Control Systems: Proportional and Integral Control

Proportional Controller

• Proportional control is a common control strategy in process control systems.
• In a proportional controller, the output is proportional to the error signal, which is the difference between the desired set point and the actual process variable.
• The constant of proportionality is called the controller gain, denoted by Kc.
• A higher controller gain implies a greater output change for a given error.
• A larger controller gain leads to a faster response, but it also makes the system more prone to instability.
• The drawback of proportional control is that it results in a steady-state error called offset. This offset is never eliminated as the proportional action alone cannot entirely correct the error.

Integral Control

• Integral action is introduced to address the offset inherent in proportional control.
• The integral action of a controller continuously accumulates the error over time and adds a corresponding correction to the output signal.
• Integral action can be used to eliminate offset but can lead to overshooting if the controller gain is too high or the integral time constant is too small.
• If the integral time constant is too large, the system response will be sluggish.
• The integral time constant refers to the time taken for the integral term to completely contribute to the output. It is denoted by 𝛕I.

Integral Windup

• Integral windup occurs when the controller output saturates, but the integral term keeps accumulating the error.
• This leads to a large overshoot when the controller output is eventually able to change.
• Integral windup can be prevented by using anti-reset windup strategies.
• Anti-reset windup prevents the integral term from accumulating error when the controller output is saturated by stopping the integral action when the controller output reaches its limits, ensuring that it doesn't accumulate excessive error.

Derivative Control

• Derivative action is used to improve the response of a control system by anticipating future changes in the process variable.
• It estimates the rate of change of the error and adds a corrective term to the output signal.
• Derivative action helps to reduce overshoot and oscillation but can be sensitive to noise in the process measurement.
• Derivative action is often used in combination with proportional and integral action to create a PID controller.
• The time constant of the derivative term is denoted by 𝛕d. A small time constant implies a faster response of the derivative term.

PID Control

• PID (Proportional-Integral-Derivative) control combines all three types of control actions: proportional, integral, and derivative.
• A PID controller can be used to provide a stable and responsive control system.
• The challenge in PID control is to properly tune the three gains.
• Improper tuning can lead to instability, overshoot, or poor performance.
• The proportional gain (Kc), integral time constant (𝛕I), and derivative time constant (𝛕d) must be carefully chosen to provide the best possible control of the process.

Applications of Different Control Strategies

• In industrial applications, PID controllers are widely used due to their adaptability and ability to achieve stable and responsive performance.
• Proportional control is useful in situations requiring quick and direct response, but it struggles with eliminating offset.
• The integral component compensates for offsets by adding a continuous correction based on cumulative error.
• When an improved response with reduced overshoots and oscillations is desired, the derivative component is integrated with a PID controller.
• However, due to the potential for noise amplification, derivative action is often excluded from practical implementation.
• The ideal choice often involves considering the specific characteristics of the process and the desired control performance.