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By the end of this section, you should be able to
Understand benefits/drawbacks of state-space (SS) models versus transfer functions (TF)
Know when each may be appropriate to use
Create SS models for linear mechanical systems and identify state vector and matrices that describe system
Do this for SISO, SIMO, MISO and MIMO systems
Convert SS model to TF and vice-versa in MATLAB
Numerically solve SS models using MATLAB (ode45)
State Space Form
State Space Form
Draw all FBDs
Write EOM(s) for each FBD in the time domain
Identify state and input variables
Create input vector (u) and state vector (x)
State variables include one less than the highest derivative for each dependent variable
Rewrite equations using state variables such that there is only one first derivative in any one equation
If a variable can be replaced by a state variable, it must be
Isolate all first derivatives on LHS of equations
Group coefficients in front of state and input variables on RHS
Add “mapping” equations to relate derivatives of state variables
Put system of equations into matrix form
Create A and B
Create the output matrix, C, and feedthrough matrix, D
Outputs of the system will be state variables themselves, combinations of state variables or scaled versions of state variables
Often matrices of zeros and ones for this course
C can be complicated by using sensors with relative measurements
If there are state variable, inputs and outputs/observables
A will be
B will be
C will be
D will be
State-Space and Transfer Functions
State-Space and Transfer Functions
Numeric Solutions
Numeric Solutions
Runge-Kutta
Runge-Kutta
Using ODE45
Using ODE45
MATLAB Resources
MATLAB Resources
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