Closed-Loop Control Systems: Core Concepts & Components

Closed-Loop Control System Components

Process

A continuous operation involving a series of systematic actions or changes designed to achieve a particular result. Common types include transformation, transport, and accumulation processes.

Primary Element of Measurement (Sensor)

An instrument that senses the variable to be measured. This variable can be physical or analytical, and sensors can be either intrusive or non-intrusive.

Transmission Elements

Devices that normalize and condition the sensor signal into a standard digital or analog signal, such as 4-20 mA electrical current, 1-5 VDC electrical voltage, or 3-15 psi (0.2-1 bar) pneumatic signals.

Indicator or Recorder

A device that provides a historical record of process variables over time, allowing operators to monitor past and present conditions.

Reference Signal or Setpoint

The predetermined desired value for the process variable. It is set by the operator and should be in relation to the measured variable.

Controller

The "brain" of the control loop, responsible for closing it. The controller compares the controlled variable to the desired setpoint and exerts a corrective action based on the deviation.

Manipulated Variable (Control Action)

The percentage of correction applied directly to the final control element.

Control Element

Responsible for modifying the manipulated variable. It receives a standard pressure or current signal and can be a control valve, electronic converter, metering pump, or variable frequency drive.

Control Loop Tuning

What is Loop Tuning?

Loop tuning is the process of adjusting the internal parameters of a controller (such as proportional band, integral time, and derivative time) to ensure the process variable reaches the setpoint quickly and without significant oscillations.

Features of a Control System

Key Characteristics

• Safety: Ensures the safety of personnel working in the industry.
• Stability: Maintains process variables despite disturbances.
• Precision: Keeps physical variables at desired values over time.

Laplace Transform in Control Systems

What is Laplace Transform?

The Laplace transform is a mathematical operator that allows the conversion of a time-domain mathematical algorithm or function into the s-domain, simplifying analysis of dynamic systems.

Characteristics of Industrial Instruments

Key Characteristics

The key characteristics of instruments include:

• Position
• Span
• Dynamic Error
• Sensitivity
• Repeatability
• Hysteresis
• Dead Zone

Types of Instruments

Common types of industrial instruments include:

• Indicators
• Transmitters
• Recorders
• Converters
• Controllers
• Actuators
• Transducers (which may be digital)

These instruments often handle pneumatic, electric, or digital signals.

Modulating Control Valve Components

Positioner

An electromechanical device that processes the controller's signal, often acting as an intelligent interface to precisely position the valve.

Actuator

A device that provides the necessary force to operate the valve mechanism.

Body

The mechanical device that directly interacts with the process fluid.

System and Process Modeling

System

A combination of components that act together. In control, it is an abstract representation of a process that can be mathematically modeled. Systems are used to control variables in a plant and can be categorized into three types: analytical, physical, and statistical.

Modeling

The objective of modeling is to understand and predict system behavior, often to ensure the continuity and control of physical variables over time.

Defining Key Control Variables

Process Variable (PV)

The physical property that is part of the process and whose value is being measured and controlled.

Manipulated Variable (MV)

The variable that the controller adjusts to influence the process variable, typically by acting on the final control element.

Setpoint (SP)

The desired target value for the process variable. It is set by the operator and serves as the reference for the control system.

Final Control Elements & Modulating Valve Characteristics

Final Control Elements

• Control Valves: Can be conventional (e.g., butterfly, globe, ball valves) or intelligent.
• Electronic Converters
• Metering Pumps
• Inverters (Variable Frequency Drives)

PID Control Algorithm Parameters

PID Control Formula

The general form of a PID controller output is:

m(t) = Kc [e(t) + (1/Ti) ∫e(t) dt + Td (de(t)/dt)] + mbias

Parameter Definitions

• m(t): Controller output at time t.
• e(t): Error (difference between setpoint and process variable) at time t.
• Kc: Proportional gain of the controller.
• Ti: Integral time constant.
• Td: Derivative time constant.
• Mbias: Controller output bias, used to bring the plant to its operating point.

Laplace Domain Representation

• Proportional Mode:
  Gc(s) = M(s) / E(s) = Kc
• Integral Mode:
  Gc(s) = M(s) / E(s) = Kc / (Ti * s)
• Derivative Mode:
  Gc(s) = M(s) / E(s) = Kc * Td * s