# Tag Info

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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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### 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 ...

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 ...

### 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 ...

### 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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### 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 ...

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 \... 3 votes Accepted ### 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 ... 3 votes Accepted ### 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 ... 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 ... 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 ... 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} $$where: \ K \rightarrow  DC Gain of the system \ \tau \rightarrow  Time ... 3 votes Accepted ### Help understanding a control system represented by coefficients of theta? In mathematics,which are very closely related and broadly applied in control engineering, the derivatives with respect to time are often notated using the so-called: dot notation. You can check this ... 3 votes Accepted ### mass-friction-spring system with closed loop Based on the information you've given, I believe your professor is suggesting that a friction term can be represented as shown in the following block diagram. The transfer function G(s) relates ... 3 votes Accepted ### How to get a transfer function from this block diagram? You are going in the right direction! Lets take these two equations:$$(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}$$now ... 2 votes ### Practical examples of LTI transfer function Imagine hitting a pendulum by a hammer with same force and same direction. The pendulum's response will be always same, yesterday, today, tommorow, and 1 year after. It means, between your impact ... 2 votes ### What do the zeros of the transfer function tell you about a system? I would refer you to "Poles and Zeros of Linear Multivariable Systems: A Survey of the Algebraic, Geometric and Complex Variable Theory", A. G. J. Macfarlane, N. Karcanias for a very detailed analysis ... 2 votes ### What do the zeros of the transfer function tell you about a system? You can think of poles as low pass filters and zeros as high pass filters. They are in some way two sides of the same coin. You can't decide stability solely by looking at poles, any more than ... 2 votes ### How can I calculate the z-transformation of this transfer function of a time-discrete controller? Observe that G(s) is formed by$$\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^{...
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.