Steady-state in the context of PID algorithm

A proportional–integral–derivative controller (PID controller or three-term controller) is a feedback-based control loop mechanism commonly used to manage machines and processes that require continuous control and automatic adjustment. It is typically used in industrial control systems and various other applications where constant control through modulation is necessary without human intervention. The PID controller automatically compares the desired target value (setpoint or SP) with the actual value of the system (process variable or PV). The difference between these two values is called the error value, denoted as ${\displaystyle e(t)}$.

It then applies corrective actions automatically to bring the PV to the same value as the SP using three methods: The proportional (P) component responds to the current error value by producing an output that is directly proportional to the magnitude of the error. This provides immediate correction based on how far the system is from the desired setpoint. The integral (I) component, in turn, considers the cumulative sum of past errors to address any residual steady-state errors that persist over time, eliminating lingering discrepancies. Lastly, the derivative (D) component predicts future error by assessing the rate of change of the error, which helps to mitigate overshoot and enhance system stability, particularly when the system undergoes rapid changes. The PID output signal can directly control actuators through voltage, current, or other modulation methods, depending on the application. The PID controller reduces the likelihood of human error and improves automation.

Pioneer species are resilient species that are the first to colonize barren environments, or to repopulate disrupted biodiverse steady-state ecosystems as part of ecological succession. Various kinds of events can create good conditions for pioneers, including disruption by natural disasters, such as wildfire, flood, mudslide, lava flow or a climate-related extinction event, or by anthropogenic habitat destruction, such as through land clearance for agriculture or construction or industrial damage. Pioneer species play an important role in creating soil in primary succession, and stabilizing soil and nutrients in secondary succession.

Because pioneer species quickly occupy disrupted spaces, they are sometimes treated as weeds or nuisance wildlife by humans, such as the common dandelion or stinging nettle. Even though humans have mixed relationships with these plants, these species tend to help improve the ecosystem because they can break up compacted soils and accumulate nutrients that help with a transition back to a more mature ecosystem. In human-managed ecological restoration or agroforestry, trees and herbaceous pioneers can be used to restore soil qualities and provide shelter for slower growing or more demanding plants. Some systems use introduced species to restore the ecosystem, or for environmental remediation. The durability of pioneer species can also make them potential invasive species.