M4.6 Summary

The MATLAB Control Toolbox can be used to create LTI objects. These objectives can then easily be converted to other forms. Conversion from continuous to discrete is particularly useful when implementing a digital control algorithm. The commands used include the following:

sys   =  ss(a,b,c,d)        % state space form
sys   =  tf(num,den)        % transfer function form
sys   =  zpk(z,p,k)         % zero-pole-gain form
sysd  =  filt(num,den,Ts)   % backward shift form
sysd  =  c2d(sys,Ts,'zoh'   % continuous to discrete
sys   =  d2c(sysd,'zoh')    % discrete to continuous
pi    =  pole(sys)          % poles
zi    =  tzero(sys)         % zeros
[y,t] =  step(sys)          % step response
[y,t] =  impulse(sys)       % impulse response

In addition, the following do not require the Control Toolbox:

[num,den] = ss2tf(a,b,c,d,iu)  % state space to transfer function
[a,b,c,d] = tf2ss(a,b,c,d)     % transfer function to state space

Examples for the most important commands can be found in Section M4.1.