Implementing the Basic Regulatory Control

I.Objective

The objective of this article is to correlate control systems in theory and real practice through calculation by using available data from engineering documents.

II. Background

Throwback, it was the writer’s responsibility to design, and programmed, both HMI and PLC. The objective was to control fuel gas as a supply to the generator power plants.

In the initial condition, the pressure is controlled using a pneumatic controller. The electronic controller was introduced as backup and improved pressure control.

The control valve regulates fuel gas is to maintain the minimum pressure and flow rate requirement of the power generator. The objective to control pressure downstream is to meet the requirement of power generation. If the pressure is not controlled and tends to be high it will not meet the requirement.

The control valve functions as regulator pressure (reducing pressure) while limiting the maximum flow rate. The basic controller is PID. The selector of two controllers is based on the maximum setpoint either flowrate or pressure operates as a high selector. Therefore one control valve will have 2 controllers i.e., pressure control loop (PIC) and flow control loop(FIC). The input was pressure. It is to control downstream pressure. The control valve act as pressure reducing. It is placed after the control valve between 3D-5D. The pressure loop for gas pressure can be characterized as fast and noise-free. While, the flow loop can be characterized as relatively fast, nonlinear, and often noisy.

The usual application for this type of situation is that one process variable controlling variable during normal operation. In the event of abnormal operation, however, some other process variables should be limited. The limiting controller is said to “override” the normal process controller, hence, this technique is often termed “override control”.

Control method for high selector using electric controller could be implemented directly using the program. Another scenario to limit flow rate is using a mechanical stopper. It is often used for pneumatic controllers but still applicable for an electronic controllers. However, the mechanical stopper is more feasible if it is already purchased initially. Installation mechanical stopper in the middle cycle of the valve will have to consider many things and consult with the control valve manufacturer.

The setpoint between FIC and PIC should be bumpless transfer. Bumpless transfer means that transition is based on the latest position of output.

II. BLOCK DIAGRAM

As in general PID block diagram. As seen below. It uses feedback control. to control the fluid parameter.

Since the pressure and flowrate controller doesn’t interact with each other. It could be considered as a separate controller. Therefore we could evaluate each loop with a different setting value.

The writer’s objective is to implement value from theory to actual. To create a seamless integration between theory and actual in order for control theory to work on the plant. Let us walk through all blocks.

III. PROCESS

III.1 Process Dynamic Model

III.1.2. Degrees of Freedom

The number of degrees of freedom for a system is defined as

The first step is to identify the system. All models will be approached using mathematical models to predict a system’s behavior. Many process models are based on the ideal first-order plus dead-time(FOPDT). The FOPDT is commonly used for single-input, single-output (SISO) loops.

DOF = NV- NE,

with DOF equal to the number of freedom, NV equal to the number of dependent variables, and NE equal to the number of independent equations.

NV, equal to the number of dependent variables, and NE is equal to the number of independent equations.

III.1.2.a Pressure Control

III.1.2. b. Flow Control

Manipulated Variables	Description
flowrate (Q) =38.3	Volumetric Flowrate (MMSCFD)
Independent Variables	
rho = 1000	Density of water (kg/m3)
gravity = 9.8	Gravity (m/s2)
Differential States	
Qset	36 MMSCFD

III.1.3 Balance Equations

Overall Material Balance

In ideal state Qin = Q out, however since we will consider loss flowrate due to friction and control valve pressure drop.

{mass out} – {mass in}+Accumulation of mass=generation

where

∇⋅ is divergence,

ρ is the amount of the quantity q per unit volume,

j is the flux of q,

t is time,

σ is the generation of q per unit volume per unit time. Terms that generate q (i.e., σ > 0) or remove q (i.e., σ < 0) are referred to as a “sources” and “sinks” respectively.

Pressure drop in the piping system in this system consider:

1. Loss due to friction

2. Loss pressure in control valve

Using Bernoulli’s principle and Darcy-Weinbach as pressure drop along the pipe.

For pipe illustration as follows:

Based on the Bernoulli’s principle.

No change elevation and fully developed flow through a constant area pipe. Hence the equation will be in the form

III.1.4 Loss due to friction

Resistance coefficient, abbreviated as K, a dimensionless number, is how much resistance to the flow an obstacle has. This is the opposite of the flow coefficient which is how much flow capacity an obstacle allows.

Loss pressure drop across the valve:

a₁,a₂, G_f, k_L, and C_v ar independent variables (NE)

The valve is 4 in valve with Cv_max = 720 is selected and the pressure around the valve is independent of flow. Consider both a valve with linear characteristics and an equal percentage valve with a rangeability parameter of 50.

In general, the resistance of the liquid level system is expressed as:

The process model for a single loop is often First Order Plus Dead Time (FOPDT). First-order could be solved in the time domain or in frequency response.

There are 3 unknown parameter

III.2 Gain (K)

The gain of any signal-processing device (think of an electronic amplifier) is the ratio of output to input or the ratio of the change of output to the change of input. Since the signal to the valve is the process input the measurement is the process output, then Gain could be contributed from 3 different areas.

There are several models that could be approached using the First Order model such as

• Filling a Tank
• A disk flywheel
• Resistor and Capacitor Schematic

• Gain(Kp)
• Time Constant
• Apparent Dead Time

The characteristic form of the transfer function of a first-order plant is

III.2.1 Process Gain

Process gain is the change in the output y induced by a unit change in the input x.

In simplification, the gain for pressure and flow control :

Pressure Transmitter range: 0-15 barg with setpoint 9.9 barg

Flow Transmitter = 0 – 50 MMSCFD with setpoint 36 MMSCFD

Gain, Output = Flow, Input : Controller output signal

Gain Process (PIC) = 100 – 0/ 15-0 = 9.5

Gain Process (FIC) = 100 – 0/50 -0=2

However, I will try to approach the piping system (pressure loss and valve) with the control valve in the first-order model plant.

Chain rule of differentiation

Equal percentage characteristic

Therefore the gain valve for pressure drop 21.75 psig and C_v=720 is 135,478. During the regulating valve will travel between 30-70 %. We will take at opening

III.2.2 Time Constant

The time constant, usually denoted by the Greek letter τ (tau), is the parameter characterizing the response to a step input of a first-order, Linear Time-Invariant (LTI) system. The time constant is the main characteristic unit of a first-order LTI system. Therefore, the process time constant is the amount of time needed for the output to reach 63.2% of the way to steady-state conditions. The process time constant affects the speed response.

If the initial condition y(0)=0 and at t = time constant, the solution is simplified to the following 0.632K_p x input

III.2.2.a Determining time constant

Determining time constant is using

• HMI and graphic chart
• Calculation

III.4 Time delay

III.4.1 Determining Delay Time

The time delay is expressed as a time shift in the input variable. The time delay from a single control loop is contributed from

a). Transducer

b).Controller

The filter could cause an additional time delay. The filter is used to eliminate unwanted noise and background.

• a).Transducer
  • The sensor is pressure transmitter Rosemount 30151. In gage applications, it is important to minimize pressure fluctuations to the low side isolator. Reducing process noise. Rosemount 3051CD draft transmitters are sensitive to small pressure changes. Increasing the damping will decrease output noise, but it will further reduce response time.
  • Damping. The damping command changes the response time of the transmitter, higher values can smooth variations in output readings caused by rapid input changes. Determine the appropriate damping setting based on the necessary response time, signal stability, and other requirements of the loop dynamics with your system. The damping command uses floating-point configuration, allowing you to input any damping value within 0-60 seconds.
  • The pressure transmitter contributes a dead time of 45 ms. The dead-time function is also called the time-delay, transport-lag, translated, or time-shift function (Fig 2.3). It is defined such that an original function f(t) is “shifted” in time. One method of reducing fluctuations in atmospheric pressure is to attach the length of tubing to the reference side of the transmitter to act as a pressure buffer.
  • Output damping. At the factory, Emerson sets the output damping for the Rosemount 3051CD to .32. If the transmitter output is still noisy, increase the damping time. If you need a faster response, decrease the damping time.

b).Controller / PLC

The controller will add a two-component delay time

• Input filter on channel analogue input
• Scan time

Therefore the total delay time = Dead Time (Transmitter) + Input Filter (AI) + Scan Time (PLC) = 45 ms + 1s + 250 ms

Filter(AI) + Scan Time (PLC) = 1295 ms

The total loop dead time is seen as the time it takes for the process variable to start to respond in the correct direction for a change in a controller’s setpoint or manual output.

IV. SIMULATING

Data from process input and output could be plotted using python (via jupyter notebook) for this simulation. I will try to compare the model for first-order and model approach using data as calculated. The input is using step function which

Model-based on FPDOT	Model-based on Process data
Kp=135 time constant = 5.0	Kp=135 time constant=5 delay time= 1.295 s

V. IMPLEMENTING CONTROL STRUCTURE

The controller could be electrical, pneumatic, or hydraulic. The electrical controller is usually represented as PLC or PID modular form.

The controller could be implemented as a pneumatic controller and electronic controller. Both have advantages and disadvantages. This variety of products depends on the availability of electrical sources.

If the process is in live condition. The control valve could start in manual mode. As informed in the previous section, the PID form is using PLC SoMachine Basic. PID Controller to implement a mixed (serial-parallel) PID correction. The integral and derivative actions are both independent and in parallel. The proportional action acts on the combined output of the integral and derivatives actions

The component PID controllers is

• Proportional, The proportional controller directly affects the gain.
• Integral, eliminate transient error
• Differential, reduce error rate.

PID control form consists of

• Parallel
• Ideal

Classic systems identification methods to obtain the first-order model of the system as:

• Ziegler-Nichols method;
• Smith’s method;
• Sundaresan’s method
• Nishikawa’s method

However, often this method is not directly applied during the commissioning of the control valve and PLC. Most of the time it is tuned by trial.

All of the methods, in a simple way, it could measure and gather to obtain the trending on HMI and PLC database in time series.

• Field sensors/Instrumentation Gain
• Process Gain,One term that will be used frequently is process gain, designated Kp.
• Final Element/Valve Gain
  • Valve gain (Kv) is the slope of the valve characteristic curve. The slope is the ratio of the change in flow to the change in travel. Thus, Kv=dQ / dY.
  • There are four factors that influence gain: valve characteristic, flow, valve size, and pressure drop.

In live process, changing the input process is difficult.

The other way more feasible is using simulation in PLC or current injection while the process is shut down. However the downside is it could not represent the real reaction of the system.

V.1 Electronic Controller, PLC (Programmable Logic Controller)

Both PLC and HMI is using the same brand manufacturer i.e. Schneider

The PLC is using PLC Schneider M221. The Analog input is 16 bit (maximum raw data is 65536) but it is limited to 16221 discretization level. The analog output is 12 bits. The maximum raw data is 4096. The disadvantage different bit Analogue Input, and Analogue Output.

The consequence is when processing the PID. There are 2 flow conversion data.

Any analog filtering that may be required (to reduce the problem of aliasing)

Interactive or Non-Interactive Controller?

It could be different between the PLC. SoMachine PID consists of AutoTuning, PID, and PWM functions.

V.1 Computational Algorithms

Two different computational algorithms are used depending on the value of the integral time constant (Ti)

if Ti=0, an incremental algorithm is used

If Ti=0, a positional algorithm is used, along with +5000 offset that is applied to the PID Output

IV.2 Pneumatic Valve Controller

The proportional band adjustment knob positions the nozzle on the flapper. Increasing (widening) the proportional band moved the nozzle to a position where less input and more feedback motion occurs, which decreases the gain of the controller.

The fuel valve is designed as a fail-to-close type, then both controllers will be set for reverse action.

The reverse action means increasing process variable (pressure or flowrate) will decrease percentage output.

A direct-acting controller is one whose output tends to increase as the measurement signal increases.

A reverse-acting controller is one whose output tends to decrease as the measurement signal increases.

However in case, the fuels valve is designed as a fail-to-open type, then both controllers will be set for direct action.

Don’t forget that the reverse or direct action in consequence both Positioner and Controller action should be same

• Proportional-Only Controllers
• Proportional-Plus-Reset
• Proportional Plus Reset Plus Rate Controllers

Proportional Band: 5 yo 500% of process scale span

Reset: Adjustable from 0.01 to more than 75 minutes per repeat (from 100 to less than 0.0135 repeats per minute)

Rate: Adjustable from 0 to 20 minutes

Typical Frequency Response: 1.5 hertz and 90-degree phase shift with 3.05 m (10feet) of 6.4mm (1/4 inch) tubing and 1639 cm3 (100 cubic inches) volume

The application is for reducing pressure so if the upstream increase the valve will reduce the opening. In reverse when the upstream pressure is reduced the valve will increase the opening to the setpoint.

So with this condition, it could apply direct control

• 4mA represent valve close

• 20mA represent valve open

Now, we decide the direction flow to open or flow to close. It depends on the valve alignment. If you stated flow to open then the valve will be marked the direction from left to right meaning the left side will be upstream. If you stated flow to close then in the valve will be marked flow direction from right to left meaning the right-side will be upstream.

The controller function represents by PLC or pneumatic controller.

For Proportional-Only Controllers: Full output
pressure change adjustable from 2% to 100% of the
sensing element range for 0.2 to 1.0 bar (3 to 15 psig)
or 4% to 100% of the sensing element range for 0.4 to 2.0 bar (6 to 30 psig)

For Proportional-Plus-Reset Controllers: Full output
pressure change adjustable from 3% to 100% of the
sensing element range for 0.2 to 1.0 bar (3 to 15
psig), or 6% to 100% of the sensing element range
for 0.4 to 2.0 bar (6 to 30 psig)

Reset Adjustment
For Proportional-Plus-Reset Controllers: Adjustable
from 0.01 to 74 minutes per repeat (100 to 0.01
repeats per minute)

VI. Actuator and Valve

The actuator and valve is the final element to manipulate the variable process. Understanding the objective process is essential before determining the next requirement

Based on the actuator it determined fail close or fail open. This selection is coordinated with the process team during HAZOP to define the safety state position or which is more safety inherent. An additional feature could be added if the position of the control valve is the last position.

Fail open means if the pneumatic/electric to drive actuator is loss, the actuator’s spring will work to open

Failure close means if the pneumatic/electric to drive actuator is loss, the actuator’s spring will work to close.

Normally, the actuator acting mode is direct acting for fail-open valves and reverse-acting for fail closed valves. When ‘Fail-Lock’ position is selected, the control valve action in case of lock-up device failure shall be specified as well.

The type of actuator diaphragm or piston depends on the design differential pressure during the shutoff valve.

The most common use of a control valve is a globe valve. The relation between Globe valve consists of 3 different characters

Gain

Quick Open	Gain increases as the valve open
Linear Valve	Constant gain
Equal Percentage Valve	Gain decreases as the valve opens

Differential pressure across

Linear Valve	dP does NOT vary with flow
Equal Percentage Valve	dP varies with flow & processes with decreases in gains

V. CONCERN

Using I (Integral) to eliminate error could lead to a windup mechanism. Output saturation limits and built-in anti-windup mechanism

Selector pressure control and flow control should use signal tracking for bumpless control transfer and multiloop controls

Supply

Pressure reducing when it does not sense pressure it will fully open

IV. Reference

• http://web.mit.edu/2.151/www/Handouts/FirstSecondOrder.pdf
• https://www.electrical4u.com/time-constant/
• https://www.slideshare.net/AdgonzalezD/control-valves-characteristics-gain-transfer-function?qid=1a07753c-6131-4350-b8e4-18433d425070&v=&b=&from_search=7
• https://neutrium.net/fluid-flow/pressure-loss-in-pipe/
• https://instrumentationtools.com/air-to-open-air-to-close-valves-and-direction-of-control-action/#:~:text=A%20direct%20acting%20controller%20is,as%20the%20measurement%20signal%20increases.&text=It%20is%20important%20to%20get%20the%20correct%20direction%20of%20control%20action.