Rise time: The rise time is the time required for the response to rise from 10% to 90%.5% to 95%. or 0% to 100% of its final value. For under-damped second-order systems the o% to 100% risetime is normally used For over-damped systems the 10% to 90% rist time is commonly used. The 0% to 100% rse time may be calculated by using Eqn(3. 13) y(T)=1-e SIn (o+0)=1(3314) Solving for yields 元 (3-3-15) On the other hand it is difficult to obtain the exact analytic expressions for the 10% to 90% rise time T. The following graph shows T for0.05≤5≤0.95 2022-2-3 16
2022-2-3 16 Rise time: The rise time is the time required for the response to rise from 10% to 90%, 5% to 95%, or 0% to 100% of its final value. For under-damped second-order systems, the 0% to 100% rise time is normally used. For over-damped systems, the 10% to 90% rise time is commonly used. The 0% to 100% rise time may be calculated by using Eqn(3.13). T r 1 Tr Tr 1 1 sin 1 nTr r d r y T e T Solving for yields Tr r d T On the other hand, it is difficult to obtain the exact analytic expressions for the 10% to 90% rise time . The following graph shows for . 1 Tr 1 Tr 0.05 0.95 (3-3-14) (3-3-15)
The linear approximation formula for Tn effective for 03≤550 may be found as 2.165+0.6(3-3 The swiftness(or fastness)of a response to a step input Is dependent on both s and , For a given the response is faster for a larger @ as 1.6 0.= 10 rad/ 1.4 I rad/s l.2 1.O 0.8 0.6 O.4 0.2 4 9 10 Time(seconds) 17
2022-2-3 17 The linear approximation formula for effective for may be found as 1 Tr 0.3 0.8 1 2.16 0.6 r n T The swiftness (or fastness) of a response to a step input is dependent on both and . For a given , the response is faster for a larger as n n (3-3-16)
For a given the response is faster for lower s as shown below 1.2 1.0 =0.7 0.8 o.= 5 rad/s 0.6 0.4 0.2 1.0 1.5 2.0 2.5 3.0 Ti Ime (seconds 2022-2-3 18
2022-2-3 18 For a given , the response is faster for lower as shown below. n