Define stability in a control system.

Stability is a critical characteristic in control systems because an unstable system can lead to erratic behavior, uncontrollable oscillations, and even system failure. There are different types of stability:

Stable System: A stable control system will return to its equilibrium or desired state after experiencing a disturbance. The output will eventually settle at a constant value without oscillating indefinitely.

Unstable System: An unstable control system, on the other hand, will lead to uncontrollable and unbounded oscillations or diverging behavior. The output of the system will grow without bound or diverge away from the desired state.

Marginally Stable System: A marginally stable control system teeters on the edge of instability. It neither grows without bound nor returns to its equilibrium in a finite time. Instead, it remains on the boundary between stability and instability, leading to prolonged oscillations.

Stability in a control system is typically assessed through mathematical analysis, such as stability criteria and stability margins. Engineers use different methods, such as the Routh-Hurwitz criterion or the Nyquist stability criterion, to evaluate and design control systems that maintain stability under various conditions and disturbances. By ensuring stability, engineers can create reliable and predictable control systems that effectively regulate and maintain desired outcomes in a wide range of applications, from simple household appliances to complex industrial processes and aerospace systems.