Modelling state space equation from simulink file

I need help modelling the above simulink model in state space form

I have attached the simulink file with transfer functions .

drillstring model =(2.618s+6.233)/(9.898s+8.917)

stick slip disturbance =(-6.7323s-0.45)/(2.342s^2+3.22s+1)

motor = 8.917/(0.42s+1)

Can I please get some help

Thanks.

Answer 1

[Sam Chak]

Hi @Abdul Hamid Vorajee

The following script allows you to convert the system transfer function into the state-space model in controllable canonical form. After that, use the State-Space block to implements the system accordingly.

https://www.mathworks.com/help/simulink/slref/statespace.html

s = tf('s');
Gp = (2.618*s + 6.233)/(9.898*s + 8.917)	    % drillstring model (plant)
Ga = 8.917/(0.42*s + 1)                             % motor (actuator)
Gd = (-6.7323*s - 0.45)/(2.342*s^2 + 3.22*s + 1)    % stick slip disturbance
Gap = Ga*Gp
G = Gap + Gd;                                       % assumed ++ Sum block is used
G = minreal(G)                                      % system transfer function
[Gnum, Gden] = tfdata(G, 'v');
[a, b, c, d] = tf2ss(Gnum, Gden);
sys = ss(a, b, c, d);
csys = canon(sys, 'companion');
A = csys.A';
B = csys.C';
C = csys.B';
D = csys.D;
csys = ss(A, B, C, D)   % display state-space model in controllable canonical form

csys =

A =

x1 x2 x3 x4

x1 0 1 0 0

x2 0 0 1 0

x3 0 0 0 1

x4 -0.9159 -4.35 -7.084 -4.657

B =

u1

x1 2.741

x2 -1.3

x3 0.6176

x4 -0.2972

C =

x1 x2 x3 x4

y1 1 0 0 0

D =

u1

y1 0

Continuous-time state-space model.

Suggest you to find the book "Modern Control Systems", 14e, by Richard C. Dorf and Robert H. Bishop.

https://www.pearson.com/us/higher-education/program/Dorf-Modern-Control-Systems-RENTAL-EDITION-14th-Edition/PGM100003053839.html

[Abdul Hamid Vorajee]

Thanks, works great