ME 357 09 K Converting State Space to Transfer Function Form

Описание: State Space Modeling for a Spring Mass Damper System (Force Input)

In this video, we build a continuous-time linear time-invariant state-space model for the classic spring-mass-damper system with an external force input and displacement output.
State-space reference (A, B, C, D form): https://en.wikipedia.org/wiki/State-s...
MATLAB state-space model object (ss): https://www.mathworks.com/help/contro...

What you will see in this lesson
Start from the equation of motion: m*xddot + b*xdot + k*x = F(t)
Choose state variables x1 = x and x2 = xdot
Rewrite the second-order ODE as two first-order ODEs
Assemble the A matrix and B matrix from the resulting equations
Choose an output (here: displacement), then build the C matrix and D matrix
Write the final model in compact matrix form: xdot = A x + B u, y = C x + D u

Why this matters in ME 357
State-space models are the go-to time-domain representation for multi-input and multi-output systems, and they connect cleanly to controller design, simulation, and conversion to transfer functions.
If you are working through ME 357, this is a great checkpoint for #SystemDynamics, #ControlSystems, and #MATLAB.

Related ME 357 videos on this channel
More ME 357 content:    / @drjmm84  

Timestamps
00:00 Problem setup and what state-space modeling means
00:47 Free body diagram and sign conventions
02:22 Equation of motion for the spring-mass-damper system
03:32 Identify input and output variables
05:51 Choose the state variables
06:02 Define x1 and x2
12:56 Write x1dot and x2dot in first-order form
15:27 Build the A matrix and B matrix
16:43 Build the C matrix and D matrix for displacement output
20:59 Recap: final state-space model (A, B, C, D)