PHYSICS 3K03 Midterm: 360 Foms
15 Sep 2017
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Pendulum oscillator eq at = 0, t( ) = 0. , 1 underdamped: 1, critical damped: 1, overdamped: 1. 0 . Completely controllable : there exists a control u(t) that can transfer any initial state x(0) to any desired x(t) in a finite time t. Completely observable : there exists a finite time t such that, given the input u(t), the initial state x(0)can be determined from the observation history y(t) Gk is large at low frequency and small at high frequency: 0 0 1; 0 1 0. E(t) = y(t) r(t), as t --> in response to a step input. E = r/(1+kg), using the final value theorem, e=1/(1+k(0)g(0)) Sin 1 , 1 lim lim lim . : , 1 , , . : 1, , . : , 1, , , . Has steady state error (with h(s)=1) lim lim .
