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2

Phase margin is indeed read from an open-loop transfer function, but the rationale behind it is to prevent the closed-loop from going unstable. As you might recall: $$T(s) = \frac{GC}{1+GC}$$ Looking at this function from a mathematical viewpoint, this function explodes when $GC = -1$. In bode-plot terms, $GC = -1$ if $|GC| = 0dB$ and $\angle GC = -180 \deg$...

0

In the absence of detailed information and assuming that the existing fasteners and connections are strong enough just as an illustration and with the understanding that this is not advice, I would consider using 4 Simpson Strong-tie fasteners with, uplift rating of $12000/4= 3000lbs\ 3000*1.5= 4500lbs$ Using 1.5 safety factor we look for a fastener with the ...

1

The problem is complicated by the fact that the function f(t) and the point at which its minimum/maximum x∗ is located, generally speaking, are not known to us. So if I understand it correctly: $f(t)$ is a unknown function, of which your controlled system should approach either the maximum or the minimum value $f(t)$ has over $t$. If I look at your system ...

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After some research, I found out that the valve is 0-24v DC and the output from the feedback sensor is 0-20ma. They are designed to work with a Bosch controller but can be used with any PLC if an amplifier with the correct gain is used.

2

Basic control theory is very useful in a wide range of situations. Really advanced control theory is specialized and useful to theory and complex design of certain actual control systems. I had math in grad school, and EE undergrad, worked as a Systems Engineer. I had control theory in both undergrad and grad school. I do not see any use for control theory ...

2

Let's start by obtaining the state space form of the closed-loop system (closed loop means that you plug in the equations the expression of the controller). The controller of this specific system has the following form: $$u = -Kx+r$$ This is a full state feedback controller with feedforward gain of $1$ (feedforward is the gain by which the input signal is ...

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I believe that the formulation is correct apart from $M(k+1)$ which should be $$M(k+1)=\frac{\partial \boldsymbol{h}_k}{\partial \boldsymbol{v}}\bigg\vert_{\hat{\boldsymbol{x}}(k+1|k)}$$

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MPC finds the optimal input $u^*$ which is the input that minimizes the cost function $J$ or $c$. This means that regardless of what this actual value is, its proven to be its minimum. As such, multiplying the cost function with any constant value does not change this minimum, it just scales the value. Therefore, $\frac{t_{hor}}{N}$ does not affect the ...

3

When identifying a system, you effectively compute a system that happens to have the same response to your inputs as the physical system. However, this does not mean that the states do physically represent the same. You find a transformed system that can be represented as such: $$T\dot{x} = (TAT^{-1})Tx + TBu$$ $$y = (CT^{-1})Tx + Du$$ where $T$ is a ...

2

Due to the fact that you are mentioning the $A,B,C,D$ matrices I assume that your model is a linear one of the form: $$\dot{x} = Ax + Bu$$ $$y = Cx + Du$$ where $x$ is the state vector and $y$ the output of the system. One thing you can do, at least I would go like this, is transform your system to the $\text{s-domain}$, that is obtain the input to output ...

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