How to use the state space model block in simulink for modeling of Brushless dc motor ?

Hi ,

I need to model the Brushless dc motor using state space equations.I have the matrices A,B,C,D with me.In that the elements of matrix A are time varying (i.e)(varies with the rotor position). I am not sure how to give input and interpret the output from the state space model block in simulink.I have attached my equations with this.could anyone please help me with this?

The below shown are my equations. in that fas,fbs,fcs are the parameters that are varying with time(rotor position) %===================================== %State Space Model% %===================================== A= [-Rs/Ll,0,0,-(Lamda/Ll)*fas,0; 0,-Rs/Ll,0,-(Lamda/Ll)*fbs,0; 0,0,-Rs/Ll,-(Lamda/Ll)*fcs,0; (Lamda/J)*fas,(Lamda/J)*fbs,(Lamda/J)*fcs,-B/J,0; 0,0,0,P/2,0]; B= [1/Ll,0,0,0; 0,1/Ll,0,0; 0,0,1/Ll,0; 0,0,0,-1/J; 0,0,0,0]; C= [1,0,0,0,0; 0,1,0,0,0; 0,0,1,0,0; 0,0,0,1,0; 0,0,0,0,1]; D= 0;

[K E]

You might be interested in this video demonstrating modeling a motor in SimScape.

[MAQBUL]

what are the exact values of matrix x and u of state space equations.

Answer 1

[Ryan G]

I see two options for this which shouldn't be to hard given the SS equations.

1) Break up the SS into a series of transfer functions and utilize time varying transfer functions

2) Break up the system into the ss equations and model it that way.

 x' = A*x + B*u
 y = C*x

which, given 4 states here, should be trivial.

[Ramya devi]

Hi Ryan,

Thanks for your fast response.I am new to state space modeling.Could you please elaborate on this. How to find the value of 'x' from the state space equations?

[Ryan G]

Hmmm, it sounds like you are learning this backwards!

Anyway,

A statespace model is simply a representation of the equations of motion of a system. Given what I wrote above, I'll show what happens when it's expanded with a 2-state system with 1 input

x1' = a11*x1 + a12*x2 + b11*u
x2' = a21*x1 + a22*x2 + b21*u
y = c11*x1 + c12*x2

You can see how it's simply matrix algebra with the states and the statespace matrices. You have 4 states so this is a bit longer process but just as easy as matrix algebra.

Once you establish these equations you can model them in simulink very easily. The parameters (A B and C matrix components) would be modeled as gains and you use integrator blocks to integrate x' to x components.