State Space unit step and initial conditions

I am trying to get MATLAB to show a state space response with both a unit step input and initial conditions. All documentation shows only how to do one or the other, as if I try using step() or initial(), the second overrides the first. Thanks!

Answer 1

[Daniel Stankowski]

The above method works but you can also use an lsim command.

Do the following:

lsim(sys,u,t,x0)

where;

• sys - defines your state space
• u defines your input signal which in case of step input can be defined as u=ones(length(t)) % cause we know for step u(t)=1 (you can see it from laplace transform tables)
• t - time, for example; t=linspace(0,5,10)
• x0 = is a vector of initial conditions

[shivam sahil]

A small correction, it should be:

u=ones(length(t),1) ;

instead of

u=ones(length(t)) 

[Xiaohan Tang]

Thank you!!!

Answer 2

[Youngsik Kim]

You can get the zero input response from initial() and zero state response from step() separately, and then you can add up later to plot the response.

[yi,ti,xi]=initial(systm,xinitial); [ystep,ts,xs]=step(systm,ti);

Then, the superposition of them is what you want. ytotal=yi+ystep; Then plot time .vs. ytotal.

Answer 3

[Drishya Dinesh]

how to get a response with initial value of 10.

t2=400;
u_del=(0.0022*k*(s+0.06931)*(s^2+0.4852*s+0.1492))/((s+0.04833)*(s+0.004352)*(s^2+0.06012*s+0.01331));
figure
step(u_del,t2);
ylabel('Velocity,u (m/s)','fontsize',10);
title('Time Response');
grid