In this study, scientists simulated a cascade system to understand how it behaves over time. They found that using a simplified model of the system doesn't always match what happens in real life. The equivalent object frequently used in modeling is not exactly like the cascade system itself. As a result, the transients (how the system behaves over time) predicted by the simplified model may not match what actually occurs in a cascade control system. By studying this, they were able to develop an expression that accurately describes how a cascade system works.