PCI1

Note: The source of the technical material in this volume is the Professional

Engineering Development Program (PEDP) of Engineering Services.

Warning: The material contained in this document was developed for Saudi

Aramco and is intended for the exclusive use of Saudi Aramco’s employees. Any material contained in this document which is not

CONTENTS PAGE

STANDARD PROCESS CONTROL TERMINOLOGY ... 1

Purpose And Role Of Standard Control Terminology... 1

History Of Standards Organization ... 1

SAMA - Scientific Apparatus Makers Association... 1

ANSI - American National Standards Institute (of ASME)... 1

ISA - Instrument Society Of America... 1

API - American Petroleum Institute ... 2

Standard Process Control Terms ... 2

CONTINUOUS CLOSED LOOP CONTROL ... 7

History of Control ... 7

Hardware Software Evolution ... 8

Consequences of Open Loop Control ... 9

Advantages of Closed Loop Control ... 10

Increased productivity... 10

On Spec Products ... 10

Energy and Material Conservation ... 10

Safety... 10

Types of Control... 11

Continuous Control... 11

Sequential... 11

Batch... 12

DETERMINING CONTROLLER ACTION REQUIRED FOR NEGATIVE FEEDBACK... 13

Elements in Series ... 16

Direct Acting Elements In Series... 16

Control Valves... 18

Valves... 18

Valve Plugs... 19

Pneumatic Valve Actuators And Plugs... 20

Transmitters ... 22

Processes ... 23

Energy Flow Process ... 23

Mass Flow Process ... 25

Select Control Action Per Application ... 27

Rule for Achieving Negative Feedback ... 28

Additional Benefits of Open Loop Data... 30

IDENTIFYING ACCEPTABLE NEGATIVE FEEDBACK LOOP RESPONSES ... 31

Loop Gain and Loop Response ... 33

Steady State Gain (K) ... 34

Magnitude of Total Gain Vector (KG or / → G _{/) ... 34}

Total Gain Vector → G     _{... 35}

Phase Shift (f) ... 36

Dynamic Response Based on the Gain Function... 37

STANDARD PROCESS CONTROL TERMINOLOGY Purpose And Role Of Standard Control Terminology

The purpose of having standards for measurement and control terminology is to define uniform terminology in the process control and instrumentation field. This allows people in the instrumentation and control industry to communicate more efficiently. Also, by defining standard terms and definitions for the Industrial Measurement and Control field it facilitates user and vendor understanding and interpretation of product specifications.

History Of Standards Organization

SAMA - Scientific Apparatus Makers Association

SAMA PMC 20.1-1973 ("Process Measurement and Control Terminology") - This particular

document applies to the terminology associated with industrial process instrumentation and control used in various industries, including petroleum. The terminology defined consists of common terms used in measurement and control.

SAMA PMC 22.1-1981 ("Functional Diagraming of Instrument and Control Systems")

-Presents both symbols and diagramming format for use in representing measuring, controlling and computing systems as used in the process industry. This document is still popular in boiler applications.

ANSI - American National Standards Institute (of ASME)

ANSI C85.1-1963 ("Terminology for Automatic Control") - Published by the American

Society of Mechanical Engineers.

ISA - Instrument Society Of America

ISA-S51.1-1979 ("Process Instrumentation Terminology") - This Standard consists of terms selected primarily from SAMA Standard PMC 20.1-1973 and the ANSI Standard

C85.1-1963. Additional terms have been selected from other recognized standards.

This ISA Standard is probably the most widely accepted in the process measurement and control industry.

ISA-S5.1 ("Instrument Symbols and Identification") - This standard establishes a uniform means of designating instruments and instrumentation systems used for measurement and control. The designation system includes symbols and an identification code.

API - American Petroleum Institute

API RP 550 ("Manual on Installation of Refinery Instruments and Control Systems") - These

specifications (standards) published by API are recommended practices prepared to aid people involved in the petroleum industry. The aim of the document is to assist the user in the proper installation of measuring and control instrumentation in order to achieve the best results.

API RP 550 consists of the following four parts:

Part I Process Instrumentation and Control Part II Process Stream Analyzers

Part III Fired Heaters and Inert Gas Generators Part IV Steam Generators

Standard Process Control Terms

The following standard measurement and control terms are commonly used in the process control and instrumentation field.

Process. Is defined as a physical or chemical change of matter or conversion of energy; e.g., change in pressure, temperature, speed, electrical potential, etc. A second definition of a process from a Chemical Engineering point of view is as follows: a process is a collection of vessels, pipes, fittings, gauges etc., built for the purpose of producing a product or group of products.

Process Control. The regulation or manipulation of variables influencing the conduct of

a process in such a way as to obtain a product of desired quality and quantity in an efficient manner.

The reason for having a process is to make a product. To do so you have to put something into the process. The input is the material and energy required to make the product.

Input to Process. Mass or energy applied to the process.

Output of Process. The product delivered by the process. This is a dynamic variable. Supply. Source of mass or energy input to process.

Control Valve. Consists of the final actuator and final controlling elements. This is the forward controlling element which directly changes the value of the manipulated variable.

Load. Anything that affects the value of the controlled variable under a constant supply

input.

Open Loop. Control without feedback. Open loop can not cope with load upsets.

Example of open loop: automatic dishwasher, automatic water sprinkling system, a control loop with the controller in manual.

PROCESS PRIMARY ELEMENT MASS OR ENERGY SUPPLY HEADER LOAD " q " PRODUCT T ΣΣ TRANSMITTER CONTROLLED VARIABLE CONTROLLED ALGORITHM CONTROLLER OUTPUT MANIPULATED VARIABLE SET POINT ERROR CONTROLLER " m " " e " " r " ( dynamic variable ) " c "

AUTOMATIC FEEDBACK CONTROL LOOP

Primary Element. The measuring element that quantitatively converts the measured

variable energy into a form suitable for measurement.

Note: The sensing portion is the primary element for transmitters that do not have external primary elements.

Transmitter. A transducer which responds to a measured variable by means of a sensing element, and converts it to a standardized transmission signal which is a function only of the measured variable.

Controlled Variable. A variable the value of which is sensed to originate a feedback

signal. (Also known as the process variable.)

Error. In process instrumentation, the algebraic difference between the real value and

ideal value of the measured signal. It is the quantity which when algebraically subtracted from the indicated signal gives the ideal value.

Manipulated Variable. A quantity or condition which is varied as a function of the algebraic error signal so as to cause a change to the value of the directly controlled variable.

Feedback Control. Control action in which a measured variable is compared to its desired value to produce an actuating error signal which is acted upon in such a way as to reduce the magnitude of the error.

Cascade Control. Control in which the output of one controller is introduced as the set

point for another controller.

PRIMARY LOOP PRODUCT T C T C CASCADE CONTROL

( OVERCOMES EFFECTS OF SUPPLY UPSETS )

r₁ r2 m1 m₂ SUPPLY HEADER c1 PROCESS SECONDARY LOOP PE c2

Feedforward Control. Control action in which information concerning one or more

conditions that can disturb the controlled variable is converted, outside of any feedback loop, into corrective action to minimize deviations of the controlled variable.

PROCESS PRODUCT T STEADY STATE MATH MODEL T T LOADS SUPPLY HEADER FEEDFORWARD CONTROL

CONTINUOUS CLOSED LOOP CONTROL History of Control

Instrumentation historically has been used for monitoring or measuring purposes. Examples of instrumentation measurements go back to Roman times and even earlier to Egypt, where orifice plates were used for water distribution in aqueduct systems. Prior to this century however, there was no process industry and not many processes that required control. Obviously at this time, the instrumentation and control companies had not evolved yet, and hardware was not available for this purpose.

In the early part of the twentieth century, production was made through manual operations. Control was achieved manually, by an operator walking through the plant, looking at gauges and opening and closing valves to meet momentary demand. In effect, the operator acted as a controller as he closed the loop. To achieve continuous, closed-loop control, the operator had to stay with the process, continuously making adjustments. The first automatic control application was built to control the speed of a steam engine. James Watt's flyball governor in 1775 was the first automatic control scheme using feedback control.

In the second half of the twentieth century as the need to make more and newer products grew, a new industry, known as the process industry, came into being. The growth of the industry accelerated substantially during World War II, driven by the demand to make more products for the war effort. The demands of the process industry, led to the formation of process instrumentation and control companies whose products were designed to measure, control and regulate processes. Automatic control replaced manual control and evolved continually in its capabilities as more advanced products became available.

Hardware Software Evolution

Some milestones to remember: In the 1930's the hardware used in the industry was mechanical. In order to control a process, it was necessary to directly connect the instrumentation to the process, there was no remote or transmission capability.

In the 1940's pneumatic transmission was introduced enhancing the control capabilities considerably. With pneumatic transmission remote control of processes became a reality along with centralized control rooms. These allowed for the implementation of more sophisticated control strategies, such as feedforward or calculation control. Pneumatics was a major improvement over the directly connected mechanical systems. The speed of sound turned out to be the major limitation for pneumatic transmission. The distance that pneumatic signals could be carried effectively was limited to a few hundred feet. Longer distances were not practical due to the dead time produced through the pneumatic tubing. The delay and additional dead time made control more difficult and sometimes impractical.

This major deficiency of pneumatics was solved in the 1950's with the introduction of electronic instrumentation. Electronic transmission, limited by the speed of light, was considerably faster than pneumatics and allowed transmission over longer distances. Initially electronic hardware was more expensive and considerably heavier and bulkier than pneumatics. In time however, the advantage shifted to electronics as they became more cost effective and more efficient in size and capability. Analog electronics was an improvement over pneumatics; it diminished the use of pneumatic hardware considerably, allowing further centralization of control rooms and implementation of significantly more sophisticated control strategies.

The only disadvantage of electronic transmission related to safety. In those applications where the environment was flammable or explosive, the electrical energy used to power the equipment could cause a hazard, requiring the development of intrinsically (inherently non-incendiary) safe electronic components.

In the mid 1960's, computers and digital devices were introduced to the process industry. The introduction took place slowly and with a lot of reluctance from users who were comfortable with analog electronics; but gradually, the comfort level increased and to-day these devices are widely used with no limit to their capabilities. The early process computers were expensive, unreliable and quite bulky. Initially they were used either in rudimentary supervisory functions or for control purposes with analog backup. In these applications, analog backup controllers took control of the process during computer failure. As the user confidence and hardware reliability increased, the acceptance of computers in the process industry increased and computers were trusted to control processes directly. Direct digital control (DDC) with or without redundancy has been in use for over two decades.

The industrial process control field today, relies heavily on digital instrumentation and control products, with computers in full control of various operations. Today's terminology has increased with words such as "microprocessors," "distributed control systems," and "programmable controllers."

Consequences of Open Loop Control

Open loop control, described earlier, where the operator walked up and down a plant, looking at gauges and opening and closing valves is effective only at the time when the operator moves the valve. At that instant the loop is closed. This will work until the next load change or supply upset occurs. Since the loop is open during the next upset, the product quality will be affected and quite possibly go beyond acceptable specifications (go off-spec).

In conclusion, open loop control works only when the load(s) on the process are constant. Any load change or supply upset can affect the product quality. The most common example of open loop to-day is when an automatic controller is placed in manual. When manual conditions exist, we have the equivalent of an operator looking at gauges and manually opening or closing valves.

Safety is another issue with open loops. When a loop is open, due to the controller being placed in manual, we lose regulatory control, our first line of defense. Depending on the type of process, we could either have a safe operation with the next load upset,or a dangerous unstable situation.

Advantages of Closed Loop Control

As described earlier open loop control is inefficient, it can not handle load or supply upsets and is potentially dangerous. Therefore, the need for closed loop automatic control. Most of the advantages of closed loop automatic control are derived from either economic considerations or safety concerns to plant and personnel. Cost reduction normally improves with automatic control, and the driving force for various optimization techniques within automatic control, generally tend to improve profitability.

Increased productivity

Automatic closed loop control allows the amount of products made in a particular process to be maximized.

On Spec Products

Industrial products are produced to meet certain purity levels. (Specific physical and chemical properties). Off-Spec products decrease the profitability. If the product is bellow the specification, it has to be reprocessed or blended with above-spec product. On the other hand, if it is above specification, excessive energy was used in its production.

Energy and Material Conservation

A closed loop control application minimizes the amount of material and energy used in production. Optimizing the control loop provides additional savings.

Safety

In most plants there are certain processes where safety is of paramount concern, because of the potential risk of fires, explosions or toxic chemical gas releases. The concern for safety extends to personnel as well as process vessels. Closed loop control is the first line of defense before Emergency Shutdown Devices (ESD) override regulatory control devices.

Types of Control

Continuous Control

Continuous control is used on continuous processes. A continuous process is one in which process material is continually flowing through the process equipment. Continuous processes are usually measured by analog devices and controlled by digital controllers, although digital signal transmitters are being introduced by many vendors.

Continuous control can be as simple as maintaining a flow rate or pressure in a single pipeline, or as complex as control of an entire distillation column or hydrocracker.

Continuous control involves the continuous measurement of a process variable via an analog device and the adjustment of a final control element (such as a control valve) to keep the process measurement at a desired value. Process values are maintained close to their targets or setpoints despite changes in the process or process upsets. Disturbances in the process caused by changes in feed composition and rate, fuel gas composition, or pressure are kept to a minimum.

Continuous control is used predominately throughout the Company's refinery, gas plants, GOSPs and pipeline facilities.

Sequential

Sequential control is often referred to as on/off control. It is a series of discreet control actions performed in a specific order or sequence. These actions can be the opening or closing of valves or the starting or stopping of devices. The control actions can be initiated by either an operator or a process condition or as a result of the passage of a given period of time.

Sequential control is often used at the Company's offshore and pipeline locations for valve line-up sequencing and pump compressor startup/shutdown. Examples of non-oil-related sequential control can also be found within the Company's refinery applications. The applications within the refinery and process plants handle process utilities such as dehydration operations and process metering.

Batch

Batch control is a combination of sequential and continuous control. A batch process is a process where the operation is time-dependent and repeatable. The similarity between a batch process and a continuous process is that both processes can be time-dependent; however, in a continuous process, startup theoretically occurs only once. In a batch process, a sequence of events is repeated over and over again. For example, consider a reactor and a series of storage tanks. Ingredients or reactants are charged into the reactor vessel, left to react, separated, and then sent to storage. Once this sequence of events is complete, the sequence starts all over again from the beginning. The sequence can be simple or complex, and can entail hundreds of sequence steps.

Continuous control takes place within the individual steps of a batch; for example, temperature is controlled while a reaction takes place. Sequential control is used to move between the steps of the sequence. For example, a sequence of valve and pump manipulations must take place to transfer the contents of the reactor to another vessel.

DETERMINING CONTROLLER ACTION REQUIRED FOR NEGATIVE FEEDBACK

There are two ways in which a loop can be closed. Positive feedback and negative feedback. Special care should be taken to make sure that the loop is designed to operate in the negative feedback mode of operation. This is unconditional, meaning all automatic feedback loops, have to be set up this way. At this point we should define positive and negative feedbacks.

Positive Feedback

In a closed loop, positive feedback can be defined as the control action in which the error is reinforced until a limit is eventually reached. This obviously is not a desirable outcome of control action and should be avoided. To illustrate positive feedback, imagine a tank in which level is being controlled. When the level exceeds the set point, the control action will increase the level further until the tank overflows. In the opposite direction, if the level falls below the set point, the control action will allow the tank to run dry.

Consider positive feedback in an air conditioning application. It will not be too comfortable, since the system will operate when the temperature falls below set point and drive the temperature to the minimum value that it can. If the temperature is above the set point the cooling system will not come on, allowing the temperature to reach maximum value.

Positive feedback must be avoided.

Negative Feedback

In a closed loop, negative feedback can be defined as the control action in which the error is minimized, made as small as possible, depending on the algorithm of the controller. This obviously is a desirable outcome of the control action and should be achieved in all feedback loops. In the tank example with negative feedback, if the level

exceeds the set point, the control action will bring the level down. In the opposite direction, if the level falls below the set point, the control action will be to increase the level. The achievement of negative feedback depends on the overall action of the elements of the loop. Every loop is made up of several elements.

Each element has an action which can be described as direct or reverse, sometimes referred to as Increase/Increase(I/I) or Increase/Decrease (I/D)

Direct Acting Element

A direct acting element is one in which the value of the output signal increases as the value of the input signal increases. The value of the input and output signals have the same direction.

DIRECT ACTING ELEMENT ( INCREASE / INCREASE )

IN I OUT

I

I

III

Reverse Acting Element

A reverse acting element is one in which the value of the output signal decreases as as the value of the input increases. The input and output have opposite directions.

REVERSE ACTING ELEMENT ( INCREASE / DECREASE )

IN I OUT

I

I

Elements in Series

When a number of elements are combined together such as in a control loop they are said to be, "in series." See Figure 1. The overall action of these elements dictates whether the loop is set up as negative feedback. For negative feedback, the combination of the elements has to result in an overall reverse action. See Figure 2.

Direct Acting Elements In Series

COMBINATION OF DIRECT ACTING ELEMENTS

I II I II I II I II I II I II I II I II I II I II III I II I II I II I II I II I II I II

COMBINATION OF REVERSE ACTING BLOCKS I II D I II D I II D I II D I II D I II D FIGURE 2

Control Valves

A control valve consists of a valve connected to an actuator mechanism. The actuator, in response to a signal from the controlling system, can change the position of a flow-controlling element in the control valve.

The action of the final actuator is the first choice and is based on:

"Fail-Safe Control Valve Action". This is not a control consideration but a fail-safe consideration which depends on the given process and comes from answering the following question. Where should the final actuator and final control element go if there is a failure with the air or utility supply system? The choice of failure positions are as follows, open, closed, and in place.

Valves

The most common final flow-controlling element is the valve. Valve action is analyzed in the diagram below:

STEM POSITION (INPUT)

FLOW (OUTPUT)

The input of the valve is the stem position, while the output is the flow. To illustrate valve terminology , consider the valves we use at home. See Figure 3. If you increase the stem position, by opening the valve, you increase the flow through the valve. So the valves (faucets) are direct-acting valves.

Valve Plugs

The valve plug itself can be direct or reverse acting.

FLOW

PLUG

DIRECT ACTING PLUG REVERSE ACTING PLUG

FLOW

STEM STEM

Pneumatic Valve Actuators And Plugs

The most common valve in use is the air-operated pneumatic valve (shown below).

Air signals coming from either a pneumatic controller or a current-to-air converter enters the valve motor and provides a force on the actuator diaphragm. The force works against the spring force and tends to open the valve by moving the stem upwards. This type of valve is known as Air To Open (ATO), or Direct-Acting Valve and it fails closed as shown in Figure 4.

FIGURE 4

AIR TO OPEN VALVE ( FAILS CLOSED )

STEM MOVEMENT PLUG SPRING SPRING FORCE AIR PRESSURE - 3 - 15 PSI RUBBER DIAPHRAGM FLOW AIR FORCE

In the air to close valve the forces are reversed, as the air signal tends to close the valve and its failure mode now is Fail Open as shown in Figure 5.

AIR TO CLOSE VALVE ( FAILS OPEN )

FIGURE 5 STEM MOVEMENT AIR FORCE RUBBER DIAPHRAGM SPRING FORCE AIR PRESSURE IN

Another way to achieve direct or reverse action in a valve is through the use of a valve positioner. This would be discussed in PCI 102.02.

Transmitters

Transmitters can be set up (calibrated) as either direct acting or reverse acting. The input of a transmitter is the measurement span and the output is 0 to 100 %. If the output of a transmitter increases as its input increases, the transmitter is direct acting. If the input increases while the output decreases, the transmitter is reverse acting. Most transmitters are set up to be direct acting. See Figure 6.

100% OUTPUT 0% DIRECT ACTING TRANSMITTER REVERSE ACTING TRANSMITTER

T

Processes

Processes can be either direct or reverse acting. Most processes are direct acting.

Consider the following processes.

Energy Flow Process

1. Heat Exchanger

In this process, the input is steam flow and the output is temperature. If the steam flow increases, the temperature or the output will increase, making this a direct-acting process.

2. Refrigeration

In this process, the input is refrigerant and the output is temperature. If the refrigerant flow increases, the temperature or the output decreases, making this a reverse-acting process.

Mass Flow Process

1. Level Tank

PROCESS – MASS FLOW

LEVEL TANK LT LEVEL OUTPUT FLOW IN INPUT FLOW OUT

In this process, the input is flow in and the output is level. If the flow input increases, the level output increases, making this a direct acting process.

2. Pipe Flow FLOW IN INPUT PRESSURE OUTPUT P SUCTION PIPE PROCESS - MASS FLOW

TO PUMP INLET

In this case the process is a pipe on the suction side of a pump (or compressor) and our interest is to control the suction pressure to prevent cavitation or surge. In this process the input is flow and the output is suction pressure. If the flow rate increases, the suction pressure decreases, making this a reverse acting process.

Select Control Action Per Application

The selection of the controller action depends on the action of the elements in the loop. Controller action is a selectable item. In analog hardware the selection is done through a switch, either direct or reverse. In digital applications the choice is made in the configuration process of the controller.

The action of the controller depends on how the error is calculated. The error (e) is the difference between measurement (c) and set point (r). This error calculation can be done in two different ways. The

Σ

e = r - c This is reverse action

e = c - r This is direct action

m

e

_r

c

e = r - c

e = c - r

•

To decide the action of the controller, start with the chosen valve action and consider the action of each element in the loop, and finally select the controller action for

Rule for Achieving Negative Feedback

To achieve negative feedback in a control loop you must have an odd number of

reverse acting elements in the loop.

CONTROLLER

T

m

r

c

I/I

I/I

I/I

I/I

I/

D

In the loop shown above, the controller must be set in a reverse acting, I/D mode to provide the odd number of reverse acting elements for negative feedback.

CONTROLLER

T

m

_r

c

I/I

I/

D

I/I

In this loop since the odd number of reverse acting elements already exists in the elements external to the controller, the controller must be set up in a direct acting mode I/I for negative feedback.

The odd number of reverse-acting elements for negative feedback can be determined through an open loop test, conducted in the following manner. Place the controller in manual (open loop), and step up the output of the controller (5-10%) and observe (record) the output of the transmitter. The information obtained allows us to determine whether the combined effect of the valve, the process and the transmitter is direct or reverse action, and select the necessary controller action for negative feedback.

(NOTE: Another approach is to consider a feedback loop as though it was made up of two elements, the controller and a process, made up of the final actuator, the process and the transmitter as shown below:)

OPEN LOOP TESTING

CONTROLLER PROCESS

T

m

r

c

IDENTIFYING ACCEPTABLE NEGATIVE FEEDBACK LOOP RESPONSES

Now that we have built a negative feedback loop let us investigate the identification of these loop responses. Keeping in mind that we have closed the loop in order to take care of load upsets, we subject the loop to step-load upsets and observe the responses. The diagram in Figure 7 shows the possible responses of a feedback loop. Note: C4 and C5 are not acceptable responses. (To simulate a load change, put the controller in manual, change the output, and go back to automatic.)

OVERDAMPED CRITICALLY DAMPED UNDERDAMPED CONSTANT AMPLITUDE CYCLING INCREASING OSCILLATION

STEP - LOAD UPSETS

q_I t r r r r r L G L G L G L G L G q₀ C C C C₅ 4 3 C₂ 1 q LOAD << 0.5 = < 0.5 - 0.5 = 1 - 360° > 1 - 360°

The loop designed to handle load upsets frequently handles supply upsets and set-point changes, also. How well it handles set-set-point changes depends on the linearity of the loop. The controller has no idea what causes an error, it acts on any error regardless of whether it is caused by a set-point change or a load change. Its action depends on various controller adjustments (tuning). It is possible to adjust the feedback control loop to give you any one of the responses shown. Which one of these is the best response, depends on the particular process being controlled and the desired response. See Figure 8. Except for unacceptable C4 and C5 responses shown below, each of the other responses could be justified.

r₁ c₁ c₂ c₃ c₄ c₅ r₂ r₁ r₂ r₁ r₁ r₂ r₂ r₁ r₂ r₁ FIGURE 8 r₂

Loop Gain and Loop Response

The dynamic responses (obtained in Figures 7 and 8) depend on the total loop gain vector of the open loop. Recalling that a vector has magnitude as well as direction, we can say that the dynamic responses depend on the magnitude and phase of the open loop gain vector. By making controller gain adjustments, it is possible to change the loop gain and obtain any one of these responses.

Let us investigate how this can be done by defining the various gain terminology along with its relationship to the open loop gain.

The gain of an element may be defined in several ways. One definition simply states that the gain of an element is the ratio of change of output over the change of input.

Gain = D(Output)_D(Input)

The above expression does not completely define gain.

Gain G→ is a vector, having magnitude and direction. A more complete definition of gain is as follows:

G

→

= KG–f

i.e., the gain function is made up of three components: K, is the steady-state gain; G is the scalar portion of the dynamic gain; and f, is the phase shift across the device.

We will see that every element in the loop, i.e., the process, transmitter, controller, or final controlling element, can be fully characterized by this gain function.

Steady State Gain (K)

The steady state gain of an element is the ratio of the output amplitude to the input amplitude when both are time invariant. It can be determined as follows:

K K = A B STEP INPUT STEP OUTPUT

...

K is a scalar value. Just a number, with no associated phase shift.

Magnitude of Total Gain Vector (KG or /

→ G _/)

The magnitude of the gain of a device is the ratio of the output amplitude to the input amplitude when the input signal is time varying or sinusoidal.

G SINUSOIDAL INPUT SINUSOIDAL OUTPUT A B

Total Gain Vector

→ G    

The total gain vector of an element, →

G_{, may be calculated as follows:}

→

G ₌ d/dt [Output]

d/dt [Input]

To determine, the total gain vector →

G_{, subject the element to a sinusoidal input and}

observe the sinusoidal output. The ratio of the derivative of the output to the derivative of the input is the total gain vector,

→ G_. A ELEMENT B

t

t

τ

Input A sin wot Output B sin wot

A sin _2p_{to t} B sin _2p_{to t} Æ_G = d [B sin wot]/dt_{d [A sin wot]/dt} = Bwo cos wot_{Awo cos wot}

B

A cos w t - cos w to o

= B_A O°

Phase Shift (f)

Phase shift or phase angle, f, is the difference in phase between the input signal and the output signal. Depending on the device this angle may be a phase lead (positive angle) or a phase lag (negative angle).

e.g.

Φ

Φ

− Φ

− Φ

Φ

Φ

This is a phase lag, i.e., the output is a negative phase angle with respect to the input.

e.g.

Φ

Φ

+ Φ

+ Φ

This is a phase lead where the output is a positive phase angle with respect to the input.

Dynamic Response Based on the Gain Function

If every component in our control loop is defined by a particular gain function, we can now define a gain function for the entire loop. This gain is called the loop gain (short for open loop gain). It is a dimensionless number defined as the product of the component gain functions.

i.e. Æ_GL = Æ_GT x Æ_GC x Æ_GV x Æ_GP where Æ_GL = gain function of the loop

Æ

GT = gain function of the transmitter Æ

GC = gain function of the controller Æ

GV = gain function of the valve Æ

GP = gain function of the process

and if each of these gains is of the form G = KG–f, then the loop gain may be rewritten as: Æ GL = KL GL –fL Æ GL = KT GT –fT x KP GP –fP x KV GV –fV x KC GC –fC KL GL –fL = (KT×KP×KV×KC () GT×GP×GV×GC ) φT+ φP+ φV + φC

The loop can have oscillatory response (uniform oscillation), fL = nx (-360°), i.e. if the phase shift around the loop is -360° or some integrable multiple of -360°. If the phase shift around the loop is not -360° or a multiple of -360°, response will have some damping and will not reach the limit of stability. We will see, unfortunately, that every real process is capable of oscillatory response. If this were not true then instability would not be a problem.

Refer to Figures 7 and 8 and qualify the responses shown with the following open loop gain values.

C1 overdamped response ½Æ_GL ½ <<0.5 C2 critically damped response ½Æ_GL ½ <0.5 C3 underdamped response ½Æ_GL ½ ª0.5 C4 uniform oscillation Æ_GL = 1 –-360°

C5 unstable Æ_GL > 1 –-360°

Now that the responses are qualified, we can see that uniform oscillation will occur at a phase of -360°. The damped responses will eventually stabilize. The time it takes to reach steady state will depend on the magnitude of the loop gain and the particular process characteristics. The damped responses have phases of less than -360°. All damped loops have a phase margin, that is the difference between -360° and the actual loop phase; eg., if f = –-345°, there would be a phase margin of 15°. This means the loop will damp and reach steady state.

Dynamic Response as a Function of Loop Phase Shift

For oscillatory response to take place, the phase shift around the loop must be -360°, and each component in the loop makes some phase contribution to this -360°. If the fL < -360°, there is no danger of oscillation and our loop gain can be as great as required, i.e. GL>>1: the greater the loop gain, the tighter the control. The only limiting factor is that in a real process there is always the necessary -360° phase shift to result in instability if the loop gain exceeds 1.

CONTROLLER

ALGORITHM

ΣΣ

m _e

c

r

Depending on the process, the control algorithm may vary. Phase contribution by the control algorithm depends upon the algorithm employed and particular settings.

Let's consider the summer for a moment. This portion of the controller is present regardless of the control algorithm employed and in all products, analog to digital.

ΣΣ

–

+

Considering the output of the summer to be the error signal e, and the input to be the measurement c we can investigate the phase shift across the summer. See Figure 9. Assume some set point, r, and compare the phase for direct and reverse actions.

0% +50% FIGURE 9 r = 50% 50% -50% 0% r c e e = r - c e = c - r

If S in reverse action (I/D); fS = -180°

If the input c varies as shown, we see the error varying also. However, notice that the phase difference between the error and measurement c is -180°; i.e. there is a -180° phase lag between the input and output of the summer. Since the summer will always be present, we can see that -180° of the -360° necessary for oscillatory response has already been supplied by the summer. This is true if the controller is I/D. If it is I/I, this -180° is supplied by some other loop component.

If the controller is in I/I or direct action, we see a 0° phase between measurement and error. In this case the entire -360° has to come from other loop components, including the controller algorithm.

The phase contributions by the remaining components, i.e. the final actuator, process, transmitter and control algorithm will be considered in future modules.

WORK AID 1: PROCEDURE FOR DETERMINING REQUIRED CONTROLLER ACTION FOR NEGATIVE FEEDBACK

Rule For Negative Feedback

For a feedback loop to be of the negative-feedback type there must be an odd number of reverse acting (I/D) elements in the loop.

The procedure(s) for determining controller action requires the finding of all the other elements' actions and selecting the controller action to get an odd number of reverse-acting elements.

Procedure # 1

Put an input on each element. Observe the output and record the action of each element.

Control valve action

Process action

Transmitter action

Procedure # 2

Obtain a process reaction curve using the following steps.

1. Let the system stabilize at the normal operating point (set point and load at normal).

2. Open the loop up by placing the controller in manual. The output should hold at the same value as in Step 1.

3. Make sure the system is at steady state, the output and the controlled variable maintaining their values.

4. Introduce a small disturbance by manually stepping up the output of the controller.

5. Record the reaction of the controlled variable. Use a fast speed recorder at the output of the transmitter (in the order 1 in./min.).

6. Bring the output back to the normal operating point and switch to auto.

CONTROLLER IN MANUAL PROCESS

T

PID

e

r

_•

If the process reaction curve is as shown in this diagram the conclusion is as follows: the combination of final actuator, process and transmitter is direct acting. The controller must be placed in reverse action for negative feedback. On the other hand,

WORK AID 2: IDENTIFICATION SUMMARY OF ACCEPTABLE NEGATIVE FEEDBACK RESPONSE TYPES

The open loop gain dictates the response of a negative feedback loop.

The magnitude of the open loop gain is the product of the gains of each of the elements in the loop and should be a dimensionless number.

      Æ GL =      Æ GV x      Æ GP x      Æ GT x      Æ GC Æ

Thus, the value of G dictates the response.

The subsequent pages of this Work Aid have a summary of all the responses possible due to a step-load change or a step set point change.

NOTE: The only acceptable responses are C1, C2, C3 and CQAD.

Constant amplitude cycling C4 or increasing oscillation C5 are not acceptable.

C1 OVERDAMPED RESPONSE       Æ GL << 0.5 C2 CRITICALLY DAMPED RESPONSE ½Æ_GL ½ < 0.5

C3 UNDERDAMPED RESPONSE _ _

Æ

GL ª 0.5

CQAD QUARTER AMPLITUDE DECAY _ _

Æ GL = 0.5 A A/4 A/16 C_QAD *C UNIFORM OSCILLATION Æ 

OVERDAMPED CRITICALLY DAMPED UNDERDAMPED CONSTANT AMPLITUDE CYCLING INCREASING OSCILLATION

STEP - LOAD UPSETS

q I t r r r r r L G L G L G L G L G q₀ C C C C₅ 4 3 C₂ 1 q LOAD << 0.5 = < 0.5 - 0.5 = 1 - 360° > 1 - 360°

r₁ c₁ c2 c₃ c4 c₅ r₂ r₁ r2 r1 r1 r₂ r₂ r1 r₂ r₁ r2

GLOSSARY

cascade control Control in which the output of one controller is the set point for another controller.

closed loop Several automatic control units and the process connected so as to provide a signal path that includes a forward path, a feedback path, and a summing point. The controlled variable is consistently measured, and if it deviates from that which has been prescribed, corrective action is applied to the final element in such direction as to return the controlled variable to the desired value.

control loop Starts at the process in the form of a measurement or variable, is monitored, and returns to the process in the form of a manipulated variable or "valve position" being controlled by some means.

controlled variable In a control loop, the variable the value of which is sensed to originate a feedback signal.

controller A device which operates automatically to regulate a controlled variable.

controller algorithm (PID)

A mathematical representation of the control action to be performed.

DCS Acronym for Distributed Control System.

DDC Acronym for Direct Digital Control wherein a computer

performs all the functions of error detection and controller action.

error In process instrumentation, the algebraic difference between the indication and the ideal value of the measured signal. It is the quantity which algebraically subtracted from the indication gives the ideal value.

feedback control Control in which a measured variable is compared to its desired value to produce an actuating error signal which is acted upon in such a way as to reduce the magnitude of the error.

feedforward control Control in which information concerning one or more conditions that can disturb the controlled variable is converted, outside of any feedback loop, into corrective action to minimize deviations of the controlled variable.

final actuator (or final controlling element)

The forward controlling element which directly changes the value of the manipulated variable.

gain (magnitude ratio) The ratio of change in output divided by the change in input that caused it. Both output and input must be expressed in the same units, making gain a pure (dimensionless) number.

input to process Mass or energy applied to the process.

instrument In process measurement and control, this term is used broadly to describe any device that performs a measuring or controlling function.

instrumentation The application of instruments to an industrial process for the purpose of measuring or controlling its activity. The term is also applied to the instrument themselves.

intrinsically safe equipment and wiring

Equipment and wiring which are incapable of releasing sufficient electrical or thermal energy under normal or abnormal conditions to cause ignition of a specific hazardous atmospheric mixture in its most easily ignited concentration.

loop gain The combined output/input magnitude ratios of all the individual loop components multiplied to obtain the overall gain.

manipulated variable A quantity or condition which is varied as a function of the actuating error signal so as to change the value of the directly controlled variable.

margin gain The sinusoidal frequency at which the output/input magnitude ratio equals unity and feedback achieves a phase angle of -180 degrees.

open loop Control without feedback; for example, an automatic sprinkler or an automatic washing machine.

output of process A product related signal delivered by the process.

overdamped Damped so that overshoot cannot occur.

overshoot The persistent effort of the control system to reach the desired level, which frequently results in going beyond (overshooting) the mark.

phase The condition of a periodic function with respect to a reference time.

phase difference The time, usually expressed in degrees, by which one wave leads to or lags another.

primary element The system element that quantitatively converts the measured variable energy into a from suitable for measurement.

process Is defined as a physical or chemical change of matter or conversion to energy; e.g., change in pressure, temperature, speed, electrical potential, etc. A second definition of a process from a Chemical Engineering point

process control The regulation or manipulation of variables influencing the conduct of a process in such a way as to obtain a product of desired quality and quantity in an efficient manner.

reaction curve In process control, a reaction curve is obtained by applying a step change (either in load or set point) and plotting the response of the controlled variable with respect to time.

response Reaction to a forcing function applied to the input; the variation in measured variables that occurs as the result of step sinusoidal, ramp, or other kind of input.

set point An input variable which sets the desired value of the controlled variable.

stability That desirable condition in which input and output are in balance and will remain so unless subjected to an external stimulus.

static gain (zero-frequency gain)

The output/input amplitude ratio of a component or system as frequency approaches zero.

steady state A state in which static conditions prevail and all dynamic changes may be assumed completed.

step change A change from one level to another (ideally in zero time.)

supply Mass or energy input to process.

transmitter A transducer which responds to a measured variable by means of a sensing element, and converts it to a standardized transmission signal which is a function only of the measured variable.