III - Analytical Soln. of Dynamic System Eqns.

What kind of soln. is preferred for understanding the system better?

analytical solutions

Analytical Systems Limitations

limited to LTI systems of low order and driven by small set of inputs (specific inputs so not common)

What is always a a worthwhile first step in dynamic systems analysis?

simplifying model equations for analytical soln.

LTI (LCCDEs) with output response, y(t) with x(t) input

y(t) = yn(t) + yf(t) where yn(t) - natural response from initial conditions and yf(t) is the forced response by the input, x(t); sum is the basis to solve y(t) upside down A t > 0

Examples of First-Order Dynamic Systems

height of water in a single tank, parallel RC circuit, systemic arterial circulation

Form of First-Order Dynamic Systems

y’(t) + ay(t) = bx(t)

Natural Response

can be solved from the autonomous/homogenous eqn.