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Mechanical System Transfer Function - Systems Modelling

Your system of equations can be written in matrix form $$\mathbf{M}\ddot{\mathbf{x}}=\mathbf{K}\mathbf{x}+\mathbf{B}\dot{\mathbf{x}}+\mathbf{F}$$ Assuming the direction of positive state variables are ...
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Linearization about equilibrium point 0 in the presence of unknown input

One way to solve this is to create a new input variable $v$ and set it equal to to $u\ x_4$. $(v = u\ x_4)$ This can be used to obtain a linear system with $x_i$ as states and $v$ as input, and will ...
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Measure a frequency response function

In the context depicted in the diagram, the transfer function estimate can be shown to be biased (wrong in expectation) due to the feedback loop. The input will, due to the feedback, be correlated ...
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Control Engineering: Formal vs. Trial-and-Error

Here are some perspectives from someone who was taught rigorous control systems theory and then spent 34 years working in high tech. Imagine you have a programmable PID controller box with which you ...
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Which controller is more suitable in this scenario? P, I or PI controller?

It all depends on what you want. The easiest is a pure proportional (P) controller. It will give you an output that is proportional to the difference from the target value. Pro: It's pretty stable (as ...
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How to determine the components of a feedback control loop given following context?

$z$ could be a change in wind direction, a change in the supply voltage (requiring adjustment of the PWM to the motors to compensate), a change in the slope of the surface that the objects are on due ...
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Contradiction of bandwidth and damping

Assuming bandwidth is the frequency where the magnitude response is 0.7079 times the DC response, I don't think damping and bandwidth are neither proportional or inversely proportional. Strictly, if ...
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Second Order Transfer Function Question regarding Overshoot Formula

Formula is derived for pure 2nd order TF without any zeros. The validity of the formula for cases with zeros depends on relative position of the zero with regard to poles. The poles of $T(s)$ are \...
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