Controller Output % Flow %
Control Valve Dynamic Specification
1.0 Competitive Marketplace
The global market’s continuing demand for quality and
uniformity in manufactured products means there is even
greater focus being given to process control equipment and
its performance. EnTech Control Engineering Inc. has
specialized in the optimization of process performance,
particularly in pulp and paper manufacturing where product
uniformity specifications are now approaching 1%, and
product can be rejected when it deviates outside of these
limits. Equally important is the fact that process variability
impacts operating constraints causing lower manufacturing
efficiency and throughput, and thereby reducing the
economic potential for the plant. Plant process variability
audits frequently find that product variability is increased by
individual control loops that limit cycle because their control
valves are unable to track their controller output signals
closely enough (Figure 1). This undesirable behaviour of
control valves is the biggest single contributor to poor
control loop performance and the destabilization of
process operation.
55
53
51
49
47
0 500 1000
Time seconds
Figure 1 – Typical Control Valve Induced Limit Cycle
(Version 3.0, 11/98)
Control Valve Dynamic Specification - Purpose
The purpose of the Control Valve Dynamic Specification is to define the degree to which control valves can be nonlinear and still allow
acceptable process control to be achieved in the highly competitive process industry environment. Minimizing the impact of the control
valve on process variability is a key consideration. Intended uses of this specification include: in-process control valve end-use
performance; control valve sizing; purchase requirements; and control valve design, manufacture and maintenance requirements. The
specification has three parts 1) Nonlinear, 2) Dynamic Response, and 3) Valve Sizing. Parts 1) and 2) - nonlinear and dynamic
response, deal with issues such as dead band and speed of response, and are intended for the control valve manufacturer. A given
control valve can be expected to meet one of the categories called out in the first two parts of the specification. The third part – valve
sizing, is intended for the process/instrumentation-engineering designer who is selecting and sizing a control valve for a particular
process application. A given valve selection and process design can be expected to meet one of the categories called out in the third
part of the specification.
About Version 3.0
The original EnTech Control Valve Dynamic Specification was issued in 1992 and was last updated in 1994 (Version 2.1). Although it
targeted performance in pulp and paper processes, it quickly migrated to other industries such as chemicals, hydrocarbons, food
processing and energy where similar problems exist. It has been adopted by valve manufacturers as a performance guideline for
design. More currently it has provided the impetus for the formation of the ISA SP75.25 subcommittee, which is preparing an ISA
standard for small step change performance of control valves. Version 3.0 aligns the language with ISA terminology, considers the end
user’s process control requirements, defines a valve step response performance index, and broadens the applicability to all process
industries where flow regulation affects throughput of quality products. Version 3.0 replaces all previous versions. Sections 1, 2 & 3
give background, Section 4 is the specification, and Section 5 gives testing methods. Note: italicized words are defined in Section 6.0
at the end of the document.
Copyright EnTech 1998 – All Rights Reserved
Control Valve System
The Specification considers the control valve as a dynamic system, from input signal through to the flow coefficient that determines the
fluid flow in the pipe. The control valve system includes the actuator, drive train, positioner and valve, under normal process operating
conditions. The key to determining performance is that there is a measured change in a process variable in response to small input
step-changes (1% and less). This indicates that the valve flow coefficient has actually changed in the pipe. Valve stem movement
is not an adequate indication, especially for rotary valves, and may even be in error for sliding stem valves if there is instability in the
fluid passing through the valve body. However, valve stem indication, is considered to be a good measure of control valve system
speed of response for step changes large enough to cause valve motion. (In the text the words valve and control valve are used to
mean control valve system where ambiguity is avoided).
2.0 Control Problem Definition
Most control valves are used as final control elements in feedback control loops with PID control algorithms. The dynamic response of
the control valve system is inherently nonlinear in a complex way and has the potential to create the following problems for the control
loop:
1. For very small input signal changes, valve nonlinearities and variable dead time cause limit cycles. Figure 1 displays a typical limit
cycle where the tendency of the valve to stick or delay forces the controller to continue correcting for the error from setpoint. Once
a limit cycle occurs, effective control is lost and unwanted process variability is created.
2. The speed of response of the control valve system must be sufficiently fast to allow the desired control loop speed of response
to be achieved.
3. The control valve system response often introduces dead time into the loop, which can vary with the magnitude of the valve input
signal. Dead time is extremely destabilizing for a control loop. Variable dead time even more so.
4. For larger input changes valve nonlinearities cause the valve dynamic response to be inconsistent, making it difficult or
impossible to tune the controller for consistent performance. For effective control the control valve system must deliver a
consistent dynamic response over a specified range of step sizes.
Linear Control
Most feedback controllers are essentially linear. If all elements of a control loop were also linear, there would be far fewer control
problems. What does 'linear' mean in the control context? A linear dynamic system responds to its input signal with the same dynamic
response (same gain, time constants, dead time etc.) regardless of the size of the change in the input signal. Due to their mechanical
nature control valve systems are highly nonlinear, and this is a major source of problems for control loop performance.
Ideal Control Valve System Step Response
Ideally, a control valve system should respond to a step change in a fashion which allows the control loop the greatest possible chance
of controlling the process effectively without inadvertently generating additional variability. This ideal step response would be much like
a first order response and would rise monotonically to its final value. It would have a time constant and a T86 suitably fast to satisfy
the control loop speed of response needed for the process application. It would reach steady state at a time Tss that would be equal
to five time constants or 2.5 times T86. It would have zero dead time, no ringing or hunting, zero overshoot, and a travel gain of
1.0. Such a response would appear to be essentially linear to the control loop. It would be free of all characteristics that could
potentially generate variability though overshoot, hunting and dead time.
2.1 Speed of Response
The speed of response of a control valve system can be gauged by its approximate time constant 'τ. The speed of response of a
control loop is usually determined by the desired closed loop time constant, often referred to as Lambda (λ), which should be selected
to allow the process manufacturing objectives to be met. In order to ensure control loop stability and robustness margins consistent
with low process variability operation, the speed of response (time constant) of all of the internal dynamic elements in the control loop
including the process (non-integrating), the transmitter and the control valve system, should be at least five times faster than that of the
control loop. In some cases the control valve system is the slowest or dominant dynamic in the control loop, and as a result, it
determines how the loop can be tuned. It is this limiting case that forms the argument for the relationship between the control loop
expected speed of response and the control valve system speed of response slow limit in this specification. Unfortunately because of
their nonlinear nature, control valve systems have a variable speed of response. When the valve is slower than an expected speed of
response, it can destabilize the control loop and cause oscillations to occur. On the other hand when the valve is faster than this
expected speed of response, this seldom has a harmful effect. Hence a control valve system with a speed of response no slower than a
certain slow limit is capable of being used successfully in any control loop, as long as the speed of response limit of the control valve
system is at least five or more times faster than the intended speed of response of the control loop.
2
Copyright EnTech 1998 – All Rights Reserved
Input, Stem %
Input
λ
τ
Perhaps 80% of flow and pressure control loops in most industrial plants can be tuned for a speed of response range from 5 seconds to
one minute. This range is determined by the typical dynamics of many existing control valves, transmitters and distributed control
systems. These loops would all work satisfactorily if their control valves had an effective time constant of 1 second. In some cases
however it is critically important to achieve a faster speed of response, such as a hydraulic header pressure control loop which may
need a speed of response as fast as one second, and hence a minimum control valve speed of response of 0.2 seconds. At the other
end of the scale, many flow and pressure loops are tuned for 10 seconds and slower, while other variables including many temperature
and tank level controllers are often tuned as slow one minute or even one hour. To satisfy a control loop speed of response of one
minute requires a minimum control
valve speed of response of 12
seconds. Based on this, four
classes of control valve speed of
response can be defined, and are
shown in Table I:
Control Loop Speed of response
Nominal (10 seconds) 2 seconds
Table I - Control Valve Speed of response Classes
Control Valve Maximum Time constant
Very Fast (1 second) 0.2 seconds
Fast (5 seconds) 1 seconds
'
Slow (1 minute) 12 seconds
2.2 Measuring the Control
Valve Dynamic Response
The control valve system is expected to produce consistent dynamic responses over a certain range of input signal step sizes. The
speed of response of the valve system can be measured via the stem or shaft position, and requires a transducer to be mounted on the
valve. This must be calibrated to agree
with the input signal, and must have a
measurement time constant at least 20
times faster than the valve (T86). A typical
step response is shown in Figure 2. The
response often has dead time (Td) which
may vary considerably. Prior to analyzing
39
38
Initial Overshoot to 38.11 = 23 %
Stem
Final Steady State Average Values
Input = 37.84, Stem = 37.65
the dynamic response the initial and final
values should be established for both the
input signal and the stem position. For the
input signal and stem position the initial
37
Travel gain = 0.91, Tss = 18.3 sec
and final values should be averaged over
the initial and final steady state periods of
the response. The measurement of T86,
the time at which the response crosses
86.5% of the step change, captures the
majority of the total dynamic response
including the dead time. The amount of
dead time is of interest and should be
recorded. To avoid ambiguity, dead time
can be measured as the time after the step
change where the response crosses 10%
of the full value of the response. After T86
36
35
0 10 20 30
Figure 2 – Step Change Speed of Response
Note: T86, Initial Overshoot, Travel Gain, Tss
,
86.5% of response, T86 = 2.06 sec
Dead time Td = 1.6 sec
Initial Steady State Average Values, Input & Stem = 35.67
Time - Seconds
the settling behaviour becomes of interest. The response may or may not overshoot. It may ring or hunt by overshooting and
undershooting several times. The rate of change may slow down considerably as it approaches steady state. It may or may not reach
the right steady state value. The initial overshoot is the point where the stem position reaches its maximum value after the step change
(in either the up or down direction). The % overshoot is calculated as the amount over the steady state value expressed as a
percentage of the change in steady state value of the stem position (the term overshoot applies to both increasing and decreasing steps
as in Figure 6). The % undershoot (not present in Figure 2 – see Figure 6 which overshoots, undershoots and overshoots) is
calculated as the amount under the steady state value expressed as a percentage of the change in steady state value of the stem
position. Overshoots and undershoots over 1% should be measured and counted. The travel gain is calculated by dividing the change
in steady state value of the stem position by the change in input signal. Ideally, the travel gain should have a value of 1.0. The time at
steady state (Tss) is the point where the stem position reaches within plus and minus 1% of the steady state value.
2.3 Tss as a Function of T86
A linear first order system reaches steady state in four to five time constants. In four time constants the step response has reached
98.2% of its final value, while in five time constants it has reached 99.3% of the final value. Ideally, the settling behaviour of the valve
response should be as close to linear as possible, hence the Tss upper limit should be no longer than 2.5 times T86. A slower settling
3
Copyright EnTech 1998 – All Rights Reserved
Input, Stem %
TC = 0.2 sec
λ
λ
time will also tend to de-stabilize the control loop. Hence in order to have a speed of response which is fast enough for a givem control
λ
loop desired speed of response, the control valve system should have both T86 and Tss values which are equal to or faster than their
respective specification limits.
2.4 T86, Dead time and Control Performance
Whereas T86 is a convenient
way of capturing the valve
step response time, it is
important to recognize the
consequences of various
valve response dynamics with
the same T86. Figure 3
shows three idealized valve
step responses all with the
same T86 of 2.8 seconds.
Response #1 is an ideal first
order response with a time
constant of 1.4 seconds.
Such a response, if it were
possible, would be ideal for a
valve and would allow the
38
37.5
37
36.5
36
Input
T86 = 2.8 sec
86.5%
of step
#1
1st Order
TC = 1.4 sec
#2
Slew
Slew time = 3.3
#3
Td + 1st Order
Td = 2.4 sec
loop to be tuned for a Closed
Loop Time Constant (λ ) of 7
seconds, which is five times
slower than the time constant
of the valve. (In fact because
of its ideal nature it would be
35.5
6 7 8 9 10 11 12 13 14 15
Time seconds
Figure 3 T86 for Various Responses
safe to tune it even faster).
Response #2 is more typical of an electric valve driven by a fixed speed motor. The response reaches steady state in 3.3 seconds for
this step change. The dead time is zero, and the response is roughly equivalent to a first order time constant of 1 second. Hence the
loop could be tuned for a closed loop time constant of 5 seconds. Response #3 is much more typical of a pneumatic control valve, and
includes 2.4 seconds of dead time. Dead time is the most destabilizing dynamic parameter for a control loop. The T86 of 2.8 seconds
is 86% dead time. Dead time in a control loop causes resonance to occur, in which the loop has a tendency to cycle at its natural
frequency and amplify process variability. The frequency of the cycle is determined by the amount of dead time and the closed loop
time constant. The amount of resonance or
amplification can be expressed in dB’s,
amplitude ratio or as a percentage. It
expresses how much bigger the variability
that already exists in the process at the
natural frequency would be as a result of the
loop’s control action. The faster the tuning,
the stronger this tendency. Table II
Closed Loop TC
Table II – Loop Resonance as a Function of λand Td
Resonance
Period of Oscillation
% dB
2 x Td 35% +2.6 6.0 x Td
3 x Td 26% +2.0 6.6 x Td
4 x Td 19% +1.5 6.9 x Td
5 x Td 16% +1.3 7.2 x Td
quantifies the relationship. Based on this
result it is advisable to limit the Closed Loop Time Constant (λ) to 4 x Td, in order to limit the resonance to less than 20%. For the
example of Figure 3, Response #3, since T86 is mainly dead time it is advisable to limit the tuning to 11 seconds (4 x T86). A simple
rule can be generated from these three results as summarized in Table III. Put
in other words, all T86’s are not equal. A control loop can achieve effective
process control as long as the control valve speed of response is at least five
times faster than that of the control loop. As T86 is twice 'τ, it means that
T86 for the control valve should be 2.5, or more, times faster than the fastest
Table III - λas a Function of T86 and Td
Td/ T86 Ratio
(minimum)
Low (<0.5) 2.5 x T86
High (>0.5) 4 x T86
planned for the control loop, as long as the Td / T86 ratio is not high. If it
the ratio is high, then T86 should be faster still by a factor of 2.5 / 4 or 62.5% in order to handle the additional dead time. This allows
Table I to be restated in terms of the above discussion as shown in Table IV below:
4
Copyright EnTech 1998 – All Rights Reserved
Table IV - Control Valve Speed of response Classes
λ
Control Loop Speed of response
1 second 0.4 seconds 0.25 seconds
5 seconds 2 seconds 1.25 seconds
10 seconds 4 seconds 2.5 seconds
1 minute 24 seconds 15 seconds
Control Valve T86
Td / T86 < 0.5
Control Valve T86
Td / T86 > 0.5
3.0 Control Valve Nonlinearities
Control valve systems have nonlinear behaviour that can be categorized as follows:
1. control valve tracking nonlinearities,
2. flow characteristic nonlinearities.
3.1 Control Valve Tracking Nonlinearities
Control valve tracking nonlinearities represent the inability of the control valve system (valve, actuator, and positioner) to faithfully track
changes in the input signal, and to ensure that changes in flow coefficient actually occur as a result. Tracking nonlinearities consist of
dead band and step resolution, which combine in a complex way to produce total hysteresis. This determines the degree to which the
valve closure member (trim, plug, etc.) fails to track step changes in the input signal. Ideally, the valve system should track input
changes with a travel gain of 1.0. However, due to the mechanical nature of the valve system (clearances, flexibility, and static friction,
dynamic friction), it stands to reason that it is impossible to execute very small step changes uniformly. This specification is intended to
quantify the valve behaviour for step changes that approach the ultimate limit of movement.
3.1.1 Nonlinear Regions
Tracking nonlinearities are caused by problems in the positioner/actuator/drive train part of the control valve system and prevent the
valve closure member from following the input signal in a linear and repeatable fashion. For a pneumatically actuated control valve,
there are four regions of nonlinear operation (referred to as Regions A, B, C and D). For a very small input signal step change (say
0.1%), the closure member does not move at all (Region A – less than dead band or step resolution) in a reasonable time after the step
change. Above some initial threshold (say 0.1% to 1%), motion occurs (Region B), but due to the nonlinearities and other effects the
responses are not consistent. For larger step changes the closure member moves in a more consistent manner, and it is possible to
classify responses in this region (Region C) such that their step response times (T86) all fall below the acceptable limit which is required
for effective control. For step changes which are larger still (Region D), it is likely that the motion of the control valve system will
become velocity limited (steps of say 10% and greater), hence causing the step response times (T86) to become progressively longer.
The control valve system transitions continuously through Regions A, B, and C as the control loop regulates the process. Under normal
process regulation it will transition though Regions A, B and will penetrate slightly into Region C, as most of the control moves made by
a controller are small under normal process regulation. The controller must transition through Region A, as here the loop is essentially
open due to the fact that the control valve system does not respond. The controller will also transition through Region B as here the
responses are inconsistent and may have very long dead times. Only once the controller output transitions into Region C can it be
expected that the control valve system will respond reliably enough for feedback control to work. For this reason it is expected that the
controller output will have frequent but shallow penetrations into Region C. Only for major setpoint changes or very large process
disturbances will the control valve transition through Region C and into Region D. As a process disturbance occurs, the control loop
takes corrective action. Initially, this action tends to be small (inside Region A). However, because the control valve system will not
respond to these small changes, the controller will “wind-up” and produce larger control actions which eventually reach Region B. Here
the control valve moves but not consistently. Sometimes small step changes result in a long dead time before the valve actually moves,
again causing the controller to “wind-up”. When the valve does finally move after the dead time, it is trying to match an input signal
(controller output) which actually exceeds the value needed to have the process variable achieve setpoint. It is this that causes the limit
cycle to occur. This variable dead time phenomenon produces a region of local instability where the dead time is far too long for the
existing controller tuning. The variable dead time phenomenon is a very common mechanism for inducing control valve limit cycles.
The amplitude of such limit cycles is a complex function of the nonlinearities causing Region A, as well as the variable dead time of
Region B. An important point is that the behaviour of the control valve system just inside Region C is key to determining the
effectiveness of a control loop under the condition of normal regulation (some 98% of the time). The actual degree of penetration into
Region C is a function of process gain, the controller tuning and the amount of noise present in the control loop.
For large setpoint changes or major process disturbances, the controller will make larger changes (Region C) in the valve input signal.
The valve responds to each of these changes relatively quickly and with reasonable consistency. As long as the valve response is fast
5
Copyright EnTech 1998 – All Rights Reserved
enough for the controller tuning that has been installed, the loop response will be as anticipated by the controller and effective control
will be established. Should the valve be faster than expected, this will not generally upset the controller. When even larger control
corrections are needed, the control valve may become velocity limited (Region D) and take progressively longer to complete larger
changes. This will appear to the controller as if the process has a slower time constant than anticipated, with the result that the control
loop will tend to oscillate and cause increased variability.
Hydraulically actuated control valves have a similar behaviour to that described above, except that Regions A and B will likely be
much narrower than for a pneumatic valve.
Electrically actuated valves using fixed speed electric motors usually have a narrow dead band that applies for small step changes.
Here the motor is turned off. This dead band determines Region A. Depending on the electric motor increase/decrease control logic,
there may not be a Region B. Beyond this point, electric valves are velocity limited for steps of all sizes as they move at a fixed speed.
As long as the step response time T86 is less than a user-specified limit this defines an acceptable Region C. The point at which T86
exceeds the high limit defines the start of Region D.
User Selection of Minimum and Maximum Step Sizes
The specification requires the valve user to specify the desired minimum and maximum step sizes that are to apply in Region C. These
limits determine the range of controller output step sizes over which the control valve system dynamic response should consistently
conform to the dynamic response specification limits (T86, overshoot, travel gain and Tss) and will allow the control loop to operate in a
near linear fashion as a result. Also, the test procedure identifies what the actual minimum step size is at which T86 (and other
parameters) actually meet the specification limits. This point is the upper limit of Region B and the lower limit of Region C. Clearly, the
minimum step size is the most important as it determines the limits of effective control, as well as the amplitude of a potential limit
cycle. Under normal conditions of regulatory control, the controller output transitions through Regions A and B and far enough into
Region C to cause the control valve system to respond and allow feedback control to occur. The amount of penetration into Region C
varies inversely with process gain, and directly with controller gains and process noise. If the process gain is high, the tuning fast and
the process noise substantial, the controller output will continually be making changes that are large enough to be inside Region C all
the time. In this case there will be no limit cycle and the control valve system will not impact control performance in any adverse way.
The minimum step size determines where the lower limit of Region C should occur. It in turn depends on the size of the valve
nonlinearities (dead band, step resolution, total hysteresis) in Region A, as well as the size of Region B. If the user wants to have a
tighter minimum step size, this determines Region B. In turn it also requires tighter limits to be set for the nonlinear parameters in
Region A. Roughly a factor of two can be applied to the total hysteresis (Region A) in order to estimate a feasible value for the
minimum step size, although this is clearly very dependent on the design of the valve system. Alternatively, the total hysteresis must be
smaller than the specified minimum step size, and a factor of one half can be used to estimate a reasonable total hysteresis limit from
the minimum step size.
Selection of the maximum step size is far less important for regulatory control. The maximum step size determines the ability of the
control loop to handle large changes with consistent dynamics as well as small ones. Large step changes occur only at certain times,
such as when the control loop is responding to major setpoint changes, large disturbances or some form of sequence such as process
start-up, shutdown or product transition. In-process testing will not normally allow step sizes larger than some practical limit, such as
10%, to be applied under process operating conditions. Hence, under these conditions it is only possible to imply conformance for large
step changes by extrapolation. For instance, if T86 as measured, is well below the specification limit and is decreasing as step changes
increase (see Figure 4), then it is likely that it will also meet specification for 10% and possibly even for 50% changes.
This concept is illustrated in Figure 4, which shows how the step response time T86 might vary with step size for a given pneumatic
valve. For very small step sizes, T86 is expected to be very long. In fact in Region A where no motion occurs, T86 is infinitely long. In
Region B, it is expected that small step changes will cause ever longer dead times. As the step size becomes larger, T86 is expected
to become much smaller. Then as the step size becomes larger still, T86 is expected to become progressively larger as the valve
system becomes velocity limited. In the example of Figure 4, the user specified parameters are consistent with the default values for
minimum and maximum step size (2% and 10%), as well a control loop speed of response (λ) of 10 seconds, which calls for
“consistent movement” as follows:
1. T86 less than 4 seconds for step sizes ranging from 2.0% to 10%. Since in Figure 4 the T86 vs. step size curve crosses 4 seconds
at a step sizes of 1.4% and 15.9%, this requirement is far exceeded.
2. A travel gain of 1.0 +/- 0.2 for all of the step changes specified in 1. above.
3. An overshoot of less than 20% for all of the step changes specified in 1. above.
6
Copyright EnTech 1998 – All Rights Reserved
14
T86 seconds
Test Results
12
10
User Min Step Size
= 2.0 %
Region C
User Specification
Actual - based on tests
Consistent Movement
8
6
T86 < 4 sec
0.8 < Travel Gain < 1.2
Overshoot < 20%
Minimum step size found by test
User Max Step Size
= 10 %
Region D
Velocity
Limit
4
2
0
0 2 4 6 8 10 12 14 16 18
T86 Max Spec = 4 seconds
T86 vs. Step Size
Step Size %
Figure 4 – Region C – Consistent Responses
Figure 4 also illustrates how the user specification of minimum and maximum step sizes may differ with the actual performance of the
control valve system. Clearly the example of Figure 4 exceeds the minimum and maximum step size specifications, which for
illustration use the specification default values of 2% and 10%. The example valve actually conforms to 1.4% and 15.9%. The Actual
minimum step size is the boundary between Regions B and C. This value is the real measure of the control valve system nonlinear
performance and is measured during the testing.
Figure 4 illustrates the expected results for a typical pneumatic valve only. Other results are also possible. A fixed speed electrically
actuated valve is expected to have a fixed dead band when due to the fact that the motor must be deactivated when the valve is at rest.
When the valve is moving it will do so at fixed speed. This translates into a characteristic that would parallel the Region A demarcation
line in Figure 4 to a minimum T86 value for the smallest step change the valve can execute. From this point there would be a line of
rising T86 with step size, which would cross the T86 limit at a T86 value which would be the demarcation between Regions C and D.
The pneumatic valve illustration in Figure 4 assumes that control valve systems have the tendency to have longer T86 values as the
step size becomes smaller at the bottom of Region C. The specification recognizes only four control loop speed of response classes (1,
5, 10 and 60 seconds) with eight T86 limits (0.25, 0.4, 1.25, 2, 2.5, 4, 15, 24) which in turn are a function of dead time. These limits
have been designed to handle typical pneumatic valve characteristics. As control valve system designs continue to improve, this may
no longer be the case. In an ideal design, as soon as the valve starts to move for the smallest step size possible (Region A upper limit),
it will do so at a T86 which is well below the T86 limit for the speed of response class. In this case the testing methods should record
the longest T86 observed, as this is a real measure of the true performance of the control valve system.
3.1.2 Control Valve System Step Response Performance Index - Weighting Factor W
7
Copyright EnTech 1998 – All Rights Reserved
Loading...