PID (proportional-integral-derivative) control, a foundational control technology for process manufacturers, has been with us since the early 1900s. In a Control Engineering article, Evolving PID Tuning Rules – A Brief History, Starting With The Earliest PID Controllers To The Most Recent Developments. There Is More Continuity Than You Might Expect, Emerson’s Terry Blevins and Willy Wojsznis, explore the history and advancement of this control technology.
They highlight the opening chapter in the history of PID control:
…the first real PID-type controller developed by Elmer Sperry in 1911. The first theoretical analysis of a PID controller was published by Nicolas Minorsky in 1922. His observations grew out of efforts to design automatic steering systems for the U.S. Navy.
The authors explore two categories of PID control–model free and model based. The first does not require a process model, but instead is:
…based on the observation of a process which is under control, and became among the first initially applied for controller tuning.
Manual tuning and the Ziegler Nichols tuning methods are examples of this approach. With the manual tuning approach the loop is in automatic mode and the:
…integral and derivative actions are removed by setting Ti to infinity (or very high) and Td to zero. Then, controller proportional gain Kp is increased until the loop oscillates with constant amplitude. After that, the proportional gain Kp should be set to approximately half of that value for a quarter amplitude decay type response. Ti is adjusted until any offset is corrected in sufficient time for the loop operation.
Ziegler Nichols also has the loop go to an oscillatory state with constant amplitude. The period of this oscillation is measured and parameters set per fixed ratios.
Terry and Willy note the inherent difficulties in these approaches in the time to create the oscillations and the risks associated with placing the loop in an oscillatory state. An innovation called relay-oscillation auto-tuning addressed these drawbacks. It:
…delivers loop oscillation with amplitude limited by the relay step size…
With the loop at steady state, an initial step change is made to the process input. The amplitude of the step change is set to control the amplitude of oscillations in the process output. The ability to control the amplitude of process oscillation is a significant advantage over the closed loop technique to identify ultimate gain and ultimate period.
The authors note that although these tuning methods were classified as model free, the fact that they were based upon the ulltimate gain:
…directly relates to the inverse of the process gain and ultimate period relates to the process dead time and lag.
The model-based algorithms take into account different process types such as self-regulating and integrating, as well as process deadtimes. They share some common algorithms:
…first-order-lag-plus-dead-time model is the most common approximation for self-regulating processes…, and linear-integrator-with-gain-and-dead-time is used for integrating processes…
Internal Model Control (IMC), Lambda tuning, and recently developed SIMple Control (SIMC) rules are common model-based control algorithms. We’ve highlighted lambda tuning in several posts. Terry and Willy highlight the strength in these model-based approachesas the:
…ability to shape control loop performance and robustness by using a tuning parameter. The tuning parameter relating to the speed of response is used to vary the trade-off between performance and robustness, coordinate response among loops, and achieve process control objectives (averaging level, tight control, etc.).
Historically, PID controller tuning started from observing a loop with proportional action on the verge of stability, and then decreasing proportional gain to get stable operation and calculating integral and derivative terms from the loop oscillation period. In fact, all above indicators are related in some way to the process model parameters. Therefore, if all process model parameters are explicitly known, it is possible to satisfy tuning requirements in the best way. There are several model-based tuning rules which give a simple and intuitively understandable method to set a desired loop performance and robustness for a given process.
Read the article in full to better understand the strengths and tradeoffs of the various tuning approaches.