Extract vector of positions from a parmetric piecewise

i have a problem with piecewise. i need to extract values for each time instant. then substitute a vector of times (for example, t = 1:10) for the symbolic variable.

the end goal is to get a vector that has within it the values calculated at the instants of time.

below I have attached the qd function.

I know I have to use the children function and the subs function. but I don't know how to use them

syms t
qd=piecewise(t<tk(k),qd,tk(k)<=t<tk(k+1),a0(k)+a1(k)*(t-tk(k))+a2(k)*(t-tk(k))^2+a3(k)*(t-tk(k))^3)

Answer 1

[Pratheek]

Hi Teodoro,

I understand that you want to extract the values for each time instant and substitute a vector of times for the symbolic variable. You can follow these steps to do that:

1. Use the `children` function to get the conditions and expressions within the `piecewise` function:

[pw_conditions, pw_expressions] = children(qd);

This will give you two arrays: `pw_conditions` with the conditions and `pw_expressions` with the expressions.

2. Use the `subs` function to substitute the vector of times `t = 1:10` for the symbolic variable `t` in each expression:

pw_expressions_at_t = subs(pw_expressions, t, 1:10);

This will give you the values of the expressions at each instant of time.

3. Now combine the values of the expressions at each instant of time into a vector:

values = [pw_expressions_at_t{:}];

This will concatenate the array of values from each expression into a single vector.

Putting it all together:

syms t
qd = piecewise(t<tk(k),qd,tk(k)<=t<tk(k+1),a0(k)+a1(k)*(t-tk(k))+a2(k)*(t-tk(k))^2+a3(k)*(t-tk(k))^3)
 
[pw_conditions, pw_expressions] = children(qd);
pw_expressions_at_t = subs(pw_expressions, t, 1:10);
values = [pw_expressions_at_t{:}];

This should give you the vector of values calculated at the instants of time.

You can refer to this documentation link for more info: Conditionally defined expression or function - MATLAB piecewise (mathworks.com)