ME 357 09 L Converting State Space to Transfer Function Form 1DOF System

Описание: Convert State-Space to Transfer Function in MATLAB (ss2tf)

This video shows how to convert a state-space model into an equivalent transfer function, and how to interpret what you get back in terms of poles and system behavior. We use the spring-mass-damper example from the setup video and then run the conversion in MATLAB so you can check your hand work quickly.

Example setup video (state-space model for this system):
   • ME 357 09 B 1DOF State Space Example  

What we do in MATLAB:
Convert A, B, C, D into numerator and denominator coefficients using ss2tf
Reference: https://www.mathworks.com/help/matlab...
Build the transfer function model with tf(b,a)
Reference: https://www.mathworks.com/help/contro...
Connect poles to the system by comparing roots(a) with eigenvalues of A
References: https://www.mathworks.com/help/matlab... and https://www.mathworks.com/help/matlab...
If you need to go the other direction (transfer function to state space), use tf2ss
Reference: https://www.mathworks.com/help/signal...

Key relationship (continuous-time):
G(s) = Y(s)/U(s) = C*(sI - A)^-1*B + D

#SystemDynamics #ControlSystems #MATLAB

Timestamps
0:00 Why convert between state space and transfer function
2:26 Relationship between the two model forms
5:02 Taking the Laplace transform of the state equations
7:11 Solving for G(s) = Y(s)/U(s)
8:48 Summary of the conversion formula
9:29 MATLAB ss2tf syntax and inputs
10:45 Building the transfer function with tf(b,a)
11:55 Poles from roots(a) and eigenvalues from A
13:28 Going the other direction with tf2ss