6 votes
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Which equations of a state space model influence the poles and zeroes?

Half of your statement is correct: If we are considering the following system: $$G : \begin{aligned} \dot{x} &= Ax+Bu \\ y &= Cx \end{aligned}$$ then $A$, $B$, and $C$ all influence the zeros ...
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6 votes
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How does load force impact load inertia?

Let's first compute the model. The control design is a separate effort. The torque applied to the drum is $n T_M $, where n is the gear ratio and $T_M$ is the output produced by the motor. $T_M= K_T ...
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  • 1,876
5 votes

Frequency Response of a Discrete System

If you want to evaluate a continues time transfer function at a specific frequency $\omega$ in rad/s you substitute $s$ with $j\,\omega$. For a discrete time transfer function you substitute $z$ with $...
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  • 1,603
5 votes
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Square wave transfer function?

I thought I would expand a little on the answer offered by Karlo. Long story short, I would not try to calculate the analytical time response of a system to a square wave. That would be a serious ...
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5 votes
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Determine the range of values for a PI controller

There is a mistake in your expressions. The coefficient of $s$ is $2+k_p$. The conditions are: $$\frac{1}{3} \left(3 \left(k_p+2\right)-k_i\right)>0$$ $$k_i>0$$ $$k_p>0$$ This simplifies ...
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  • 1,876
5 votes

What do the zeros of the transfer function tell you about a system?

Zeros are very important when you are looking at how to control a system. A good way to look at this is to examine a root locus plot. There are several rules on how to sketch a root locus, but the ...
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5 votes
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How do I interpret the following Bode, Nyquist and Nichols diagrams?

Your systems shows extremely close pole-zero cancellation. So much even that it nearly removes 4 poles and zeros. Lets look at why, starting with the Bode plot: The magnitude plot is constantly ...
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  • 1,079
4 votes

How does load force impact load inertia?

Stretch in the spring delta $ Y = A.sin(\omega.t) = A.sin\sqrt(k/m) . t $ So the delta Y is not constant but if you are interested in delt Y_max delta $Y max = m/k$, by Hooks law. Because your ...
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  • 21.1k
4 votes

How can I extract transfer function an unknown nonlinear system?

As I remember (learned it 15 yrs ago) You need to have an experimental data, which will help you to find "linear" sections and the their limits (with taking into account the things like hysteresis), ...
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4 votes
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PI controller for second order system

Step 1: Draw the root locus of the system. Here you can see the two poles of your plant $G(s)$ (marked with an x), at $p_1=-9$ and $p_2=-1$, the pole of your controller $C(s)$ at $p_c = 0$ and the ...
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4 votes

How do I find the minimum/maximum stable value of scalar gain for a closed loop transfer function?

The forward path of your control diagram consists of the following transfer functions connected in series: $$ \begin{align*} G(s) &= \frac{s+8}{s^2-2s-3}\rightarrow \text{Plant}\\ K(s) &= K \...
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3 votes
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How to solve system's general stability from transfer function?

I would like to extent the already given answer by MrYouMath. So question 1 is pretty straight forward and you already got it right. If there's no right half plane (RHP) pole then it doesn't matter ...
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  • 1,704
3 votes

What are the Singular Values of a dynamic system and how are they calculated in the *sigma* function in Matlab?

For a MIMO system $y(s) = G(s)d(s)$, with $m$ inputs and $l$ outputs. Consider a fixed frequency $\omega$ where $G(j\omega)$ is a constant $l \times m$ complex matrix. For the sake of simplicity the ...
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3 votes
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Is lead filter same as PD combined with a low pass filter?

A lead filter implies that the zero has a lower frequency than the pole. While a PD controller with a low-pass-filter does not necessarily imply that order. Also a lead filter (usually) does not have ...
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  • 1,603
3 votes

Practical examples of LTI transfer function

Why would a linear, time-invariant system require initial conditions to be zero? This is completely incorrect. A linear, time-invariant system is any system that is linear (no state terms ...
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  • 3,525
3 votes

Unexpected Results from my Transfer Function

Checking the units is an excellent way to double check your work; kudos for doing so. However, the next step in checking to see if your results make sense is to check limits. In your case, you can ...
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3 votes

How to find closed loop transfer function and use it to identify τ and k?

The general form of a transfer function for a first order system is the following: $$ T(s) = \frac{K}{\tau s+1} $$ where: $\ K \rightarrow $ DC Gain of the system $\ \tau \rightarrow $ Time ...
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3 votes
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Help understanding a control system represented by coefficients of theta?

In mathematics,which are very closely related and broadly applied in control engineering, the derivatives with respect to time are often notated using the so-called: dot notation. You can check this ...
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3 votes
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mass-friction-spring system with closed loop

Based on the information you've given, I believe your professor is suggesting that a friction term can be represented as shown in the following block diagram. The transfer function $G(s)$ relates ...
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3 votes
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How to get a transfer function from this block diagram?

You are going in the right direction! Lets take these two equations: $$(1) \quad in = \alpha+a_1\alpha z^{-1}+a_2\alpha z^{-2}$$ $$(2) \quad out = b_0\alpha+b_1\alpha z^{-1}+b_2\alpha z^{-2}$$ now ...
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  • 1,079
2 votes

Practical examples of LTI transfer function

Imagine hitting a pendulum by a hammer with same force and same direction. The pendulum's response will be always same, yesterday, today, tommorow, and 1 year after. It means, between your impact ...
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  • 354
2 votes

What do the zeros of the transfer function tell you about a system?

I would refer you to "Poles and Zeros of Linear Multivariable Systems: A Survey of the Algebraic, Geometric and Complex Variable Theory", A. G. J. Macfarlane, N. Karcanias for a very detailed analysis ...
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  • 1,876
2 votes

What do the zeros of the transfer function tell you about a system?

You can think of poles as low pass filters and zeros as high pass filters. They are in some way two sides of the same coin. You can't decide stability solely by looking at poles, any more than ...
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  • 11.3k
2 votes

How can I calculate the z-transformation of this transfer function of a time-discrete controller?

Observe that $G(s)$ is formed by $$\frac{1}{s^2} \to \frac{1}{(s+1)^2}$$ with the corresponding Z-transform/Laplace pairs $$\frac{1}{s^2} \to \frac{Tz}{(z-1)^2}$$ and $$\frac{1}{s+a} \to \frac{z}{z-e^{...
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2 votes

How can I calculate the z-transformation of this transfer function of a time-discrete controller?

In order to solve it, you have to divide $ G_s(s)$ by s first and then you have it in the form on which you can perform the Z-transform.
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  • 21
2 votes
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Closed loop response of a discrete system

The plant and controller: $$\text{sys}=\frac{4700 s^2+4393 s+3.245\times 10^8}{s^4+7.574 s^3+120200. s^2}$$ $$pid=0.287\, +0.008 s+\frac{0.5}{s}$$ The closed-loop system obtained as $\frac{pid*sys}{...
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  • 1,876
2 votes

Transfer function of a temperature controlled incubation system

The transfer function you provide is merly a model of the egg incubation system it is not a controller. In addition a lot of assumptions are made, for instance, heat does spread evenly through the egg ...
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  • 131
2 votes

How does load force impact load inertia?

I realize this is an old thread, and I am not sure how deep of a dive you finally took on this, but one thing I don't see accounted for in your equations is drum/cable friction. This will be small, ...
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  • 21
2 votes

Transfer Function of Spring-Damper System

First, create the free body diagram for this system. If you cut through the spring $k_1$ and the damper $b_1$ you will get two forces $F_{k_1}=k_1(x_i-x_0)$ and $F_{b_1}=b_1(\dot{x}_i-\dot{x}_0)$ ...
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  • 1,046
2 votes

Square wave transfer function?

You want to look for the Laplace transform of a square wave. Note: The transfer function $H(s)$ is the ratio of the Laplace transforms of output $Y(s)$ and input $U(s)$: $Y(s)=H(s)\cdot U(s)$ If ...
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  • 540

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