Design Case Studies

Yaw Damper for a 747 Jet Transport

This case study demonstrates the tools for classical control design by stepping through the design of a yaw damper for a 747 jet transport aircraft.

The jet model during cruise flight at MACH = 0.8 and H = 40,000 ft. is

• A = [-0.0558   -0.9968    0.0802    0.0415
        0.5980   -0.1150   -0.0318         0
       -3.0500    0.3880   -0.4650         0
             0    0.0805    1.0000         0];
  
  B = [ 0.0729     0.0000
       -4.7500     0.00775
        .15300     0.1430
             0         0];
  
  C = [0     1     0     0
       0     0     0     1];
  
  D = [0     0
       0     0];
  

The following commands specify this state-space model as an LTI object and attach names to the states, inputs, and outputs.

• states = {'beta' 'yaw' 'roll' 'phi'};
  inputs = {'rudder' 'aileron'};
  outputs = {'yaw' 'bank angle'};
  
  sys = ss(A,B,C,D,'statename',states,...
                       'inputname',inputs,...
                       'outputname',outputs);
  

You can display the LTI model sys by typing sys. MATLAB responds with

• a = 
                        beta          yaw         roll          phi
           beta      -0.0558      -0.9968       0.0802       0.0415
            yaw        0.598       -0.115      -0.0318            0
           roll        -3.05        0.388       -0.465            0
            phi            0       0.0805            1            0
   
   
  b = 
                      rudder      aileron
           beta       0.0729            0
            yaw        -4.75      0.00775
           roll        0.153        0.143
            phi            0            0
   
   
  c = 
                        beta          yaw         roll          phi
            yaw            0            1            0            0
     bank angle            0            0            0            1
   
   
  d = 
                      rudder      aileron
            yaw            0            0
     bank angle            0            0
   
  Continuous-time model.
  

The model has two inputs and two outputs. The units are radians for beta (sideslip angle) and phi (bank angle) and radians/sec for yaw (yaw rate) and roll (roll rate). The rudder and aileron deflections are in radians as well.

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