<jupyter_start><jupyter_text>Vt = 500ft/s<jupyter_code>s = control.tf([1, 0], [0, 1])
pitch_rate_control_design(500, -900*((s + 2)/s), [-8, 2], [-4, 4])<jupyter_output>{'x0': array([500.,   0.,   0.,   0.,   0.,   0.]), 'u0': array([0.  , 0.  , 0.25, 0.  , 0.  ]), 's': array([0., 0., 0., 0.]), 'g': array([[-2.28 ],
       [ 0.013],
       [ 0.134]])}
u_norm max 851.0608200266253<jupyter_text>Vt = 100ft/s<jupyter_code>pitch_rate_control_design(100, -9000*(s+0.5-0.125j)/(s), [-2, 0.1], [-2, 2])

# It doesnot work for 100ft/s because the plane requires more throttle than possible to generate enough lift to fly<jupyter_output>{'x0': array([100.,   0.,   0.,   0.,   0.,   0.]), 'u0': array([0.  , 0.  , 0.25, 0.  , 0.  ]), 's': array([0., 0., 0., 0.]), 'g': array([[-0.091],
       [ 0.311],
       [-0.012]])}
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