% This example illustrates the symbolic approach for modelling % the continuum of the linearized models of a nonlinear system. % Here, the considered system is a simplified missile model. First, % the symbolic expression of the system equations are computed % (see the manual): missiledata syms Al q Ma 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; % Now, the state-space matrices of the linearized models are computed % by deriving the above expressions: fg = [A1;A2;C1]; ABCD = [diff(fg,'Al') diff(fg,'q') diff(fg,'dp')]; % The system matrix [A B;C D] is realized using the tree % decomposition (function "symtreed"), then, the input/output % corresponding form is computed using "abcd2lfr". The result % is reduced using "minlfr". ABCD = symtreed(ABCD); sys = abcd2lfr(ABCD,2); sys = minlfr(sys,1000*eps); % The parameter variations must be normalized. sys = normalizelfr(sys,{'Al','Ma'},[Al_0-Al_S Ma_0-Ma_S],[Al_0+Al_S Ma_0+Ma_S]); % Finally, the actuator is added in series at the system input: sys = sys*ss(tf([omegaa^2],[1 2*kia*omegaa omegaa^2])); sys_6_1 = sys;