Formally, PID (Proportional-Integral-Derivative) control is a three-parameter linear control algorithm based on the current error, its integral, and its derivative. Its simplicity has led to widespread adoption in industrial applications, while also making it a frequent subject of research, comparison, and improvement. Despite its straightforward structure, PID has consistently remained at the forefront of feedback control, evolving from pneumatic, mechanical, and electronic physical implementations to digital algorithms. Invented and applied in industry even before the formalization of control theory, PID has endured through the rise of modern control theory. In 2020, a century after its introduction, the International Federation of Automatic Control (IFAC) Industrial Committee recognized PID as the most influential control algorithm. Thus, PID is rightly called the timeless legend of feedback control.
Although some predict that PID’s dominance may wane with advancements in hardware, I believe that as long as feedback control remains the fundamental approach to mitigating uncertainty, PID will continue to be a cornerstone in industrial applications for the long term. In practice, the PID algorithm is typically a control module within a larger control system. It is not a standalone solution but rather a class of error-based control algorithms. Industrial PID implementations incorporate various enhancements, such as dead zones, variable gains, proportional-derivative precedence, incomplete differentiation, setpoint filtering, and two-degree-of-freedom configurations. To further reduce uncertainty, advanced structures like cascade control, feedforward control, and complex multi-loop PID schemes are employed. These enhancements imbue PID with characteristics of higher-order algorithms, demonstrating that industrial PID is far from simplistic.
Industrial systems are engineered with operability in mind, and controlled processes typically exhibit self-balancing or integrating characteristics. For processes with nonlinear or non-self-balancing dynamics, engineers often constrain operating conditions to achieve approximate linearity and self-balancing behavior. Research shows that PID can achieve optimal performance with robustness for such inherently monotonic controlled processes. Are there processes with double-integrator or open-loop unstable dynamics? Certainly, but they are rare and complex, often requiring specialized control algorithms that are challenging to implement and less common. For process control, studying, applying, and tuning PID remains highly practical from an engineering perspective.
Process industries face inherent uncertainties, including model uncertainty and disturbances. The larger and more complex the system, the greater the uncertainty. For example, in a distillation column, whether the reboiler temperature and steam flow form a cascade control loop significantly affects the impact of reflux on temperature. With cascade control, reflux influences temperature by enhancing separation precision, resulting in a lower model gain. Without cascade control, reflux primarily affects temperature through energy balance. In such cases, cascade control reduces operational uncertainty. For instance, pairing the overhead temperature with reflux flow in a cascade loop may introduce nonlinearities or collinear coupling with reboiler temperature control. Selecting an alternative controlled variable (CV) can mitigate this uncertainty. In cases where dual temperature control loops (overhead and reboiler) perform poorly, I typically recommend prioritizing the more critical temperature loop. In high-precision distillation for separating isomers, where temperature does not reflect composition changes, temperature-based control may be entirely unsuitable.
The most cost-effective approach to addressing uncertainty is feedback PID control. Due to the inherent uncertainty in controlled processes, advanced control algorithms reliant on precise models struggle to gain widespread adoption in process control. Even within PID, industrial applications often rely solely on PI control. Our research demonstrates that PID is universally effective for first-order plus dead-time (FOPDT) processes, from large time constants to significant dead times, achieving consistent control performance. While the underlying theory may be complex, PID tuning methods are straightforward. The characteristics of industrial processes make PID well-suited to address their dynamics, and the inherent uncertainties often necessitate PID as the only viable solution. This unique adaptability has made PID the enduring star of process control, a timeless legend in control algorithms.