reject
`disturbances. For the fastest possible setpoint response, structures 1 and 2 are
`used. If preventing overshoot is more important than minimizing rise time, struc-
`ture 3 is used. If the ability to customize the balance between fast rise time and
`minimum overshoot for a setpoint response is needed, structure 8 is used. This
`structure also offers the ability to achieve both good load and setpoint responses.
`
`14.1.4 Dynamic Reset Limit (External Reset)
`
`When an external signal is used as the input to a “Filter” block in the positive
`feedback implementation of the integral mode, the integral action will not drive
`the controller output faster than the external reset signal is changing. This capabil-
`ity is particularly important for slow final control elements (large valves and vari-
`able frequency drives), cascade control, and override control.
`
`If the external reset signal is the actual valve position or variable frequency
`drive (VFD) speed, the PID controller output will not ramp faster than the valve or
`VFD can respond [25]. Control valves and dampers have a slewing rate that in-
`creases with actuator size and stroke length. Damper slewing rate is particularly
`slow due to the need to prevent positive feedback from negative torque require-
`ment. VFDs have velocity limiting of the command signal to prevent overloading
`the motor. If the external reset signal is the secondary loop process variable (PV)
`for cascade control, the primary PID cannot ramp the setpoint of the secondary
`PID faster than the secondary PID PV can respond. This capability is important
`for inherently preventing severe oscillations from breaking out for large setpoint
`changes or large disturbances [24,32]. The use of the selected PID output as an ex-
`ternal reset signal for override control also inherently prevents the unselected PID
`controllers from ramping off-scale. PID algorithms without the positive feedback
`implementation of integral action, add a “Filter” block to the external reset signal
`with a filter time equal to the PID reset time to prevent the ramping off-scale of
`the unselected PID output. The dynamic reset limit is a key feature that enables
`the development of an enhancement of the PID for wireless measurements that
`also has the ability to eliminate oscillations from sensitivity and resolution limits
`and feedforward timing errors [20, 22, 25].
`
`The dynamic reset limit can open opportunities important for sustainable manu-
`facturing and in particular abnormal situation management and optimization. If a
`set point velocity limit is set in the analog output block, the dynamic reset limit
`prevents the PID from going faster than the velocity limit. The PID can achieve a
`slow approach to an optimum and a fast recovery upon encroachment of a con-
`straint such as encountered in the prevention of compressor surge, exothermic re-
`actor runaway, RCRA pH violation, and Bioreactor biomass starvation. Previ-
`
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`14 Industrial Applications of PID Control
`
`11
`
`ously, an open loop back-up (kicker) has been used for these applications because
`the tuning of the controller for drastically different speeds of actuation is problem-
`atic. The dynamic reset limit option eliminates the need to tune the controller
`based on direction and the concern about the exact value of the velocity limit. The
`tuning is set for the fastest recovery. The velocity limit is adjusted for the slowest
`approach to the optimum.
`
`There are many more examples where an intelligent adaptation of the speed of
`actuation of the final control element or secondary loop could be beneficial. In
`general, you want to approach optimums slowly to minimize disruption but as you
`operate close to the edge, you depend upon a fast recovery to prevent going over
`the edge. With compressor surge control the edge is literally a cliff. While other
`applications might not be as dramatic, the technique opens a wide spectrum of PID
`techniques for sustainable manufacturing, which in its broadest definition includes
`efficiency, flexibility, operability, maintainability, safety, and profitability [34].
`
`14.1.5 Enhancements for Wireless
`
`Wireless measurement devices have a “default update rate” (time interval for
`periodic reporting) and a “trigger level” (threshold sensitivity limit for exception
`reporting) set as large as possible to conserve battery life. The integral mode in the
`traditional PID will continue to ramp while the PID is waiting for an updated
`measurement from a wireless device. Also, when an update is received, the tradi-
`tional PID considers the entire change to have occurred within the PID execution
`time interval ((cid:39)Tx). If derivative mode is used, the rate of change of the measure-
`ment is the difference between the new and old measurement divided by the PID
`execution time interval. The result is a spike in the controller output.
`
`The non-continuous update scenario occurs for many applications besides wire-
`less devices. During the time when a measurement is not updated due to a failure,
`resolution limit, threshold sensitivity limit, or backlash, the PID output continues
`to ramp from the integral mode. Failures, resolution limits, and threshold sensitiv-
`ity limits can originate in an analyzer, sensor, transmitter, communication system,
`or control valve. Analyzers also have a time interval between updates determined
`by the sample time and cycle time.
`
`The enhanced PID for wireless executes the PID algorithm as fast as wired de-
`vices. A change in setpoint, feedforward signal, and remote output translates im-
`mediately (within PID execution time interval) to a change in PID output. How-
`ever, integral action does not make a change in the output until there is an update.
`When an update occurs, the elapsed time between the updates is used in an expo-
`nential calculation that mimics the action of the filter block in the positive feed-
`back implementation of integral action. If derivative action is used, the elapsed
`time rather than the PID execution time interval, is used to calculate the rate of
`
`

`

`12
`
`
`
`Gregory K. McMillan
`
`
`
`change of the process variable. The integral and derivative calculations are exe-
`cuted only once upon a change in setpoint or measurement [22,24,25]. A threshold
`sensitivity setting is used to prevent an update from noise. Figure 14-4 compares a
`simplified block diagram of the traditional PID to the enhanced PID.
`
`
`
`
`
`Fig. 14-4 Enhancements of PID for Wireless Prevent the Ramping from Inte-
`gral Action and the Spikes from Derivative Action for Discontinuous Updates [22]
`
` traditional PID will have to be detuned to prevent instability for a large in-
`crease in the time between updates. The enhanced PID will continue to be stable
`for even the longest update time interval. For a measurement update time interval
`larger than the process response time, the enhanced PID controller gain can be set
`equal to the inverse of the open loop gain (product of valve, process, and meas-
`urement gain) to provide a complete correction for setpoint change or update. Sub-
`sequent sections show the enhanced PID can suppress oscillations from a wide va-
`riety of sources. This reduction in variability results from the suspension of
`integral action and the wait in feedback correction till there is a more complete re-
`sponse is beneficial [27]. To achieve these benefits, the user simply enables the
`
` A
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`14 Industrial Applications of PID Control
`
`13
`
`enhanced PID option in the PID block, which automatically enables the dynamic
`reset limit option. No retuning is necessary to achieve a smooth response but if the
`update time is larger than the process response time the enhanced PID can be
`tuned with a much higher gain.
`
`14.1.6 Deadtime Compensation
`
`Adding a “Deadtime” block to the external reset of a positive feedback imple-
`mentation of the integral mode can provide deadtime compensation equivalent to a
`Smith Predictor but with the advantage that the process gain and time constant set-
`tings of the Smith Predictor are not needed. In the positive feedback implementa-
`tion of deadtime compensation, the user simply needs to set the deadtime parame-
`ter in the “Deadtime” block equal to the total loop deadtime. The dynamic reset
`limit option for the PID must be enabled so the external reset signal is used. The
`block deadtime is set equal to total loop deadtime. The process gain and process
`time constant parameters used in a Smith Predictor are not necessary for this im-
`plementation of deadtime compensation. To get the benefit from the PID knowing
`the effect of deadtime, the integral time needs to be decreased toward a low limit
`that is half the total deadtime [24]. Like the Smith Predictor, this deadtime com-
`pensator is more sensitive to an overestimate rather than an underestimate of the
`total loop deadtime. Normally, a PID will just become sluggish if overestimate of
`the deadtime is used for the tuning settings. For PID controllers with deadtime
`compensation, high frequency oscillations will rapidly start for overestimates of
`the loop deadtime [10,24,25]. Thus, for robustness it is better to use a deadtime
`that is always less than the minimum loop deadtime often associated with high
`production rates.
`
`In tests, the following myths about deadtime compensators were exposed [24].
`
`
`(1) Deadtime is eliminated from the loop. The smith predictor, which cre-
`ated a PV wit