You might find it convenient to use a helper function utilising the SYMBOLIC toolbox to convert P(s) to P(z) with a zeroth-order hold. function Gz = lap2ztranzoh (G) % Convert symbolically G(s) to G(z) with a ZOH. syms stk T z Gz = simplify ((1-1/2)*ztrans (subs (ilaplace (G/s),t,k*T),k,z)); 4 return Note that this routine is given in [1, Listing 2.5]. (a) Explain in detail how this function works. Specifically explain the arguments of the ilaplace and ztrans routines. (b) Modify the lap2ztranszoh routine given above to compute the result if we were to use a first order hold. Note: As opposed to Eqn. 2 for a zeroth order hold, we now use for a first-order hold Ph, p(z) = 2{H (6)P(s) } = (1 2)z {(sT+). P(s)}. (3) (c) Compare carefully the results of the discretisation using both the zeroth-order hold, Phop (z) and the first order hold, Php(z) for both a step input, and a ramp input. Comment on the results.