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Peak Time is the time required by the response to reach its first peak i.e. the peak of the first cycle of oscillation, or first overshoot. It is a key parameter in control systems and vibration analysis.
The calculator uses the formula:
Where:
Explanation: The formula calculates the time taken for a second-order system to reach its first peak response, considering the system's natural frequency and damping characteristics.
Details: Peak Time is crucial in control system design for analyzing transient response performance, stability assessment, and tuning controllers to meet specific timing requirements.
Tips: Enter natural frequency in rad/s and damping ratio (0 ≤ ζ < 1). Both values must be valid positive numbers with damping ratio less than 1.
Q1: What is the physical significance of Peak Time?
A: Peak Time indicates how quickly a system responds to a step input and reaches its maximum overshoot, reflecting the speed of response.
Q2: How does damping ratio affect Peak Time?
A: As damping ratio increases, Peak Time generally increases. For ζ ≥ 1 (critically damped and overdamped systems), there is no overshoot and thus no Peak Time.
Q3: What are typical values for natural frequency?
A: Natural frequency depends on the specific system. Higher ωn values generally result in faster response and smaller Peak Time.
Q4: Can this formula be used for all second-order systems?
A: This formula applies specifically to underdamped second-order systems (0 ≤ ζ < 1) with no zeros in the transfer function.
Q5: What units should be used for input values?
A: Natural frequency should be in rad/s, damping ratio is dimensionless, and the result is in seconds.