CONTROL THEORY BASICS

This article presents some of the basic concepts of control and provides a foundation from which to understand more complex control processes and algorithms later described in this module. Common terms and concepts relating to process control are defined in this section.

LEARNING OBJECTIVES

After completing this section, you will be able to:

Define control loop and describe the three tasks necessary for process control to occur:

• Measure

• Compare

• Adjust

 

Define the following terms:

• Process variable

• Setpoint

• Manipulated variable

• Measured variable

• Error

• Offset

• Load disturbance

• Control algorithm

List at least five process variables that are commonly controlled in process measurement industries. At a high level, differentiate the following types of control:

• Manual versus automatic feedback control

• Closed-loop versus open-loop control

THE CONTROL LOOP

Imagine you are sitting in a cabin in front of a small fire on a cold winter evening. You feel uncomfortably cold, so you throw another log on the fire. This is an example of a control loop. In the control loop, a variable (temperature) fell below the setpoint (your comfort level), and you took action to bring the process back into the desired condition by adding fuel to the fire. The control loop will now remain static until the temperature again rises above or falls below your comfort level.

THREE TASKS

Control loops in the process control industry work in the same way, requiring three tasks to occur:

Measurement

Comparison

Adjustment

 












In Figure, a level transmitter (LT) measures the level in the tank and transmits a signal associated with the level reading to a controller (LIC). The controller compares the reading to a predetermined value, in this case, the maximum tank level established by the plant operator, and finds that the values are equal. The controller then sends a signal to the device that can bring the tank level back to a lower level a valve at the bottom of the tank. The valve opens to let some liquid out of the tank. Many different instruments and devices may or may not be used in control loops (e.g., transmitters, sensors, controllers, valves, pumps), but the three tasks of measurement, comparison, and adjustment are always present.
As in any field, process control has its own set of common terms that you should be familiar with and that you will use when talking about control technology.

PROCESS VARIABLE

A process variable is a condition of the process fluid (a liquid or gas) that can change the manufacturing process in some way. In the example of you sitting by the fire, the process variable was temperature. In the example of the tank in Figure, the process variable is level. Common process variables include:

Pressure

Flow

Level

Temperature

Density

Ph (acidity or alkalinity)

Liquid interface (the relative amounts of different liquids that are combined in a vessel)

Mass

Conductivity

 

SETPOINT

The setpoint is a value for a process variable that is desired to be maintained. For example, if a process temperature needs to kept within 5 °C of 100 °C, then the setpoint is 100 °C. A temperature sensor can be used to help maintain the temperature at setpoint. The sensor is inserted into the process, and a controller compares the temperature reading from the sensor to the setpoint. If the temperature reading is 110 °C, then the controller determines that the process is above setpoint and signals the fuel valve of the burner to close slightly until the process cools to 100 °C. Set points can also be maximum or minimum values. For example, level in tank cannot exceed 20 feet.

 

MEASURED VARIABLES, PROCESS VARIABLES, AND MANIPULATED VARIABLES

In the temperature control loop example, the measured variable is temperature, which must be held close to 100 °C. In this example and in most instances, the measured variable is also the process variable. The measured variable is the condition of the process fluid that must be kept at the designated setpoint. Sometimes the measured variable is not the same as the process variable. For example, a manufacturer may measure flow into and out of a storage tank to determine tank level. In this scenario, flow is the measured variable, and the process fluid level is the process variable.

The factor that is changed to keep the measured variable at setpoint is called the manipulated variable. In the example described, the manipulated variable would also be flow.
   

ERROR

Error is the difference between the measured variable and the setpoint and can be either positive or negative. In the temperature control loop example, the error is the difference between the 110 °C measured variable and the 100 °C setpoint that is, the error is 10 °C.

The objective of any control scheme is to minimize or eliminate error. Therefore, it is imperative that error be well understood. Any error can be seen as having three major components. These three components are shown in the figure on the following page.
 

Magnitude

The magnitude of the error is simply the deviation between the values of the setpoint and the process variable. The magnitude of error at any point in time compared to the previous error provides the basis for determining the change in error. The change in error is also an important value.

 

Duration

Duration refers to the length of time that an error condition has existed.

 

Rate of Change
The rate of change is shown by the slope of the error plot

OFFSET
Offset is a sustained deviation of the process variable from the setpoint. In the temperature control loop example, if the control system held the process fluid at 100.5 °C consistently, even though the setpoint is 100 °C, then an offset of 0.5 °C exists.
 

LOAD DISTURBANCE

A load disturbance is an undesired change in one of the factors that can affect the process variable. In the temperature control loop example, adding cold process fluid to the vessel would be a load disturbance because it would lower the temperature of the process fluid.

CONTROL ALGORITHM

A control algorithm is a mathematical expression of a control function. Using the temperature control loop example, V in the equation below is the fuel valve position, and e is the error. The relationship in a control algorithm can be expressed as:
 

Control algorithms can be used to calculate the requirements of much more complex control loops than the one described here. In more complex control loops, questions such as “How far should the valve be opened or closed in response to a given change in setpoint?” and “How long should the valve be held in the new position after the process variable moves back toward setpoint?” need to be answered.

MANUAL AND AUTOMATIC CONTROL

Before process automation, people, rather than machines, performed many of the process control tasks. For example, a human operator might have watched a level gauge and closed a valve when the level reached the setpoint. Control operations that involve human action to make an adjustment are called manual control systems.

Conversely, control operations in which no human intervention is required, such as an automatic valve actuator that responds to a level controller, are called automatic control systems.

  

CLOSED AND OPEN CONTROL LOOPS

A closed control loop exists where a process variable is measured, compared to a setpoint, and action is taken to correct any deviation from setpoint. An open control loop exists where the process variable is not compared, and action is taken not in response to feedback on the condition of the process variable, but is instead taken without regard to process variable conditions. For example, a water valve may be opened to add cooling water to a process to prevent the process fluid from getting too hot, based on a pre-set time interval, regardless of the actual temperature of the process fluid.