Zero Input Response and Zero State Response

[fredthechamp]

A step function u(t) is undefined for t = 0, so you cannot make the assertion that u(0) = 1.
What you can do is evaluate at t = 0+, that is, u(0+) = 1.

[coreysaeda]

Watch at 1.25x speed to save yourself 6 minutes for studying other topics when cramming #ProTips

[lt]

Looking for your input.

Zero state solution where the initial conditions are zero i.e. at time is zero the x and dx/dt state variables are zero.

So get this, from a digital control system analysis and design textbook by Phillips 4e CH10.2: a static system is just a system without memory. Almost all systems have dynamics about the static equilibrium point, so if we assign ICs (x and dx/dt) to zero as is done in the Zero State Response solution, then the future states are not being influenced by past events. Relative to the zero IC, the future states of x and dx/dt being driven by input U, then that zero IC starting point is like a static equilibrium point.

So if say the process is quasi-static, (see Abaqus manual for example or any thermodynamic theory text), then the outputs Y and dy/dt are being driven solely by input U, so that previous instant to current instant is a static equilibrium point. As once you remove the input the output returns to the static equilibrium point which LIKE the zero state response’s state variables x and dx/dt (and likely their outputs y and dy/dt) return to the state equal to the zero initial conditions.

[purplesam-dolb]

. Swap. My example for that of a numinic. Allerchy

[RahulKumar-rzib]

can you give a example for zero state function for a complicated equation.

[emirhandemir]

Why is everyone recording videos like they are writing a goddamn I have an exam tomorrow and I didn't study and I just need to be able to solve a couple of problems and get a CC. No disrespect though. Sorry if I offended but I don't need a fancy math! I just want to see solutions :(