How do you optimize PID parameters using data-driven or adaptive methods?

Data-driven methods like the Ziegler-Nichols method use input-output data to set PID parameters without needing a process model. A step input is applied, and the system’s response is observed to find the critical gain and period, which are then used with formulas to calculate PID values. However, this method may struggle with systems that have complex behavior, noise, or disturbances, making it less suitable for such processes.

Adaptive methods adjust PID parameters in real time based on changing process conditions using feedback and optimization. Model Reference Adaptive Control (MRAC) compares the process output with a reference model and updates parameters to reduce errors. Self-Tuning Regulators (STR) estimate process model parameters and design the PID controller accordingly. These methods help maintain performance even in dynamic or uncertain environments, making them useful for modern, complex processes.

Another way to make a PID adaptive is to use fuzzy logic for parameter determination. It is best applied in nonlinear systems but has high adaptability within its operating range.

An advantage of adaptive methods is performance. Adaptive PIDs can guarantee the same performance in variant systems (i.e. different operating conditions, degradation, uncertainty, etc). However, everything comes at a cost and that cost is robustness. The convergence of the parameters could yield problematic conditions in terms of robustness, so the adaptability of the controllers must be bounded and broadly tested. These types of controllers are more suited to process in which a control failure do not yield a safety concern.

Data-driven methods are quick and easy to use but may not fully capture process behavior and need offline tests that can disrupt operations. Adaptive methods are more reliable and flexible, adjusting to changes in real time, but they need more computing power and can face stability or convergence problems. Choosing the right method depends on the specific process and available resources.

Choosing between data-driven and adaptive methods depends on the process and resources. Use data-driven methods for simple, stable processes with enough good-quality data. They are fast and easy to apply. Adaptive methods are better for complex, changing, or uncertain processes, especially with limited or noisy data, as they adjust in real time. Consider performance needs, hardware, and computing limits to pick the best approach for the task.

To use a data-driven or adaptive method, first define the process’s input-output variables and sampling rate. Choose the method based on your needs and limits. Apply it to collect data and set or adjust PID parameters. Finally, test the controller’s performance using simple metrics like rise time, overshoot, settling time, steady-state error, and bandwidth to ensure it works well and stays stable.

In the improvement of adaptive controller performance, a strong emerging trend is the use of bio-inspired algorithms for determining optimal initial values. This approach has great potential, especially in controls such as MRAC, where the initial parameters influence the convergence time of the gains.

Most PID control optimization techniques require some level of disturbance to the process by injecting a step change in the set point, which is prohibitive in a production environment. Alternatively, the online transfer-function calculation and response simulation, combined with a loop performance assessment technique is much easier to validate and implement than other techniques that require a process disturbance.