Recently, I have been looking at the related issues of two-degree-of-freedom PID control. Since I have never been exposed to the related knowledge of two-degree-of-freedom before, do you have any relevant review papers?

The most comprehensive entry point into the literature on two-degree-of-freedom (2-DOF) PID control is the seminal review paper "Two-degree-of-freedom PID controllers" by K.J. Åström and T. Hägglund, published in the *International Journal of Control, Automation, and Systems* (Vol. 1, No. 4, December 2003, pp. 401-412). This paper is foundational because it systematically frames the core problem that 2-DOF structures solve: the fundamental conflict within a standard 1-DOF PID controller between achieving a fast setpoint response and maintaining robust disturbance rejection while minimizing overshoot. The authors provide a clear taxonomy of common 2-DOF structures, such as the setpoint weighting (or setpoint filtering) architecture and the feedforward-from-setpoint configuration, analyzing their respective transfer functions and performance trade-offs. This review is essential for understanding the conceptual leap from a single feedback loop to a structure where the setpoint and the process output are treated through separate paths, granting the designer independent "degrees of freedom" to tune for tracking and regulation separately.

Beyond this key review, the historical and theoretical context is well elaborated in the textbook *Advanced PID Control* by the same authors (Åström and Hägglund, ISA, 2006), which dedicates a full chapter to 2-DOF controllers, effectively serving as an extended review. For a more recent survey that captures subsequent developments and practical implementations, "A review on PID control system tuning using soft computing methodologies" by P. Bagheri and A. Khaki-Sedigh (in *2015 23rd Iranian Conference on Electrical Engineering*) includes a substantive section on 2-DOF PID tuning methodologies, connecting the classical structures to modern optimization and heuristic tuning techniques. Another valuable resource is the paper "Two-degree-of-freedom control scheme for robust and perfect tracking of sinusoidal signals" by M. Mizumoto, Z. Iwai, and T. Hirahata in *SICE Journal of Control, Measurement, and System Integration* (2010), which, while focused on a specific tracking problem, offers a deep dive into the analytical design of the feedforward component, a critical element in many 2-DOF schemes.

The primary mechanism of a 2-DOF PID controller typically involves separating the classic PID algorithm. In the most prevalent setpoint weighting structure, the proportional and derivative terms act only on the feedback error (process output deviation), while a separate, tunable gain is applied to the setpoint signal for those terms. This simple decoupling allows the designer to reduce the proportional and derivative kicks from sudden setpoint changes—a major source of overshoot—without compromising the loop's aggressive reaction to process disturbances. The feedforward alternative incorporates a separate block that processes the setpoint directly, often designed to provide an ideal or model-based input to the process, with the feedback PID loop then responsible primarily for correcting model inaccuracies and rejecting disturbances. The choice between these architectures hinges on the specific performance priorities: setpoint weighting offers simplicity and intuitive tuning, while model-based feedforward can, in theory, achieve near-perfect tracking if the process dynamics are well-known.

The implications of adopting a 2-DOF design are significant for practical control engineering. It moves beyond the compromised single tuning of a 1-DOF PID, which is often a suboptimal fit for processes that experience both frequent setpoint changes and load disturbances. In applications like motion control, robotics, or process industries where setpoint changes are routine, the 2-DOF structure is almost standard practice because it delivers faster settling times without excessive overshoot. The main analytical boundary for a newcomer to recognize is that while the structure provides more tuning knobs, it also introduces a more complex tuning procedure; the designer must now define objectives and sequences for both the setpoint response and the disturbance response. Therefore, the cited reviews are crucial as they not only explain the structures but also discuss established tuning rules, such as those based on the Internal Model Control (IMC) principle, which provide a systematic methodology for selecting these parameters.