Appendix D: Linearization. Small-Signal Linearization Linearization by Feedback. Material covered in the P RESENT L ECTURE is shown in yellow. I. DYNAMIC MODELING Deriving a dynamic model for mechanical, electrical, electromechanical, fluid- & heat-flow systems
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Linearization by Feedback
I. DYNAMIC MODELING
II. DESIGN OF A CONTROLLER: Several design methods exist
Define the transfer function; Apply root locus, loop shaping,…
Convert ODE to state equation; Apply Pole Placement, Robust control, …
In general, we can take one of the following three options:
To summarize: why are linear models useful?
A linear function is:…
Intuitively, linearity means proportionality of the output with respect to a variable. One variable function are most familiar but functions can be linear in many variables, e.g:
Approximating the function while considering small disturbances around stable equilibrium points
small leads to:
Subtracting the nonlinear terms out of the equation of motion and adding them to the control.
Gives a linear model
then the motion is described by: