Aerospace Control Systems

The peak stability metric is sometimes called a jitter metric. It measures the peak-to-peak change in attitude in any interval of time of width T seconds. This is illustrated in the first figure to the right. The peak-to-peak change in attitude is given by the equation

Δ_p(t) = max _{τ in [0,T]} | Θ(t) – Θ(t – τ) |

The peak stability metric is given by the equation

Δ_p = max _{t in [–∞,∞]} (Δ_p(t))

The peak stability metric is highly conservative because infrequent and rapid transient attitude motions are generally inconsequential to payload performance. The infrequent nature of large transients has lead to the use of a mean-square peak-stability metric. The mean-square peak-to-peak attitude change is defined by

σ²_ps = E{(Δ_p(t))²}

The peak stability metric and the mean-square peak stability metric require significant computation to analyze, particularly for long data records. There is also the question of how small the discrete steps in τ need to be to find the peak-to-peak change in attitude. Because these stability metrics are nonlinear, they have no mathematical equivalent in the frequency domain.