PHYSICS 3K03 Final: 360_Summary
15 Sep 2017
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Laplace variable s can be considered to be the differential operator. R. o. c. (the laplace transform exists only when the integral converges) Function: ratio of the laplace transform of the output to that of the input. 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) The solution of (i. e. , when ) represents the evolution of the system"s free response to non-zero initial conditions therefore. The poles of the closed-loop system are the eigenvalues of. Requires the plant and its inverse to be stable. High gain increases performance, but decreases robustness to noise. This is the essence of control design. (when k is a constant feedback gain matrix) Sensitivity function (effect of noise on the output):
