Control Systems: Key Concepts and Modeling Principles

Open and Closed Loop Control Systems

Open Control System

An open-loop control system refers to a configuration where the controller is disconnected from the process. In this state, the controller has no influence over the controlled variable and cannot maintain the desired setpoint.

Closed Loop Control System

A closed-loop control system refers to a configuration where the controller is connected to the process. The controller continuously compares the setpoint (reference) with the controlled variable and determines the necessary corrective action.

Key Process Control Terminology

• Controlled Variable: The specific variable that must be maintained or regulated at a desired value.
• Setpoint (Reference): The target value for the controlled variable.
• Manipulated Variable: The variable adjusted to keep the controlled variable at the setpoint, used to compensate for disturbances.
• Perturbation (Disturbance) Variable: An external variable that affects the controlled variable, causing it to deviate from the setpoint.

Instrumentation and Control Components

Measurement Element (Sensor)

Instruments used to measure controlled variables, disturbance variables, and secondary endpoints. They measure a physical property and generate a mechanical, electrical, or pneumatic signal.

Transmitter or Transducer

Converts the magnitude of the physical effect produced by the sensor into a standard signal—electrical (4-20 mA), pneumatic (3-15 psi), or digital—allowing it to be transmitted over distances without interference.

Controller

Receives the signal from the measured variable and calculates the control action based on a programmed algorithm. This calculation is translated into a standard output signal sent to the final control element.

System Modeling Parameters

Lumped Parameter Models

Assumes fluid matter within a control volume is well-mixed, meaning there are no concentration or temperature gradients in any spatial direction (e.g., a stirred tank reactor). Conservation equations for these cases result in ordinary differential equations.

Distributed Parameter Models

Applies to processing units where geometry causes strong concentration or temperature gradients (e.g., a tubular reactor). Balance equations are expressed as partial differential equations with respect to time and axial position.

Dynamic Response Metrics

• Time Constant (τ): The time required to reach a new steady state if the initial rate of change were maintained constantly.
• Static Gain (K): The ratio of the change in the output level (Δh) to the change made in the input variable.