% Example ex_6_1.m illustrates modelling of a nonlinear system using % the symbolic approach. Here is illustrated the object-oriented % counter part. The main function is "difflfr". See the manual % for explanations. missiledata lfrs Al Ma [0.0 2.0] [0.349 4.0] % Bounds specified lfrs q dp Cz = z3*Al^3 + z2*Al^2 + z1*( 2 -(1/3)*Ma)*Al + z0*dp; Cm = m3*Al^3 + m2*Al^2 + m1*(-7 +(8/3)*Ma)*Al + m0*dp; A1 = q+K1*Ma*Cz*(1-Al^2/2);%+Al^4/24); A2 = K2*Ma^2*Cm; C1 = K3*Ma^2*Cz; fg = [A1;A2;C1]; fg = minlfr(fg,10000*eps); % Now, the state-space matrices of the linearized models are computed % by deriving the above expressions: ABCD = [diff(fg,'Al') diff(fg,'q') diff(fg,'dp')]; % Then, the input/output corresponding form is computed using % "abcd2lfr" and the result is reduced using "minlfr". sys = abcd2lfr(ABCD,2); sys = minlfr(sys,10000*eps); % The actuator is added in series at the system input: sys_nn = sys*ss(tf([omegaa^2],[1 2*kia*omegaa omegaa^2])); % Finally, the the parameter variations are normalized. sys = normalizelfr(sys_nn); sys_6_2 = sys; % The result of ex_6_1.m can be compared: distlfr(sys_6_1,sys_6_2)