error using ss2tf function

clear all;
clc;
%% Declaration with parameter
I = 205113.07; % kg-m^2
m= 15118.35;   % kg
c = 3.511;     % m
rho = 1.225;   % kg/m^3
Tm = 49817.6;  % N
S = 37.16;     % m^2
%% Equation of motion(Longitudinal modes)
syms alpha etta delta theta q V 
f1 = ((etta*Tm*cos(alpha))/m) - ((0.5*rho*(V^2)*S*((0.0013*alpha^2)-(0.00438*alpha)+0.1423))./m)-(9.81*sin(theta-alpha));
f2 = q-(etta*Tm*sin(alpha)/(m*V))-(0.5*rho*V*S*((0.0751*alpha)+(0.0144*delta)+0.732)/m)+(9.81*cos(theta-alpha)/V);
f3 = (0.5*rho*V^2*S*c*(-0.00437*alpha-0.0196*delta-0.123*q-0.1885)/I);
f4 = q;
%% Linearization
A = jacobian([f1,f2,f3,f4],[V alpha q theta]);
B = jacobian([f1,f2,f3,f4],[etta delta]);
%% Equillibrium
V = 94.5077;  %m/s
etta = 0.58;
delta = -0.1678; %rad
theta = 0;
alpha = 0;
q = 0;
%% Evaluate System and Control Matrix
format shortG; 
fprintf("State Matrix = ");
A = eval(A)
fprintf("Control Matrix = ");
B = eval(B)

I want to convert State Space to Single input Single Output Transfer function Transfer function but I get error when using ss2tf function.

can any one help me out?

Answer 1

[Paul]

Define the nonlinear output equation y = h(x,u), take the jacobians wrt x and u, and evaluate them at the equilibirium point. These results will be C and D. Same exact approach to derive A and B from xdot = f(x,u). Once you have C and D then if you really need the transfer function using ss2tf()

[n,q]=ss2tf(A,B,C,D)

or better

hzpk = zpk(ss(A,B,C,D))

Or just leave the model in state space form

hss = ss(A,B,C,D);

unless you have to have the explicit transfer function for some reason.

[Tenzing Thiley]

But I don't have nonlinear output I need it in form of 8 SISO transfer function.

[Tenzing Thiley]

State Matrix =

A =

-0.040493 9.8689 0 -9.81

-0.0021967 -0.030908 1 0

-0.013639 -0.015207 -0.42801 0

0 0 1 0

Control Matrix =

B =

3.2952 0

0 -0.0020488

0 -0.068204

0 0

[Tenzing Thiley]

these are my matrix

[Tenzing Thiley]

transfer function needed was in this form

v(s)/etta(s) =

alpha(s)/etta(s) =

q(s)/etta(s) =

theta(s)/etta(s) =

v(s)/delta(s) =

alpha(s)/delta(s) =

q(s)/delta(s) =

theta(s)/delta(s) =

how can I achieve is using function ss2tf

[Paul]

It looks like the output vector y = [v; alpha; q; theta] is exactly the same as the state variable vector, x. In this case, what should C and D be in this equation, where u = [etta; delta]?

y = C*x + D*u

Once you have C and D you can get all eight transfer functions at once using the second or third method in my comment above.

If sst2tf must be used, you can use

[num,den] = sst2tf(A,B,C,D,1)

to get the first four transfer functions and

[num,den] = sst2tf(A,B,C,D,2)

to get the second four transfer functions.