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9

I did my signal processing Ph.D. in a control systems department. My take is that signal processing is open loop; control systems close the loop. Apart from that, the mathematics behind both are very similar. It's the applications that are generally very different.


8

There is a lot of overlap but some differences in emphasis. Control Engineering is also older than DSP. If you have a traditional EE education, you don’t really make much of a distinction. State variables are the more typical perspective in Controls. The first edition of Oppenheim and Schafer 1975, had a chapter on state variables, but they dropped it ...


7

Both draw on Linear System Theory (a.k.a. "Signals and Systems"). So also does Communications Systems and Linear Electric Circuits, Electronic Circuits,and Distributed Networks (a.k.a. Transmission Lines). Both worry about system stability. Poles have to be inside the unit circle. DSP is actually broader than either Controls or Communications. Control ...


5

Two principles here: When dealing with a differential equation, you define intermediate state variables so everything is in terms of first derivatives. This system is nonlinear, so the state-space equations won't be in terms of matrices. Applying these principles, we define a state vector: $$ \mathbf x = [x_1, x_2]^T, $$ where: $$ x_1 = y \\ x_2 = \dot y $$...


3

A system with simple distinct poles on the imaginary axis (and note that the origin is on the imaginary axis) and no poles in the right half-plane is called marginally stable. If you have poles with multiplicity greater than $1$ on the imaginary axis, or if there are poles in the right half-plane, then the system is unstable. For discrete-time systems, the ...


3

There's a fairly simple distinction. Signal processing is a set of tools that can be used for control engineering. Control engineering is about making something move how you want it to move. Some of the tools of signal processing will help with that (and some won't; backward filtering doesn't happen in real-time without a TARDIS). Signal processing is ...


1

This is kind of hand-wavy, but you can look at this from two different perspectives: One, you can look at $z^{-1}$ as a "back-step" operator; i.e. if $X(z) = \mathcal{Z}\lbrace x_n \rbrace$, then (with a few 'i's left undotted and 't's uncrossed) $\frac{X(z)}{z} = \mathcal{Z}\lbrace x_{n-1} \rbrace$. You can also look at $s$ as a derivative operator: if $X(...


1

$$ H(s) = {K*\frac{s-z}{s-p}}\\ \\ $$ when |z| < |p|, you have a lead compensator. It adds phase between a certain band, and can help you improve your phase margin. It can also increase your bandwidth. You typically use it to improve your transient as you mentionned. You can think of it as a PD controller cascaded with a low-pass filter. The gain K is ...


1

You're right, the given pole and zero are wrong. They should be $$s_0=-\frac{1}{\tau}$$ and $$s_{\infty}=-\frac{1}{\beta\tau}$$ because for $s=s_0$ the numerator becomes zero, and for $s=s_{\infty}$ the denominator becomes zero.


1

The requirement, for causal, real-time system implementations (where time is the independent parameter) that continuously minimize an output error with respect to a reference criterion, distinguishes the control systems discipline. You could search MIT Open Courseware, such as https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-30-feedback-control-...


1

Control engineering are often taught in similar or even same courses of study, up the masters' degrees. In the general system modeling approach, where inputs ($I$) and outputs ($O$) are related through systems ($S$), I would say that, for a target $O$, they either work on $S$ or $I$: control engineers tend to put (strong) contraints on outputs of a system, ...


1

This looks like it might be able to be written as a dynamic programming problem. Bellman's equation looks very similar to the way you have expressed your control problem.


1

Switching between 2 PID controller is called gain-scheduling. There are various ways to implement gain scheduling. But basically, the idea is that the gain should change smoothly. You should not change suddenly. You could have one set of gains if T < T1, another set if T > T2 and use interpolation between the 2 sets if T1 < T < T2. You can also ...


1

UPDATE: My original answer incorrectly assumed the outer loop would not impact the result, but as pointed by Ben, this transfer function is dependent on the fast feedback. The resulting equations are found by solving for $A/X$ from the block diagram below, with X representing the disturbance input: Solving this: $$Y = P(SY+FY+X)$$ $$A/S = P(A + FA/S + X)$...


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