# Block-diagram combining two controlled subsystems

I have two subsystems which are shown in the picture below.

One of them is a system of stable and controlled differential equations of a mechanical system.

Second is a block that implements a function $$f(\theta)$$ from a signal entering its input.

$$\theta,\Omega,\omega$$ - variables, $$u(t)$$ - control signal.

I need to combine the two systems in such a way that $$\omega=\Omega$$. What will be the structure of such a system and how to generate a control signal $$u(t)$$? As control laws, it is allowed to use simple ones, including $$P-$$,$$PI-$$ and $$PID-$$ones.

I would be grateful to the community for advice and help.

• Draw it out. Connect the second block to the first, so you have $u$ going in, and $\omega$, $\Omega$ going out. Then subtract them. That difference is the output of the loop to be formed. You want to drive the difference to zero? So draw a loop now, and put in a controller block that receives $(\Omega - \omega)$, and produces $u$, closing the loop. No way to tell what form (eg PI etc) is appropriate. That depends on what's in the "boxes". I have a feeling the is something missing here, but it should become evident with a fuller diagram. Nov 18 '21 at 21:44
• Is $\theta$ a function of time? Is it controlled by the user?
– AJN
Nov 19 '21 at 0:35
• @AJN $θ$ - function of time. Perhaps I should have made an additional clarification. Well, no big deal ... In general ... A block with equations of motion is just some state-space, and $\theta$ and $\Omega$ are its variables, which are interconnected. We accept a simple dependency to begin with, i.e. $\theta = k_1 \Omega$, where $k_1$ - positive constant. As for the control of this variable. Not directly, but it is related to the $\Omega$, which is controllable and therefore indirectly regulated and $\theta$. And yet, $\theta$ is measurable.
– dtn
Nov 19 '21 at 4:12
• @PeteW A block with equations of motion is just some state-space, and $\theta$ and $\Omega$ are its variables, which are interconnected. I wrote about their interconnection in the comment above. The second block contains the function $f(\theta)$, and this dependence can be either a linear function, for example, $\omega=f(\theta) = k_2 \theta$, where $k_2$ - positive constant, or nonlinear, for example, $\omega=f(\theta) = \sin(\theta)$.
– dtn
Nov 19 '21 at 4:15
• @PeteW it turned out as follows ibb.co/ySLpc41
– dtn
Nov 19 '21 at 4:39