This kind of block diagram doesn't have anything to do with the rules for parallel and series connections of impedances. It just represents a bunch of complex algebraic equations. Each of the rectangular boxes just produces an output variable by multiplying its input by a constant, given by the text in the box.

For example,

\$ V_m = \gamma(I_{ref}-I_m)\$ comes from the first box at the upper left.

\$ I_m = \dfrac{1}{Ls+R}(V_m - E_{emf})\$ comes from the next box to the right.

You can keep making equations like this for each variable in the diagram.
At that point you should have a complete set of equations that you can reduce to get a relationship between \$\Omega\$ and *T*.

To do this for a complex system like yours, you may want to polish up your skills in a symbolic math package like Maple or Mathematica.

Disturbances considered in state-space systems are not constrained to be of any particular type. Step, sinusoidal, stochastic, impulse, disturbances are all described in the literature. Whether the system under consideration is continuous time or discrete doesn't matter; there is no distinction regarding the type of disturbance that can be / is analysed.

Sometimes one type of disturbance is more relevant to the problem at hand because they model real world phenomena; e.g. a step in a control system or a stochastic in a communications channel.

Step disturbances are popular for control system analysis because you usually require a zero steady-state error.

Stochastic disturbances are popularly analysed in Communications channels; but their application to control systems is also a well studied field; e.g. "Discrete Time Stochastic Systems", T.Soderstrom, Springer, 2002

It is true that discrete time controllers have become popular in the same era as stochastic approaches to control systems. This is partly coincidental but may also be due to easier analysis in discrete time; e.g. Soderstrom states "discrete time stochastic processes are much easier to handle than their continuous time counterparts, which have certain mathematical subtleties that are far from trivial to handle in a stringent way".

## Best Answer

In simply words:

Regulator (controller)is a device that controls the object in closed loop on the basis of difference (error of regulation) between measurements of object's output and external steering signal, regulator tries to reduce error to zero.Compensatoronly change object characteristics (transfer function), e.g. phase of output signal. Compensators are used in connection with regulators, in feedback loop (change characteristics of object's output signal) or in steering path (change steering signal from controller to object).More here: https://en.wikibooks.org/wiki/Control_Systems/Controllers_and_Compensators