Batch Linearization Across the Flight Envelope
Use the speed and the incidence angle as scheduling parameters; that is, trim the
airframe model over a grid of and values. Note that these are two of the five outputs
of the scdairframeTRIM model.
Assume that the incidence varies between -20 and 20 degrees and that the speed
varies between 700 and 1400 m/s. Use a 15-by-12 grid of linearly spaced pairs for
scheduling:
nA = 15; % number of alpha values
nV = 12; % number of V values
alphaRange = linspace(-20,20,nA)*pi/180;
VRange = linspace(700,1400,nV);
[alpha,V] = ndgrid(alphaRange, VRange);
For each flight condition , linearize the airframe dynamics at trim (zero normal
acceleration and pitching moment). This requires computing the elevator deflection and
pitch rate that result in steady and.
Use operspec to specify the trim condition, use findop to compute the trim values of
and , and linearize the airframe dynamics for the resulting operating point. See the
"Trimming and Linearizing an Airframe" example for details.
The body coordinates, , are known states for trimming. Therefore, you need to
provide appropriate values for them, which you can specify explicitly. However, in this
Approximating Nonlinear Behavior Using an Array of LTI Systems