The five time response specifications explained in the video are:
This Hindi-language video lecture focuses on time response specifications for second-order systems in control systems engineering (CS). The lecture builds upon previous lessons and explains key time-response specifications such as rise time, peak time, settling time, and peak overshoot, providing their mathematical expressions.
The video explains these time response specifications in the context of an underdamped second-order system's response to a step input. Here's a breakdown of each:
Delay Time (Td): This is the time it takes for the system's response to reach 50% of its final value for the first time. It represents the initial delay before the system begins its significant response.
Rise Time (Tr): This is the time it takes for the system's response to rise from 10% to 90% of its final value. It indicates how quickly the system reaches its target value. The video specifically focuses on the time to reach 100% of the final value as the rise time.
Peak Time (Tp): This is the time it takes for the system's response to reach its first peak (maximum) value. It shows how long it takes for the system to overshoot before settling.
Settling Time (Ts): This is the time it takes for the system's response to settle within a certain percentage (typically 2% or 5%) of its final value. It represents how long it takes for the oscillations to die out and reach a stable state.
Peak Overshoot (Mp): This is the difference between the peak value of the response and the final value, often expressed as a percentage of the final value. It quantifies the amount by which the system overshoots its target before settling. The video describes it as the difference between the maximum value reached and the final value (100%).
The video explains the time response specifications using a graphical representation of an underdamped second-order system's response. Here's an explanation mirroring the video's approach:
Settling Time (Ts): The video defines settling time as the time taken for the system's response to reach its final steady state from its initial state. The final steady state is depicted on the graph as the point where the oscillations die down. The time elapsed from the beginning of the response (the initiation of the step input) to the point where the response essentially flattens out, is the settling time. The video uses the example of turning on a fan; it takes a certain amount of time to reach its final speed.
Steady-State Error (Ess): The video notes that, upon settling, there might be a slight difference between the achieved final value and the expected final value (e.g., the fan might reach 48 RPM instead of the designed 50 RPM). This discrepancy is defined as the steady-state error. It's the error that remains after the system has settled.
Delay Time (Td): The video describes delay time as the time taken for the system's response to first reach 50% of its final value. This is indicated visually on the graph as the point where the response curve crosses the 50% line.
Rise Time (Tr): The video explains rise time as the time taken for the response to go from 0 to 100% of its final value for the first time. Visually on the graph, this is the time from the start of the response until the curve first reaches the final value line. It emphasizes that this is distinct from the time to reach other percentages (like 10% to 90%).
Peak Time (Tp): The video defines peak time as the time it takes for the system's response to reach its maximum value (the peak of the overshoot). This is identified on the graph as the time at the highest point of the initial overshoot.
Peak Overshoot (Mp): The video explains peak overshoot as the difference between the peak value (highest point on the curve) and the final value of the response. This difference, visualized on the graph, represents how much the system overshoots its target value before settling. The video emphasizes that this overshoot is a design feature intended to handle fluctuations in input, thereby preventing system damage.
