- PID Controller Definition: A PID controller is a crucial device in control systems that adjusts the control action based on proportional, integral, and derivative terms of the error.
- Control Parameters: Proportional (Kp), integral (Ki), and derivative (Kd) components each uniquely influence the response and stability of control systems.
- Proportional Control: This mode adjusts the output proportionally to the error, which is the difference between desired and actual performance.
- Integral and Derivative Actions: Integral control focuses on the accumulation of past errors, whereas derivative control predicts future errors, helping to refine the control process.
- Applications and Limitations: PID controllers are versatile and widely used in modern industrial applications, though they face challenges in noisy environments and optimal control scenarios.
PID control, representing proportional-integral-derivative control, is a feedback mechanism in control system, often referred to as three-term control. By adjusting three parameters—the proportional, integral, and derivative values of a process variable’s deviation from its set point—specific control actions are effectively tailored.
PID controllers are considered to be the best controller in the control system family. Nicholas Minorsky published the theoretical analysis paper on PID controller. For PID control the actuating signal consists of proportional error signal added with derivative and integral of the error signal. Therefore, the actuating signal for PID control is:
The Laplace transform of the actuating signal incorporating PID control is
Some control actions only require two of the PID controller’s parameters, setting the third to zero. This flexibility allows PID controllers to operate as PI (proportional-integral), PD (proportional-derivative), or simply P or I. The derivative term D manages noise, and the integral term I targets the system’s desired value. In early days PID controller was used as a mechanical device. These were pneumatic controllers as they were compressed by air. Mechanical controllers include spring, lever or mass. Many complex electronic systems are provided with a PID control loop. In modern days PID controllers are used in PLC (programmable logic controllers) in the industry. The proportional, derivative and integral parameters can be expressed as – Kp, Kd and Ki. All these three parameters have an effect on the closed loop control system. It affects rise time, settling time and overshoot and also the steady state error.
| Control Response | Rise time | Settling time | Overshoot | Steady state error |
| Kp | decrease | small change | increase | decrease |
| Kd | small change | decrease | decrease | no change |
| Ki | decrease | increase | increase | eliminate |
PID control combines the advantages of proportional, derivative and integral control actions. Let us discuss these control actions in brief.
Proportional Control: Here actuating signal for the control action in a control system is proportional to the error signal. The error signal being the difference between the reference input signal and the feedback signal obtained from input.
Derivative Control: The actuating signal consists of proportional error signal added with derivative of the error signal. Therefore, the actuating signal for derivative control action is given by,
Integral Control: For integral control action the actuating signal consists of proportional error signal added with integral of the error signal. Therefore, the actuating signal for integral control action is given by
A PID controller has some limitations also apart from being one of the best controllers in control action system.
Although applicable to various control tasks, PID controllers falter in optimal control situations due to their reliance on a feedback path without a process model. The system’s linear nature and sensitivity to noise in the derivative component also pose significant challenges, as minor noise can significantly alter the output.
